Details

analyze113.0ms (3.1%)

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
25%	25%	74.9%	0.1%	0%	0%	0%	5
37.5%	37.5%	62.4%	0.1%	0%	0%	0%	6
56.3%	56.2%	43.7%	0.1%	0%	0%	0%	7
65.6%	65.6%	34.3%	0.1%	0%	0%	0%	8
76.6%	76.5%	23.4%	0.1%	0%	0%	0%	9
82%	82%	18%	0.1%	0%	0%	0%	10
87.9%	87.8%	12.1%	0.1%	0%	0%	0%	11
90.8%	90.7%	9.2%	0.1%	0%	0%	0%	12

Compiler

Compiled 8 to 6 computations (25% saved)

sample1.5s (40.8%)

Results

1.5s

8256×

body

256

valid

Bogosity

preprocess15.0ms (0.4%)

Algorithm

2×	egg-herbie

Rules

2×	`+-commutative_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	8	14
1	10	14
0	2	2

Stop Event

1×	saturated
1×	saturated

Calls

Call 1

Inputs
0
1

Outputs
0
1

Call 2

Inputs
(+.f64 x (/.f64 y 500))
(+.f64 y (/.f64 x 500))

Outputs
(+.f64 x (/.f64 y 500))
(+.f64 y (/.f64 x 500))

Compiler

Compiled 9 to 7 computations (22.2% saved)

simplify26.0ms (0.7%)

Algorithm

1×	egg-herbie

Rules

1×	`+-commutative_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	6	7
1	7	7

Stop Event

1×

saturated

Counts

1 → 1

Calls

Call 1

Inputs
(+.f64 x (/.f64 y 500))

Outputs
(+.f64 x (/.f64 y 500))

eval0.0ms (0%)

Compiler: Compiled 7 to 5 computations (28.6% saved)

prune1.0ms (0%)

Pruning

2 alts after pruning (2 fresh and 0 done)

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

Error

0.0b

Counts

2 → 1

Alt Table

Click to see full alt table

Status	Error	Program
▶	0.0b	(+.f64 x (/.f64 y 500))

Compiler

Compiled 7 to 5 computations (28.6% saved)

localize5.0ms (0.1%)

Local error

Found 1 expressions with local error:

New	Error	Program
✓	0.0b	(+.f64 x (/.f64 y 500))

Compiler

Compiled 13 to 8 computations (38.5% saved)

series3.0ms (0.1%)

Counts

1 → 24

Calls

6 calls:

Time	Variable		Point	Expression
1.0ms	x	@	inf	(+.f64 x (/.f64 y 500))
1.0ms	y	@	inf	(+.f64 x (/.f64 y 500))
0.0ms	x	@	0	(+.f64 x (/.f64 y 500))
0.0ms	y	@	0	(+.f64 x (/.f64 y 500))
0.0ms	y	@	-inf	(+.f64 x (/.f64 y 500))

rewrite72.0ms (2%)

Algorithm

1×	batch-egg-rewrite

Rules

743×	`pow1_binary64`
701×	`add-log-exp_binary64`
701×	`log1p-expm1-u_binary64`
701×	`expm1-log1p-u_binary64`
688×	`add-exp-log_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	6	7
1	138	5
2	1889	5

Stop Event

1×	node limit

Counts

1 → 34

Calls

Call 1

Inputs
(+.f64 x (/.f64 y 500))

Outputs
((#(struct:change #<rule egg-rr> (2) ((x -.f64 (+.f64 1 (fma.f64 y 1/500 x)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (/.f64 (.f64 x x) (-.f64 x (.f64 y 1/500))) (/.f64 (.f64 (.f64 y y) 1/250000) (-.f64 x (.f64 y 1/500))))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (fma.f64 y 1/500 x) 1)))) (#(struct:change #<rule egg-rr> (2) ((x .f64 1 (fma.f64 y 1/500 x))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (cbrt.f64 (fma.f64 y 1/500 x)) (pow.f64 (cbrt.f64 (fma.f64 y 1/500 x)) 2))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (pow.f64 (cbrt.f64 (fma.f64 y 1/500 x)) 2) (cbrt.f64 (fma.f64 y 1/500 x)))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (sqrt.f64 (fma.f64 y 1/500 x)) (sqrt.f64 (fma.f64 y 1/500 x)))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (+.f64 (pow.f64 x 3) (.f64 (pow.f64 y 3) 1/125000000)) (/.f64 1 (fma.f64 x x (.f64 (.f64 y 1/500) (-.f64 (.f64 y 1/500) x)))))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (-.f64 (.f64 x x) (.f64 (.f64 y y) 1/250000)) (/.f64 1 (-.f64 x (.f64 y 1/500))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 1 (/.f64 (fma.f64 x x (.f64 (.f64 y 1/500) (-.f64 (.f64 y 1/500) x))) (+.f64 (pow.f64 x 3) (.f64 (pow.f64 y 3) 1/125000000))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 1 (/.f64 (-.f64 x (.f64 y 1/500)) (-.f64 (.f64 x x) (.f64 (.f64 y y) 1/250000))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (+.f64 (pow.f64 x 3) (.f64 (pow.f64 y 3) 1/125000000)) (fma.f64 x x (.f64 (.f64 y 1/500) (-.f64 (.f64 y 1/500) x))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (+.f64 (pow.f64 x 3) (.f64 (pow.f64 y 3) 1/125000000)) (+.f64 (.f64 (.f64 y y) 1/250000) (-.f64 (.f64 x x) (.f64 x (.f64 y 1/500)))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (-.f64 (.f64 x x) (.f64 (.f64 y y) 1/250000)) (-.f64 x (.f64 y 1/500)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (neg.f64 (+.f64 (pow.f64 x 3) (.f64 (pow.f64 y 3) 1/125000000))) (neg.f64 (fma.f64 x x (.f64 (.f64 y 1/500) (-.f64 (.f64 y 1/500) x)))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (neg.f64 (-.f64 (.f64 x x) (.f64 (.f64 y y) 1/250000))) (neg.f64 (-.f64 x (.f64 y 1/500))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (-.f64 (.f64 (.f64 y y) 1/250000) (.f64 x x)) (-.f64 (.f64 y 1/500) x))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (fma.f64 y 1/500 x) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (fma.f64 y 1/500 x) 3) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (cbrt.f64 (fma.f64 y 1/500 x)) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (sqrt.f64 (fma.f64 y 1/500 x)) 2)))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f64 (pow.f64 (fma.f64 y 1/500 x) 2))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (exp.f64 (fma.f64 y 1/500 x)))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (pow.f64 (fma.f64 y 1/500 x) 3))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (fma.f64 y 1/500 x)))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (fma.f64 y 1/500 x)))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (log.f64 (fma.f64 y 1/500 x)))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 y 1/500 x)))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 1 x (.f64 y 1/500))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 1 (.f64 y 1/500) x)))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (pow.f64 (cbrt.f64 (.f64 y 1/500)) 2) (cbrt.f64 (.f64 y 1/500)) x)))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (pow.f64 (cbrt.f64 x) 2) (cbrt.f64 x) (.f64 y 1/500))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (sqrt.f64 (.f64 y 1/500)) (sqrt.f64 (.f64 y 1/500)) x)))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (sqrt.f64 x) (sqrt.f64 x) (.f64 y 1/500))))))

