Details

analyze12.0ms (0.7%)

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)

sample831.0ms (47.5%)

Results

817.0ms

8256×

body

256

valid

Bogosity

preprocess4.0ms (0.2%)

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 (0.6%)

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%)

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)

localize6.0ms (0.3%)

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	@	inf	(atan.f64 (/.f64 y x))
0.0ms	y	@	0	(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))

rewrite51.0ms (2.9%)

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))))))))

simplify58.0ms (3.3%)

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)

prune4.0ms (0.2%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	17	3	20
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	17	4	21

Error

0.0b

Counts

21 → 4

Alt Table

Click to see full alt table

Status	Error	Program
▶	35.5b	(pow.f64 (pow.f64 (atan.f64 (/.f64 y x)) 3) 1/3)
▶	30.8b	(pow.f64 (sqrt.f64 (atan.f64 (/.f64 y x))) 2)
▶	19.6b	(-.f64 (+.f64 1 (atan.f64 (/.f64 y x))) 1)
✓	0.0b	(atan.f64 (/.f64 y x))

Compiler

Compiled 35 to 27 computations (22.9% saved)

localize8.0ms (0.5%)

Local error

Found 3 expressions with local error:

New	Error	Program
	0.0b	(atan.f64 (/.f64 y x))
✓	0.3b	(+.f64 1 (atan.f64 (/.f64 y x)))
✓	3.1b	(-.f64 (+.f64 1 (atan.f64 (/.f64 y x))) 1)

Compiler

Compiled 26 to 11 computations (57.7% saved)

series1.0ms (0.1%)

Counts

2 → 24

Calls

12 calls:

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

rewrite105.0ms (6%)

Algorithm

1×	batch-egg-rewrite

Rules

1306×	`associate-*r/`
956×	`associate-*l/`
880×	`*-commutative`
810×	`associate-/r*`
618×	`associate-/l*`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	10	40
1	217	28
2	2972	28

Stop Event

1×	node limit

Counts

2 → 165

Calls

Call 1

Inputs
(-.f64 (+.f64 1 (atan.f64 (/.f64 y x))) 1)
(+.f64 1 (atan.f64 (/.f64 y x)))

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

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

simplify116.0ms (6.6%)

Algorithm

1×	egg-herbie

Rules

1102×	`associate--l+`
1048×	`associate-+l-`
994×	`associate-+r-`
894×	`+-commutative`
520×	`distribute-lft-in`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	405	10205
1	1149	9819
2	5379	9819

Stop Event

1×	node limit

Counts

189 → 248

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

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

localize38.0ms (2.2%)

Local error

Found 3 expressions with local error:

New	Error	Program
	0.0b	(atan.f64 (/.f64 y x))
✓	0.3b	(pow.f64 (sqrt.f64 (atan.f64 (/.f64 y x))) 2)
✓	8.4b	(sqrt.f64 (atan.f64 (/.f64 y x)))

Compiler

Compiled 24 to 8 computations (66.7% saved)

series3.0ms (0.2%)

Counts

2 → 24

Calls

12 calls:

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

rewrite58.0ms (3.3%)

Algorithm

1×	batch-egg-rewrite

Rules

1754×	`add-sqr-sqrt`
1734×	`*-un-lft-identity`
1612×	`add-cube-cbrt`
1594×	`add-cbrt-cube`
180×	`pow1`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	10	26
1	205	26
2	2217	26

Stop Event

1×	node limit

Counts

2 → 42

Calls

Call 1

Inputs
(sqrt.f64 (atan.f64 (/.f64 y x)))
(pow.f64 (sqrt.f64 (atan.f64 (/.f64 y x))) 2)

Outputs

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

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

simplify60.0ms (3.4%)

Algorithm

1×	egg-herbie

Rules

904×	`+-commutative`
884×	`associate-/l*`
834×	`associate-+r+`
732×	`associate-+l+`
702×	`unswap-sqr`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	87	818
1	155	818
2	599	818
3	2616	818
4	6442	818