Outputs

((#(struct:change #<rule egg-rr> (2) ((x -.f64 (+.f64 1 (fma.f64 y 1/500 x)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (/.f64 (*.f64 x x) (-.f64 x (*.f64 y 1/500))) (/.f64 (*.f64 (*.f64 y y) 1/250000) (-.f64 x (*.f64 y 1/500))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (fma.f64 y 1/500 x) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 1 (fma.f64 y 1/500 x))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 (fma.f64 y 1/500 x)) (pow.f64 (cbrt.f64 (fma.f64 y 1/500 x)) 2))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (cbrt.f64 (fma.f64 y 1/500 x)) 2) (cbrt.f64 (fma.f64 y 1/500 x)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (sqrt.f64 (fma.f64 y 1/500 x)) (sqrt.f64 (fma.f64 y 1/500 x)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (+.f64 (pow.f64 x 3) (*.f64 (pow.f64 y 3) 1/125000000)) (/.f64 1 (fma.f64 x x (*.f64 (*.f64 y 1/500) (-.f64 (*.f64 y 1/500) x)))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (-.f64 (*.f64 x x) (*.f64 (*.f64 y y) 1/250000)) (/.f64 1 (-.f64 x (*.f64 y 1/500))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 1 (/.f64 (fma.f64 x x (*.f64 (*.f64 y 1/500) (-.f64 (*.f64 y 1/500) x))) (+.f64 (pow.f64 x 3) (*.f64 (pow.f64 y 3) 1/125000000))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 1 (/.f64 (-.f64 x (*.f64 y 1/500)) (-.f64 (*.f64 x x) (*.f64 (*.f64 y y) 1/250000))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (+.f64 (pow.f64 x 3) (*.f64 (pow.f64 y 3) 1/125000000)) (fma.f64 x x (*.f64 (*.f64 y 1/500) (-.f64 (*.f64 y 1/500) x))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (+.f64 (pow.f64 x 3) (*.f64 (pow.f64 y 3) 1/125000000)) (+.f64 (*.f64 (*.f64 y y) 1/250000) (-.f64 (*.f64 x x) (*.f64 x (*.f64 y 1/500)))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (-.f64 (*.f64 x x) (*.f64 (*.f64 y y) 1/250000)) (-.f64 x (*.f64 y 1/500)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (neg.f64 (+.f64 (pow.f64 x 3) (*.f64 (pow.f64 y 3) 1/125000000))) (neg.f64 (fma.f64 x x (*.f64 (*.f64 y 1/500) (-.f64 (*.f64 y 1/500) x)))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (neg.f64 (-.f64 (*.f64 x x) (*.f64 (*.f64 y y) 1/250000))) (neg.f64 (-.f64 x (*.f64 y 1/500))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (-.f64 (*.f64 (*.f64 y y) 1/250000) (*.f64 x x)) (-.f64 (*.f64 y 1/500) x))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (fma.f64 y 1/500 x) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (fma.f64 y 1/500 x) 3) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (cbrt.f64 (fma.f64 y 1/500 x)) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (sqrt.f64 (fma.f64 y 1/500 x)) 2)))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f64 (pow.f64 (fma.f64 y 1/500 x) 2))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (exp.f64 (fma.f64 y 1/500 x)))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (pow.f64 (fma.f64 y 1/500 x) 3))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (fma.f64 y 1/500 x)))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (fma.f64 y 1/500 x)))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (log.f64 (fma.f64 y 1/500 x)))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 y 1/500 x)))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 1 x (*.f64 y 1/500))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 1 (*.f64 y 1/500) x)))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (pow.f64 (cbrt.f64 (*.f64 y 1/500)) 2) (cbrt.f64 (*.f64 y 1/500)) x)))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (pow.f64 (cbrt.f64 x) 2) (cbrt.f64 x) (*.f64 y 1/500))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (sqrt.f64 (*.f64 y 1/500)) (sqrt.f64 (*.f64 y 1/500)) x)))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (sqrt.f64 x) (sqrt.f64 x) (*.f64 y 1/500))))))

simplify17.0ms (0.5%)

Algorithm

1×	egg-herbie

Rules

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

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	6	105
1	9	105
2	10	105

Stop Event

1×

saturated

Counts

58 → 38

Calls

Call 1

Inputs
(*.f64 1/500 y)
(+.f64 (*.f64 1/500 y) x)
(+.f64 (*.f64 1/500 y) x)
(+.f64 (*.f64 1/500 y) x)
x
(+.f64 (*.f64 1/500 y) x)
(+.f64 (*.f64 1/500 y) x)
(+.f64 (*.f64 1/500 y) x)
x
(+.f64 (*.f64 1/500 y) x)
(+.f64 (*.f64 1/500 y) x)
(+.f64 (*.f64 1/500 y) x)
x
(+.f64 (*.f64 1/500 y) x)
(+.f64 (*.f64 1/500 y) x)
(+.f64 (*.f64 1/500 y) x)
(*.f64 1/500 y)
(+.f64 (*.f64 1/500 y) x)
(+.f64 (*.f64 1/500 y) x)
(+.f64 (*.f64 1/500 y) x)
(*.f64 1/500 y)
(+.f64 (*.f64 1/500 y) x)
(+.f64 (*.f64 1/500 y) x)
(+.f64 (*.f64 1/500 y) x)

Outputs
(*.f64 1/500 y)
(+.f64 (*.f64 1/500 y) x)
(fma.f64 1/500 y x)
(+.f64 (*.f64 1/500 y) x)
(fma.f64 1/500 y x)
(+.f64 (*.f64 1/500 y) x)
(fma.f64 1/500 y x)
x
(+.f64 (*.f64 1/500 y) x)
(fma.f64 1/500 y x)
(+.f64 (*.f64 1/500 y) x)
(fma.f64 1/500 y x)
(+.f64 (*.f64 1/500 y) x)
(fma.f64 1/500 y x)
x
(+.f64 (*.f64 1/500 y) x)
(fma.f64 1/500 y x)
(+.f64 (*.f64 1/500 y) x)
(fma.f64 1/500 y x)
(+.f64 (*.f64 1/500 y) x)
(fma.f64 1/500 y x)
x
(+.f64 (*.f64 1/500 y) x)
(fma.f64 1/500 y x)
(+.f64 (*.f64 1/500 y) x)
(fma.f64 1/500 y x)
(+.f64 (*.f64 1/500 y) x)
(fma.f64 1/500 y x)
(*.f64 1/500 y)
(+.f64 (*.f64 1/500 y) x)
(fma.f64 1/500 y x)
(+.f64 (*.f64 1/500 y) x)
(fma.f64 1/500 y x)
(+.f64 (*.f64 1/500 y) x)
(fma.f64 1/500 y x)
(*.f64 1/500 y)
(+.f64 (*.f64 1/500 y) x)
(fma.f64 1/500 y x)
(+.f64 (*.f64 1/500 y) x)
(fma.f64 1/500 y x)
(+.f64 (*.f64 1/500 y) x)
(fma.f64 1/500 y x)

eval23.0ms (0.6%)

Compiler: Compiled 415 to 265 computations (36.1% saved)

prune14.0ms (0.4%)

Pruning

6 alts after pruning (5 fresh and 1 done)

	Pruned	Kept	Total
New	33	5	38
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	33	6	39

Error

Counts

39 → 6

Alt Table

Click to see full alt table

Status	Error	Program
	32.2b	x
▶	0.1b	(+.f64 (*.f64 1/500 y) x)
▶	30.7b	(*.f64 1/500 y)
▶	0.1b	(fma.f64 y 1/500 x)
✓	0.0b	(+.f64 x (/.f64 y 500))
▶	31.4b	(fma.f64 (sqrt.f64 (.f64 y 1/500)) (sqrt.f64 (.f64 y 1/500)) x)

Compiler

Compiled 40 to 29 computations (27.5% saved)

localize6.0ms (0.2%)

Local error

Found 1 expressions with local error:

New	Error	Program
✓	0.2b	(*.f64 1/500 y)

Compiler

Compiled 7 to 5 computations (28.6% saved)

series3.0ms (0.1%)

Counts

1 → 0

Calls

3 calls:

Time	Variable		Point	Expression
1.0ms	y	@	inf	(*.f64 1/500 y)
1.0ms	y	@	-inf	(*.f64 1/500 y)
1.0ms	y	@	0	(*.f64 1/500 y)

rewrite384.0ms (10.6%)

Algorithm

1×	batch-egg-rewrite

Rules

345×	`pow1_binary64`
338×	`add-sqr-sqrt_binary64`
329×	`*-un-lft-identity_binary64`
321×	`add-log-exp_binary64`
321×	`log1p-expm1-u_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	4	4
1	80	4
2	873	4

Stop Event

1×	node limit

Counts

1 → 25

Calls

Call 1

Inputs
(*.f64 1/500 y)

Outputs
((#(struct:change #<rule egg-rr> (2) ((x +.f64 (+.f64 1 (.f64 1/500 y)) -1)))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 0 (.f64 1/500 y))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (log.f64 (pow.f64 (exp.f64 y) 1/1000)) (log.f64 (pow.f64 (exp.f64 y) 1/1000)))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (log.f64 (cbrt.f64 (pow.f64 (exp.f64 y) 1/250))) (log.f64 (cbrt.f64 (pow.f64 (exp.f64 y) 1/500))))))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (+.f64 1 (.f64 1/500 y)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (-.f64 (pow.f64 (+.f64 1 (.f64 1/500 y)) 3) 1) (+.f64 (.f64 (+.f64 1 (.f64 1/500 y)) (+.f64 1 (.f64 1/500 y))) (+.f64 1 (.f64 (+.f64 1 (.f64 1/500 y)) 1))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (-.f64 (.f64 (+.f64 1 (.f64 1/500 y)) (+.f64 1 (.f64 1/500 y))) 1) (+.f64 (+.f64 1 (.f64 1/500 y)) 1))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (.f64 1/500 y) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (.f64 1/500 y) 2) 1/2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (.f64 (pow.f64 y 3) 1/125000000) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (cbrt.f64 (.f64 1/500 y)) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (sqrt.f64 (.f64 1/500 y)) 2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (E.f64) (log.f64 (.f64 1/500 y)))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (exp.f64 (sqrt.f64 (log.f64 (.f64 1/500 y)))) (sqrt.f64 (log.f64 (.f64 1/500 y))))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (exp.f64 (pow.f64 (cbrt.f64 (log.f64 (.f64 1/500 y))) 2)) (cbrt.f64 (log.f64 (.f64 1/500 y))))))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f64 (pow.f64 (.f64 1/500 y) 2))))) (#(struct:change #<rule egg-rr> (2) ((x fabs.f64 (.f64 1/500 y))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (pow.f64 (exp.f64 y) 1/500))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (.f64 (pow.f64 y 3) 1/125000000))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (.f64 1/500 y)))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (.f64 1/500 y)))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (log.f64 (.f64 1/500 y)))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (.f64 (.f64 3 (log.f64 (.f64 1/500 y))) 1/3))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (.f64 (log.f64 (cbrt.f64 (.f64 1/500 y))) 3))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (.f64 (log.f64 (sqrt.f64 (.f64 1/500 y))) 2))))))