Stop Event

1×	node limit

Counts

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

localize10.0ms (0.6%)

Local error

Found 3 expressions with local error:

New	Error	Program
	0.0b	(atan.f64 (/.f64 y x))
✓	0.6b	(pow.f64 (atan.f64 (/.f64 y x)) 3)
✓	16.4b	(pow.f64 (pow.f64 (atan.f64 (/.f64 y x)) 3) 1/3)

Compiler

Compiled 27 to 12 computations (55.6% saved)

series16.0ms (0.9%)

Counts

2 → 24

Calls

12 calls:

Time	Variable		Point	Expression
6.0ms	x	@	0	(pow.f64 (pow.f64 (atan.f64 (/.f64 y x)) 3) 1/3)
2.0ms	y	@	0	(pow.f64 (pow.f64 (atan.f64 (/.f64 y x)) 3) 1/3)
2.0ms	x	@	-inf	(pow.f64 (pow.f64 (atan.f64 (/.f64 y x)) 3) 1/3)
2.0ms	y	@	inf	(pow.f64 (pow.f64 (atan.f64 (/.f64 y x)) 3) 1/3)
2.0ms	x	@	inf	(pow.f64 (pow.f64 (atan.f64 (/.f64 y x)) 3) 1/3)

rewrite62.0ms (3.6%)

Algorithm

1×	batch-egg-rewrite

Rules

1978×	`add-sqr-sqrt`
1938×	`*-un-lft-identity`
1830×	`add-cube-cbrt`
1812×	`add-cbrt-cube`
200×	`add-exp-log`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	11	28
1	242	28
2	2564	28

Stop Event

1×	node limit

Counts

2 → 40

Calls

Call 1

Inputs
(pow.f64 (pow.f64 (atan.f64 (/.f64 y x)) 3) 1/3)
(pow.f64 (atan.f64 (/.f64 y x)) 3)

Outputs

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

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

simplify56.0ms (3.2%)

Algorithm

1×	egg-herbie

Rules

828×	`distribute-lft-neg-in`
798×	`associate-/l*`
720×	`distribute-rgt-neg-in`
662×	`sqr-pow`
658×	`*-commutative`

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	84	866
1	160	866
2	496	866
3	1869	848
4	4497	848