Outputs

((#(struct:change #<rule egg-rr> (2) ((x +.f64 (+.f64 1 (*.f64 1/500 y)) -1)))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 0 (*.f64 1/500 y))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (log.f64 (pow.f64 (exp.f64 y) 1/1000)) (log.f64 (pow.f64 (exp.f64 y) 1/1000)))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (log.f64 (cbrt.f64 (pow.f64 (exp.f64 y) 1/250))) (log.f64 (cbrt.f64 (pow.f64 (exp.f64 y) 1/500))))))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (+.f64 1 (*.f64 1/500 y)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (-.f64 (pow.f64 (+.f64 1 (*.f64 1/500 y)) 3) 1) (+.f64 (*.f64 (+.f64 1 (*.f64 1/500 y)) (+.f64 1 (*.f64 1/500 y))) (+.f64 1 (*.f64 (+.f64 1 (*.f64 1/500 y)) 1))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (-.f64 (*.f64 (+.f64 1 (*.f64 1/500 y)) (+.f64 1 (*.f64 1/500 y))) 1) (+.f64 (+.f64 1 (*.f64 1/500 y)) 1))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (*.f64 1/500 y) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (*.f64 1/500 y) 2) 1/2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (*.f64 (pow.f64 y 3) 1/125000000) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (cbrt.f64 (*.f64 1/500 y)) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (sqrt.f64 (*.f64 1/500 y)) 2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (E.f64) (log.f64 (*.f64 1/500 y)))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (exp.f64 (sqrt.f64 (log.f64 (*.f64 1/500 y)))) (sqrt.f64 (log.f64 (*.f64 1/500 y))))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (exp.f64 (pow.f64 (cbrt.f64 (log.f64 (*.f64 1/500 y))) 2)) (cbrt.f64 (log.f64 (*.f64 1/500 y))))))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f64 (pow.f64 (*.f64 1/500 y) 2))))) (#(struct:change #<rule egg-rr> (2) ((x fabs.f64 (*.f64 1/500 y))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (pow.f64 (exp.f64 y) 1/500))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (*.f64 (pow.f64 y 3) 1/125000000))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (*.f64 1/500 y)))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (*.f64 1/500 y)))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (log.f64 (*.f64 1/500 y)))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (*.f64 3 (log.f64 (*.f64 1/500 y))) 1/3))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (log.f64 (cbrt.f64 (*.f64 1/500 y))) 3))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (log.f64 (sqrt.f64 (*.f64 1/500 y))) 2))))))

simplify14.0ms (0.4%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	0	0

Stop Event

1×

saturated

Counts

25 → 25

Calls

Call 1

Inputs

Outputs

localize12.0ms (0.3%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.0b	(+.f64 (*.f64 1/500 y) x)
	0.2b	(*.f64 1/500 y)

Compiler

Compiled 13 to 8 computations (38.5% saved)

series3.0ms (0.1%)

Counts

1 → 6

Calls

6 calls:

Time	Variable		Point	Expression
1.0ms	y	@	0	(+.f64 (*.f64 1/500 y) x)
1.0ms	y	@	inf	(+.f64 (*.f64 1/500 y) x)
0.0ms	x	@	inf	(+.f64 (*.f64 1/500 y) x)
0.0ms	y	@	-inf	(+.f64 (*.f64 1/500 y) x)
0.0ms	x	@	0	(+.f64 (*.f64 1/500 y) x)

rewrite438.0ms (12.1%)

Algorithm

1×	batch-egg-rewrite

Rules

687×	`pow1_binary64`
642×	`add-log-exp_binary64`
642×	`log1p-expm1-u_binary64`
642×	`expm1-log1p-u_binary64`
629×	`add-exp-log_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	6	5
1	131	5
2	1732	5

Stop Event

1×	node limit

Counts

1 → 35

Calls

Call 1

Inputs
(+.f64 (*.f64 1/500 y) x)

Outputs

((#(struct:change #<rule egg-rr> (2) ((x -.f64 (+.f64 1 (fma.f64 1/500 y x)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (/.f64 (pow.f64 (*.f64 1/500 y) 2) (-.f64 (*.f64 1/500 y) x)) (/.f64 (*.f64 x x) (-.f64 (*.f64 1/500 y) x)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (fma.f64 1/500 y x) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 1 (fma.f64 1/500 y x))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 (fma.f64 1/500 y x)) (pow.f64 (cbrt.f64 (fma.f64 1/500 y x)) 2))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (cbrt.f64 (fma.f64 1/500 y x)) 2) (cbrt.f64 (fma.f64 1/500 y x)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (sqrt.f64 (fma.f64 1/500 y x)) (sqrt.f64 (fma.f64 1/500 y x)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (+.f64 (*.f64 (pow.f64 y 3) 1/125000000) (pow.f64 x 3)) (/.f64 1 (+.f64 (pow.f64 (*.f64 1/500 y) 2) (*.f64 x (-.f64 x (*.f64 1/500 y))))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (-.f64 (pow.f64 (*.f64 1/500 y) 2) (*.f64 x x)) (/.f64 1 (-.f64 (*.f64 1/500 y) x)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 1 (/.f64 (+.f64 (pow.f64 (*.f64 1/500 y) 2) (*.f64 x (-.f64 x (*.f64 1/500 y)))) (+.f64 (*.f64 (pow.f64 y 3) 1/125000000) (pow.f64 x 3))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 1 (/.f64 (-.f64 (*.f64 1/500 y) x) (-.f64 (pow.f64 (*.f64 1/500 y) 2) (*.f64 x x))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (+.f64 (*.f64 (pow.f64 y 3) 1/125000000) (pow.f64 x 3)) (+.f64 (pow.f64 (*.f64 1/500 y) 2) (*.f64 x (-.f64 x (*.f64 1/500 y)))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (+.f64 (*.f64 (pow.f64 y 3) 1/125000000) (pow.f64 x 3)) (+.f64 (*.f64 x x) (-.f64 (pow.f64 (*.f64 1/500 y) 2) (*.f64 1/500 (*.f64 y x)))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (-.f64 (pow.f64 (*.f64 1/500 y) 2) (*.f64 x x)) (-.f64 (*.f64 1/500 y) x))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (neg.f64 (+.f64 (*.f64 (pow.f64 y 3) 1/125000000) (pow.f64 x 3))) (neg.f64 (+.f64 (pow.f64 (*.f64 1/500 y) 2) (*.f64 x (-.f64 x (*.f64 1/500 y))))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (neg.f64 (-.f64 (pow.f64 (*.f64 1/500 y) 2) (*.f64 x x))) (neg.f64 (-.f64 (*.f64 1/500 y) x)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (-.f64 (*.f64 x x) (pow.f64 (*.f64 1/500 y) 2)) (-.f64 x (*.f64 1/500 y)))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (fma.f64 1/500 y x) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (fma.f64 1/500 y x) 3) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (cbrt.f64 (fma.f64 1/500 y x)) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (sqrt.f64 (fma.f64 1/500 y x)) 2)))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f64 (pow.f64 (fma.f64 1/500 y x) 2))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (exp.f64 (fma.f64 1/500 y x)))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (pow.f64 (fma.f64 1/500 y x) 3))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (fma.f64 1/500 y x)))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (fma.f64 1/500 y x)))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (log.f64 (fma.f64 1/500 y x)))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 1/500 y x)))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 y 1/500 x)))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 1 (*.f64 1/500 y) x)))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 1 x (*.f64 1/500 y))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (pow.f64 (cbrt.f64 x) 2) (cbrt.f64 x) (*.f64 1/500 y))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (pow.f64 (cbrt.f64 (*.f64 1/500 y)) 2) (cbrt.f64 (*.f64 1/500 y)) x)))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (sqrt.f64 x) (sqrt.f64 x) (*.f64 1/500 y))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (sqrt.f64 (*.f64 1/500 y)) (sqrt.f64 (*.f64 1/500 y)) x)))))

simplify16.0ms (0.4%)

Algorithm

1×	egg-herbie

Rules

1×	`*-commutative_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	5	15
1	6	15

Stop Event

1×

saturated

Counts

41 → 37

Calls

Call 1

Inputs
x
(*.f64 1/500 y)
(*.f64 1/500 y)
(*.f64 1/500 y)
x
x

Outputs
x
(*.f64 1/500 y)
(*.f64 1/500 y)
(*.f64 1/500 y)
x
x

localize9.0ms (0.3%)

Local error

Found 1 expressions with local error:

New	Error	Program
✓	0.1b	(fma.f64 y 1/500 x)

Compiler

Compiled 9 to 5 computations (44.4% saved)

series5.0ms (0.1%)

Counts

1 → 24

Calls

6 calls:

Time	Variable		Point	Expression
1.0ms	y	@	0	(fma.f64 y 1/500 x)
1.0ms	y	@	-inf	(fma.f64 y 1/500 x)
1.0ms	x	@	0	(fma.f64 y 1/500 x)
1.0ms	y	@	inf	(fma.f64 y 1/500 x)
1.0ms	x	@	-inf	(fma.f64 y 1/500 x)

rewrite205.0ms (5.6%)

Algorithm

1×	batch-egg-rewrite

Rules

450×	`pow1_binary64`
438×	`add-sqr-sqrt_binary64`
429×	`*-un-lft-identity_binary64`
416×	`add-log-exp_binary64`
416×	`log1p-expm1-u_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	5	5
1	100	5
2	1106	5

Stop Event

1×	node limit

Counts

1 → 21

Calls

Call 1

Inputs
(fma.f64 y 1/500 x)

Outputs

((#(struct:change #<rule egg-rr> (2) ((x +.f64 x (*.f64 y 1/500))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (*.f64 y 1/500) x)))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (*.f64 (*.f64 y 1/500) 1) x)))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (+.f64 1 (fma.f64 y 1/500 x)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (fma.f64 y 1/500 x) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 1 (fma.f64 y 1/500 x))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 (fma.f64 y 1/500 x)) (pow.f64 (cbrt.f64 (fma.f64 y 1/500 x)) 2))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (cbrt.f64 (fma.f64 y 1/500 x)) 2) (cbrt.f64 (fma.f64 y 1/500 x)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (sqrt.f64 (fma.f64 y 1/500 x)) (sqrt.f64 (fma.f64 y 1/500 x)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (+.f64 (pow.f64 (*.f64 y 1/500) 3) (pow.f64 x 3)) (+.f64 (*.f64 (*.f64 y 1/500) (*.f64 y 1/500)) (-.f64 (*.f64 x x) (*.f64 (*.f64 y 1/500) x))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (-.f64 (*.f64 (*.f64 y 1/500) (*.f64 y 1/500)) (*.f64 x x)) (-.f64 (*.f64 y 1/500) x))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (fma.f64 y 1/500 x) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (fma.f64 y 1/500 x) 3) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (cbrt.f64 (fma.f64 y 1/500 x)) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (sqrt.f64 (fma.f64 y 1/500 x)) 2)))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f64 (pow.f64 (fma.f64 y 1/500 x) 2))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (exp.f64 (fma.f64 y 1/500 x)))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (pow.f64 (fma.f64 y 1/500 x) 3))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (fma.f64 y 1/500 x)))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (fma.f64 y 1/500 x)))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (log.f64 (fma.f64 y 1/500 x)))))))

simplify34.0ms (0.9%)

Algorithm

1×	egg-herbie

Rules

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

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	6	105
1	9	105
2	10	105

Stop Event

1×

saturated

Counts

45 → 25

Calls

Call 1

Inputs
x
(+.f64 (*.f64 1/500 y) x)
(+.f64 (*.f64 1/500 y) x)
(+.f64 (*.f64 1/500 y) x)
(*.f64 1/500 y)
(+.f64 (*.f64 1/500 y) x)
(+.f64 (*.f64 1/500 y) x)
(+.f64 (*.f64 1/500 y) x)
(*.f64 1/500 y)
(+.f64 (*.f64 1/500 y) x)
(+.f64 (*.f64 1/500 y) x)
(+.f64 (*.f64 1/500 y) x)
(*.f64 1/500 y)
(+.f64 (*.f64 1/500 y) x)
(+.f64 (*.f64 1/500 y) x)
(+.f64 (*.f64 1/500 y) x)
x
(+.f64 (*.f64 1/500 y) x)
(+.f64 (*.f64 1/500 y) x)
(+.f64 (*.f64 1/500 y) x)
x
(+.f64 (*.f64 1/500 y) x)
(+.f64 (*.f64 1/500 y) x)
(+.f64 (*.f64 1/500 y) x)