Stop Event

1×	node limit

Counts

64 → 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 (exp.f64 (log1p.f64 (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 (cbrt.f64 (atan.f64 (/.f64 y x))) (pow.f64 (pow.f64 (atan.f64 (/.f64 y x)) 2) 1/3))
(*.f64 (pow.f64 (cbrt.f64 (atan.f64 (/.f64 y x))) 2) (cbrt.f64 (atan.f64 (/.f64 y x))))
(*.f64 (pow.f64 (pow.f64 (atan.f64 (/.f64 y x)) 2) 1/3) (cbrt.f64 (atan.f64 (/.f64 y x))))
(*.f64 (pow.f64 1 1/3) (atan.f64 (/.f64 y x)))
(*.f64 (pow.f64 (pow.f64 (atan.f64 (/.f64 y x)) 3/2) 1/3) (pow.f64 (pow.f64 (atan.f64 (/.f64 y x)) 3/2) 1/3))
(sqrt.f64 (pow.f64 (atan.f64 (/.f64 y x)) 2))
(log.f64 (exp.f64 (atan.f64 (/.f64 y x))))
(log.f64 (+.f64 1 (expm1.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))))
(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))))
(-.f64 (exp.f64 (log1p.f64 (pow.f64 (atan.f64 (/.f64 y x)) 3))) 1)
(*.f64 (pow.f64 (atan.f64 (/.f64 y x)) 3) 1)
(*.f64 (atan.f64 (/.f64 y x)) (pow.f64 (atan.f64 (/.f64 y x)) 2))
(*.f64 1 (pow.f64 (atan.f64 (/.f64 y x)) 3))
(.f64 (sqrt.f64 (atan.f64 (/.f64 y x))) (.f64 (sqrt.f64 (atan.f64 (/.f64 y x))) (pow.f64 (atan.f64 (/.f64 y x)) 2)))
(*.f64 (pow.f64 (atan.f64 (/.f64 y x)) 3/2) (pow.f64 (atan.f64 (/.f64 y x)) 3/2))
(.f64 (pow.f64 (cbrt.f64 (atan.f64 (/.f64 y x))) 2) (.f64 (cbrt.f64 (atan.f64 (/.f64 y x))) (pow.f64 (atan.f64 (/.f64 y x)) 2)))
(*.f64 (pow.f64 (atan.f64 (/.f64 y x)) 2) (atan.f64 (/.f64 y x)))
(.f64 (.f64 (pow.f64 (atan.f64 (/.f64 y x)) 2) 1) (atan.f64 (/.f64 y x)))
(.f64 (.f64 (pow.f64 (atan.f64 (/.f64 y x)) 2) (sqrt.f64 (atan.f64 (/.f64 y x)))) (sqrt.f64 (atan.f64 (/.f64 y x))))
(.f64 (.f64 (pow.f64 (atan.f64 (/.f64 y x)) 2) (pow.f64 (cbrt.f64 (atan.f64 (/.f64 y x))) 2)) (cbrt.f64 (atan.f64 (/.f64 y x))))
(*.f64 (pow.f64 (sqrt.f64 (atan.f64 (/.f64 y x))) 3) (pow.f64 (sqrt.f64 (atan.f64 (/.f64 y x))) 3))
(*.f64 (pow.f64 (pow.f64 (cbrt.f64 (atan.f64 (/.f64 y x))) 2) 3) (atan.f64 (/.f64 y x)))
(sqrt.f64 (pow.f64 (atan.f64 (/.f64 y x)) 6))
(log.f64 (exp.f64 (pow.f64 (atan.f64 (/.f64 y x)) 3)))
(log.f64 (+.f64 1 (expm1.f64 (pow.f64 (atan.f64 (/.f64 y x)) 3))))
(cbrt.f64 (pow.f64 (pow.f64 (atan.f64 (/.f64 y x)) 3) 3))
(expm1.f64 (log1p.f64 (pow.f64 (atan.f64 (/.f64 y x)) 3)))
(exp.f64 (*.f64 3 (log.f64 (atan.f64 (/.f64 y x)))))
(exp.f64 (.f64 (.f64 3 (log.f64 (atan.f64 (/.f64 y x)))) 1))
(log1p.f64 (expm1.f64 (pow.f64 (atan.f64 (/.f64 y x)) 3)))