Outputs
x
(+.f64 (*.f64 1/500 y) x)
(fma.f64 1/500 y x)
(+.f64 (*.f64 1/500 y) x)
(fma.f64 1/500 y x)
(+.f64 (*.f64 1/500 y) x)
(fma.f64 1/500 y x)
(*.f64 1/500 y)
(+.f64 (*.f64 1/500 y) x)
(fma.f64 1/500 y x)
(+.f64 (*.f64 1/500 y) x)
(fma.f64 1/500 y x)
(+.f64 (*.f64 1/500 y) x)
(fma.f64 1/500 y x)
(*.f64 1/500 y)
(+.f64 (*.f64 1/500 y) x)
(fma.f64 1/500 y x)
(+.f64 (*.f64 1/500 y) x)
(fma.f64 1/500 y x)
(+.f64 (*.f64 1/500 y) x)
(fma.f64 1/500 y x)
(*.f64 1/500 y)
(+.f64 (*.f64 1/500 y) x)
(fma.f64 1/500 y x)
(+.f64 (*.f64 1/500 y) x)
(fma.f64 1/500 y x)
(+.f64 (*.f64 1/500 y) x)
(fma.f64 1/500 y x)
x
(+.f64 (*.f64 1/500 y) x)
(fma.f64 1/500 y x)
(+.f64 (*.f64 1/500 y) x)
(fma.f64 1/500 y x)
(+.f64 (*.f64 1/500 y) x)
(fma.f64 1/500 y x)
x
(+.f64 (*.f64 1/500 y) x)
(fma.f64 1/500 y x)
(+.f64 (*.f64 1/500 y) x)
(fma.f64 1/500 y x)
(+.f64 (*.f64 1/500 y) x)
(fma.f64 1/500 y x)

localize21.0ms (0.6%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.1b	(sqrt.f64 (*.f64 y 1/500))
✓	0.1b	(fma.f64 (sqrt.f64 (.f64 y 1/500)) (sqrt.f64 (.f64 y 1/500)) x)
✓	0.2b	(*.f64 y 1/500)

Compiler

Compiled 22 to 15 computations (31.8% saved)

series17.0ms (0.5%)

Counts

3 → 25

Calls

12 calls:

Time	Variable		Point	Expression
5.0ms	y	@	-inf	(fma.f64 (sqrt.f64 (.f64 y 1/500)) (sqrt.f64 (.f64 y 1/500)) x)
3.0ms	y	@	inf	(fma.f64 (sqrt.f64 (.f64 y 1/500)) (sqrt.f64 (.f64 y 1/500)) x)
2.0ms	y	@	0	(fma.f64 (sqrt.f64 (.f64 y 1/500)) (sqrt.f64 (.f64 y 1/500)) x)
1.0ms	x	@	0	(fma.f64 (sqrt.f64 (.f64 y 1/500)) (sqrt.f64 (.f64 y 1/500)) x)
1.0ms	y	@	-inf	(sqrt.f64 (*.f64 y 1/500))

rewrite93.0ms (2.6%)

Algorithm

1×	batch-egg-rewrite

Rules

611×	`pow1_binary64`
565×	`add-log-exp_binary64`
565×	`log1p-expm1-u_binary64`
565×	`expm1-log1p-u_binary64`
552×	`add-exp-log_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	7	17
1	140	15
2	1562	15

Stop Event

1×	node limit

Counts

3 → 54

Calls

Call 1

Inputs
(*.f64 y 1/500)
(fma.f64 (sqrt.f64 (.f64 y 1/500)) (sqrt.f64 (.f64 y 1/500)) x)
(sqrt.f64 (*.f64 y 1/500))

Outputs

((#(struct:change #<rule egg-rr> (2) ((x -.f64 (+.f64 1 (*.f64 y 1/500)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (*.f64 y 1/500) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (sqrt.f64 (*.f64 y 1/500)) 2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (*.f64 1/250000 (*.f64 y y)) 1/2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (*.f64 y 1/500) 3) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (cbrt.f64 (*.f64 y 1/500)) 3)))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f64 (*.f64 1/250000 (*.f64 y y)))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (pow.f64 (exp.f64 y) 1/500))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (pow.f64 (*.f64 y 1/500) 3))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (*.f64 y 1/500)))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (*.f64 y 1/500)))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (log.f64 (*.f64 y 1/500)))))))

((#(struct:change #<rule egg-rr> (2) ((x +.f64 (*.f64 y 1/500) x)))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 x (*.f64 y 1/500))))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (+.f64 1 (fma.f64 y 1/500 x)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (fma.f64 y 1/500 x) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 1 (fma.f64 y 1/500 x))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 (fma.f64 y 1/500 x)) (pow.f64 (cbrt.f64 (fma.f64 y 1/500 x)) 2))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (cbrt.f64 (fma.f64 y 1/500 x)) 2) (cbrt.f64 (fma.f64 y 1/500 x)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (sqrt.f64 (fma.f64 y 1/500 x)) (sqrt.f64 (fma.f64 y 1/500 x)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (+.f64 (pow.f64 (*.f64 y 1/500) 3) (pow.f64 x 3)) (+.f64 (*.f64 1/250000 (*.f64 y y)) (-.f64 (*.f64 x x) (*.f64 (*.f64 y 1/500) x))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (-.f64 (*.f64 1/250000 (*.f64 y y)) (*.f64 x x)) (-.f64 (*.f64 y 1/500) x))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (fma.f64 y 1/500 x) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (fma.f64 y 1/500 x) 3) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (cbrt.f64 (fma.f64 y 1/500 x)) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (sqrt.f64 (fma.f64 y 1/500 x)) 2)))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f64 (pow.f64 (fma.f64 y 1/500 x) 2))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (exp.f64 (fma.f64 y 1/500 x)))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (pow.f64 (fma.f64 y 1/500 x) 3))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (fma.f64 y 1/500 x)))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (fma.f64 y 1/500 x)))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (log.f64 (fma.f64 y 1/500 x)))))))

((#(struct:change #<rule egg-rr> (2) ((x -.f64 (+.f64 1 (sqrt.f64 (*.f64 y 1/500))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (sqrt.f64 (*.f64 y 1/500)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 1 (sqrt.f64 (*.f64 y 1/500)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 (sqrt.f64 (*.f64 y 1/500))) (cbrt.f64 (*.f64 y 1/500)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 (*.f64 y 1/500)) (cbrt.f64 (sqrt.f64 (*.f64 y 1/500))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (sqrt.f64 1/500) (sqrt.f64 y))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (*.f64 y 1/500) 1/4) (pow.f64 (*.f64 y 1/500) 1/4))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (sqrt.f64 y) (sqrt.f64 1/500))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (sqrt.f64 (pow.f64 (cbrt.f64 (*.f64 y 1/500)) 2)) (sqrt.f64 (cbrt.f64 (*.f64 y 1/500))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 1 1/2) (sqrt.f64 (*.f64 y 1/500)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (pow.f64 (cbrt.f64 (*.f64 y 1/500)) 2) 1/2) (pow.f64 (cbrt.f64 (*.f64 y 1/500)) 1/2))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (*.f64 y 1/500) 1/2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (sqrt.f64 (*.f64 y 1/500)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (*.f64 y 1/500) 3/2) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (cbrt.f64 (sqrt.f64 (*.f64 y 1/500))) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (*.f64 y 1/500) 1/4) 2)))) (#(struct:change #<rule egg-rr> (2) ((x fabs.f64 (sqrt.f64 (*.f64 y 1/500)))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (exp.f64 (sqrt.f64 (*.f64 y 1/500))))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (pow.f64 (*.f64 y 1/500) 3/2))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (sqrt.f64 (*.f64 y 1/500))))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (sqrt.f64 (*.f64 y 1/500))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (log.f64 (sqrt.f64 (*.f64 y 1/500))))))))

simplify169.0ms (4.7%)

Algorithm

1×	egg-herbie

Rules

1858×	`unswap-sqr_binary64`
1116×	`sqr-pow_binary64`
531×	`fabs-mul_binary64`
528×	`cube-prod_binary64`
519×	`pow-sqr_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	10	145
1	19	100
2	32	100
3	52	100
4	101	100
5	284	100
6	970	100
7	1430	100
8	1579	100
9	1734	100
10	1911	100
11	2164	100
12	2513	100
13	2922	100
14	3383	100
15	3937	100
16	4618	100
17	5060	100
18	5306	100
19	5536	100
20	5592	100
21	5616	100
22	6167	100

Stop Event

1×	node limit

Counts

79 → 60

Calls

Call 1

Inputs
(*.f64 1/500 y)
(*.f64 1/500 y)
(*.f64 1/500 y)
(*.f64 1/500 y)
(*.f64 1/500 y)
(*.f64 1/500 y)
(*.f64 1/500 y)
(*.f64 1/500 y)
(*.f64 1/500 y)
(*.f64 1/500 y)
(*.f64 1/500 y)
(*.f64 1/500 y)
x
(*.f64 y (pow.f64 (sqrt.f64 1/500) 2))
(+.f64 (*.f64 y (pow.f64 (sqrt.f64 1/500) 2)) x)
(+.f64 (*.f64 y (pow.f64 (sqrt.f64 1/500) 2)) x)
(+.f64 (*.f64 y (pow.f64 (sqrt.f64 1/500) 2)) x)
x
(+.f64 (*.f64 y (pow.f64 (sqrt.f64 1/500) 2)) x)
(+.f64 (*.f64 y (pow.f64 (sqrt.f64 1/500) 2)) x)
(+.f64 (*.f64 y (pow.f64 (sqrt.f64 1/500) 2)) x)
x
(+.f64 (*.f64 y (pow.f64 (sqrt.f64 1/500) 2)) x)
(+.f64 (*.f64 y (pow.f64 (sqrt.f64 1/500) 2)) x)
(+.f64 (*.f64 y (pow.f64 (sqrt.f64 1/500) 2)) x)

Outputs
(*.f64 1/500 y)
(*.f64 y 1/500)
(*.f64 1/500 y)
(*.f64 y 1/500)
(*.f64 1/500 y)
(*.f64 y 1/500)
(*.f64 1/500 y)
(*.f64 y 1/500)
(*.f64 1/500 y)
(*.f64 y 1/500)
(*.f64 1/500 y)
(*.f64 y 1/500)
(*.f64 1/500 y)
(*.f64 y 1/500)
(*.f64 1/500 y)
(*.f64 y 1/500)
(*.f64 1/500 y)
(*.f64 y 1/500)
(*.f64 1/500 y)
(*.f64 y 1/500)
(*.f64 1/500 y)
(*.f64 y 1/500)
(*.f64 1/500 y)
(*.f64 y 1/500)
x
(*.f64 y (pow.f64 (sqrt.f64 1/500) 2))
(*.f64 1/500 y)
(*.f64 y 1/500)
(+.f64 (*.f64 y (pow.f64 (sqrt.f64 1/500) 2)) x)
(fma.f64 y (pow.f64 (sqrt.f64 1/500) 2) x)
(fma.f64 y 1/500 x)
(+.f64 (*.f64 y (pow.f64 (sqrt.f64 1/500) 2)) x)
(fma.f64 y (pow.f64 (sqrt.f64 1/500) 2) x)
(fma.f64 y 1/500 x)
(+.f64 (*.f64 y (pow.f64 (sqrt.f64 1/500) 2)) x)
(fma.f64 y (pow.f64 (sqrt.f64 1/500) 2) x)
(fma.f64 y 1/500 x)
x
(+.f64 (*.f64 y (pow.f64 (sqrt.f64 1/500) 2)) x)
(fma.f64 y (pow.f64 (sqrt.f64 1/500) 2) x)
(fma.f64 y 1/500 x)
(+.f64 (*.f64 y (pow.f64 (sqrt.f64 1/500) 2)) x)
(fma.f64 y (pow.f64 (sqrt.f64 1/500) 2) x)
(fma.f64 y 1/500 x)
(+.f64 (*.f64 y (pow.f64 (sqrt.f64 1/500) 2)) x)
(fma.f64 y (pow.f64 (sqrt.f64 1/500) 2) x)
(fma.f64 y 1/500 x)
x
(+.f64 (*.f64 y (pow.f64 (sqrt.f64 1/500) 2)) x)
(fma.f64 y (pow.f64 (sqrt.f64 1/500) 2) x)
(fma.f64 y 1/500 x)
(+.f64 (*.f64 y (pow.f64 (sqrt.f64 1/500) 2)) x)
(fma.f64 y (pow.f64 (sqrt.f64 1/500) 2) x)
(fma.f64 y 1/500 x)
(+.f64 (*.f64 y (pow.f64 (sqrt.f64 1/500) 2)) x)
(fma.f64 y (pow.f64 (sqrt.f64 1/500) 2) x)
(fma.f64 y 1/500 x)

eval86.0ms (2.4%)