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 (exp.f64 (log1p.f64 (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 (cbrt.f64 (atan.f64 (/.f64 y x))) (pow.f64 (pow.f64 (atan.f64 (/.f64 y x)) 2) 1/3))
(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))
(*.f64 (pow.f64 (pow.f64 (atan.f64 (/.f64 y x)) 2) 1/3) (cbrt.f64 (atan.f64 (/.f64 y x))))
(atan.f64 (/.f64 y x))
(*.f64 (pow.f64 1 1/3) (atan.f64 (/.f64 y x)))
(atan.f64 (/.f64 y x))
(*.f64 (pow.f64 (pow.f64 (atan.f64 (/.f64 y x)) 3/2) 1/3) (pow.f64 (pow.f64 (atan.f64 (/.f64 y x)) 3/2) 1/3))
(*.f64 (cbrt.f64 (pow.f64 (atan.f64 (/.f64 y x)) 3/2)) (cbrt.f64 (pow.f64 (atan.f64 (/.f64 y x)) 3/2)))
(pow.f64 (pow.f64 (pow.f64 (atan.f64 (/.f64 y x)) 3/2) 1/6) 4)
(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))
(log.f64 (+.f64 1 (expm1.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))
(exp.f64 (log.f64 (atan.f64 (/.f64 y x))))
(atan.f64 (/.f64 y x))
(exp.f64 (*.f64 (log.f64 (atan.f64 (/.f64 y x))) 1))
(atan.f64 (/.f64 y x))
(log1p.f64 (expm1.f64 (atan.f64 (/.f64 y x))))
(atan.f64 (/.f64 y x))
(-.f64 (exp.f64 (log1p.f64 (pow.f64 (atan.f64 (/.f64 y x)) 3))) 1)
(pow.f64 (atan.f64 (/.f64 y x)) 3)
(*.f64 (pow.f64 (atan.f64 (/.f64 y x)) 3) 1)
(pow.f64 (atan.f64 (/.f64 y x)) 3)
(*.f64 (atan.f64 (/.f64 y x)) (pow.f64 (atan.f64 (/.f64 y x)) 2))
(pow.f64 (atan.f64 (/.f64 y x)) 3)
(*.f64 1 (pow.f64 (atan.f64 (/.f64 y x)) 3))
(pow.f64 (atan.f64 (/.f64 y x)) 3)
(.f64 (sqrt.f64 (atan.f64 (/.f64 y x))) (.f64 (sqrt.f64 (atan.f64 (/.f64 y x))) (pow.f64 (atan.f64 (/.f64 y x)) 2)))
(pow.f64 (atan.f64 (/.f64 y x)) 3)
(*.f64 (pow.f64 (atan.f64 (/.f64 y x)) 3/2) (pow.f64 (atan.f64 (/.f64 y x)) 3/2))
(pow.f64 (atan.f64 (/.f64 y x)) 3)
(.f64 (pow.f64 (cbrt.f64 (atan.f64 (/.f64 y x))) 2) (.f64 (cbrt.f64 (atan.f64 (/.f64 y x))) (pow.f64 (atan.f64 (/.f64 y x)) 2)))
(pow.f64 (atan.f64 (/.f64 y x)) 3)
(*.f64 (pow.f64 (atan.f64 (/.f64 y x)) 2) (atan.f64 (/.f64 y x)))
(pow.f64 (atan.f64 (/.f64 y x)) 3)
(.f64 (.f64 (pow.f64 (atan.f64 (/.f64 y x)) 2) 1) (atan.f64 (/.f64 y x)))
(pow.f64 (atan.f64 (/.f64 y x)) 3)
(.f64 (.f64 (pow.f64 (atan.f64 (/.f64 y x)) 2) (sqrt.f64 (atan.f64 (/.f64 y x)))) (sqrt.f64 (atan.f64 (/.f64 y x))))
(pow.f64 (atan.f64 (/.f64 y x)) 3)
(.f64 (.f64 (pow.f64 (atan.f64 (/.f64 y x)) 2) (pow.f64 (cbrt.f64 (atan.f64 (/.f64 y x))) 2)) (cbrt.f64 (atan.f64 (/.f64 y x))))
(pow.f64 (atan.f64 (/.f64 y x)) 3)
(*.f64 (pow.f64 (sqrt.f64 (atan.f64 (/.f64 y x))) 3) (pow.f64 (sqrt.f64 (atan.f64 (/.f64 y x))) 3))
(pow.f64 (atan.f64 (/.f64 y x)) 3)
(*.f64 (pow.f64 (pow.f64 (cbrt.f64 (atan.f64 (/.f64 y x))) 2) 3) (atan.f64 (/.f64 y x)))
(pow.f64 (atan.f64 (/.f64 y x)) 3)
(sqrt.f64 (pow.f64 (atan.f64 (/.f64 y x)) 6))
(pow.f64 (atan.f64 (/.f64 y x)) 3)
(log.f64 (exp.f64 (pow.f64 (atan.f64 (/.f64 y x)) 3)))
(pow.f64 (atan.f64 (/.f64 y x)) 3)
(log.f64 (+.f64 1 (expm1.f64 (pow.f64 (atan.f64 (/.f64 y x)) 3))))
(pow.f64 (atan.f64 (/.f64 y x)) 3)
(cbrt.f64 (pow.f64 (pow.f64 (atan.f64 (/.f64 y x)) 3) 3))
(pow.f64 (atan.f64 (/.f64 y x)) 3)
(expm1.f64 (log1p.f64 (pow.f64 (atan.f64 (/.f64 y x)) 3)))
(pow.f64 (atan.f64 (/.f64 y x)) 3)
(exp.f64 (*.f64 3 (log.f64 (atan.f64 (/.f64 y x)))))
(pow.f64 (atan.f64 (/.f64 y x)) 3)
(exp.f64 (.f64 (.f64 3 (log.f64 (atan.f64 (/.f64 y x)))) 1))
(pow.f64 (atan.f64 (/.f64 y x)) 3)
(log1p.f64 (expm1.f64 (pow.f64 (atan.f64 (/.f64 y x)) 3)))
(pow.f64 (atan.f64 (/.f64 y x)) 3)

eval138.0ms (7.9%)

Compiler: Compiled 8787 to 4580 computations (47.9% saved)

prune63.0ms (3.6%)

Pruning

4 alts after pruning (0 fresh and 4 done)

	Pruned	Kept	Total
New	394	0	394
Fresh	0	0	0
Picked	0	1	1
Done	0	3	3
Total	394	4	398

Error

0.0b

Counts

398 → 4

Alt Table

Click to see full alt table

Status	Error	Program
✓	35.5b	(pow.f64 (pow.f64 (atan.f64 (/.f64 y x)) 3) 1/3)
✓	30.8b	(pow.f64 (sqrt.f64 (atan.f64 (/.f64 y x))) 2)
✓	19.6b	(-.f64 (+.f64 1 (atan.f64 (/.f64 y x))) 1)
✓	0.0b	(atan.f64 (/.f64 y x))

Compiler

Compiled 35 to 27 computations (22.9% saved)

regimes17.0ms (1%)

Accuracy

Total -40.1b remaining (-205149.9%)

Threshold costs -40.1b (-205149.9%)

Counts

4 → 1

Calls

Call 1

Inputs
(atan.f64 (/.f64 y x))
(-.f64 (+.f64 1 (atan.f64 (/.f64 y x))) 1)
(pow.f64 (sqrt.f64 (atan.f64 (/.f64 y x))) 2)
(pow.f64 (pow.f64 (atan.f64 (/.f64 y x)) 3) 1/3)

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

Calls

4 calls:

6.0ms	(/.f64 y x)
4.0ms	x
4.0ms	y
3.0ms	(atan.f64 (/.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 46 to 26 computations (43.5% saved)

simplify6.0ms (0.4%)

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%)

end11.0ms (0.6%)

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

Details

analyze12.0ms (0.7%)

sample831.0ms (47.5%)

preprocess4.0ms (0.2%)

simplify11.0ms (0.6%)

eval0.0ms (0%)

prune1.0ms (0%)

localize6.0ms (0.3%)

series1.0ms (0%)

rewrite51.0ms (2.9%)

simplify58.0ms (3.3%)

eval3.0ms (0.2%)

prune4.0ms (0.2%)

localize8.0ms (0.5%)

series1.0ms (0.1%)

rewrite105.0ms (6%)

simplify116.0ms (6.6%)

localize38.0ms (2.2%)

series3.0ms (0.2%)

rewrite58.0ms (3.3%)

simplify60.0ms (3.4%)

localize10.0ms (0.6%)

series16.0ms (0.9%)

rewrite62.0ms (3.6%)

simplify56.0ms (3.2%)

eval138.0ms (7.9%)

prune63.0ms (3.6%)

regimes17.0ms (1%)

simplify6.0ms (0.4%)

soundness0.0ms (0%)

end11.0ms (0.6%)

Profiling