Compiler: Compiled 2231 to 1627 computations (27.1% saved)

prune41.0ms (1.1%)

Pruning

6 alts after pruning (1 fresh and 5 done)

	Pruned	Kept	Total
New	207	1	208
Fresh	1	0	1
Picked	0	1	1
Done	0	4	4
Total	208	6	214

Error

Counts

214 → 6

Alt Table

Click to see full alt table

Status	Error	Program
✓	0.1b	(+.f64 (*.f64 1/500 y) x)
✓	30.7b	(*.f64 1/500 y)
✓	0.1b	(fma.f64 y 1/500 x)
✓	0.0b	(+.f64 x (/.f64 y 500))
	32.2b	x
✓	31.4b	(fma.f64 (sqrt.f64 (.f64 y 1/500)) (sqrt.f64 (.f64 y 1/500)) x)

Compiler

Compiled 40 to 29 computations (27.5% saved)

eval0.0ms (0%)

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

prune5.0ms (0.1%)

Pruning

6 alts after pruning (1 fresh and 5 done)

	Kept	Total
New	0	0
Fresh	1	1
Picked	0	0
Done	5	5
Total	6	6

Error

Counts

6 → 6

Alt Table

Click to see full alt table

Status	Error	Program
✓	0.1b	(+.f64 (*.f64 1/500 y) x)
✓	30.7b	(*.f64 1/500 y)
✓	0.1b	(fma.f64 y 1/500 x)
✓	0.0b	(+.f64 x (/.f64 y 500))
	32.2b	x
✓	31.4b	(fma.f64 (sqrt.f64 (.f64 y 1/500)) (sqrt.f64 (.f64 y 1/500)) x)

Compiler

Compiled 40 to 29 computations (27.5% saved)

eval0.0ms (0%)

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

prune5.0ms (0.1%)

Pruning

6 alts after pruning (1 fresh and 5 done)

	Kept	Total
New	0	0
Fresh	1	1
Picked	0	0
Done	5	5
Total	6	6

Error

Counts

6 → 6

Alt Table

Click to see full alt table

Status	Error	Program
✓	0.1b	(+.f64 (*.f64 1/500 y) x)
✓	30.7b	(*.f64 1/500 y)
✓	0.1b	(fma.f64 y 1/500 x)
✓	0.0b	(+.f64 x (/.f64 y 500))
	32.2b	x
✓	31.4b	(fma.f64 (sqrt.f64 (.f64 y 1/500)) (sqrt.f64 (.f64 y 1/500)) x)

Compiler

Compiled 40 to 29 computations (27.5% saved)

regimes68.0ms (1.9%)

Counts

7 → 1

Calls

Call 1

Inputs
x
x
(*.f64 1/500 y)
(+.f64 (*.f64 1/500 y) x)
(+.f64 x (/.f64 y 500))
(fma.f64 y 1/500 x)
(fma.f64 (sqrt.f64 (.f64 y 1/500)) (sqrt.f64 (.f64 y 1/500)) x)

Outputs
(+.f64 x (/.f64 y 500))

Calls

4 calls:

28.0ms	(/.f64 y 500)
14.0ms	y
11.0ms	(+.f64 x (/.f64 y 500))
11.0ms	x

Results

Error	Segments	Branch
0.0b	1	`x`
0.0b	1	`y`
0.0b	1	`(+.f64 x (/.f64 y 500))`
0.0b	1	`(/.f64 y 500)`

Compiler

Compiled 49 to 32 computations (34.7% saved)

regimes20.0ms (0.6%)

Counts

4 → 1

Calls

Call 1

Inputs
x
x
(*.f64 1/500 y)
(+.f64 (*.f64 1/500 y) x)

Outputs
(+.f64 (*.f64 1/500 y) x)

Calls

2 calls:

9.0ms	y
9.0ms	x

Results

Error	Segments	Branch
0.1b	1	`x`
0.1b	1	`y`

Compiler

Compiled 18 to 11 computations (38.9% saved)

regimes64.0ms (1.8%)

Counts

3 → 3

Calls

Call 1

Inputs
x
x
(*.f64 1/500 y)

Outputs
x
(*.f64 1/500 y)
x

Calls

2 calls:

40.0ms	y
22.0ms	x

Results

Error	Segments	Branch
13.9b	3	`x`
14.3b	3	`y`

Compiler

Compiled 13 to 8 computations (38.5% saved)

bsearch53.0ms (1.5%)

Algorithm

2×	binary-search

Steps

Time	Left	Right
27.0ms	128903.20277625337	5.084411201161055e+21
26.0ms	-1.143189810419369e-11	-1.2866612082958661e-13

Compiler

Compiled 12 to 9 computations (25% saved)

regimes15.0ms (0.4%)

Accuracy

Total 0.0b remaining (0%)

Threshold costs 0.0b (0%)

Counts

2 → 1

Calls

Call 1

Inputs
x
x

Outputs
x

Calls

2 calls:

8.0ms	x
5.0ms	y

Results

Error	Segments	Branch
32.2b	1	`x`
32.2b	1	`y`

Compiler

Compiled 10 to 6 computations (40% saved)

simplify9.0ms (0.2%)

Algorithm

1×	egg-herbie

Rules

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

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	16	33
1	19	33

Stop Event

1×	fuel
1×	saturated

Calls

Call 1

Inputs
(+.f64 x (/.f64 y 500))
(+.f64 (*.f64 1/500 y) x)
(if (<=.f64 x -442250137131625/38685626227668133590597632) x (if (<=.f64 x 4429080322189317/34359738368) (*.f64 1/500 y) x))
x

Outputs
(+.f64 x (/.f64 y 500))
(+.f64 (*.f64 1/500 y) x)
(+.f64 x (*.f64 y 1/500))
(if (<=.f64 x -442250137131625/38685626227668133590597632) x (if (<=.f64 x 4429080322189317/34359738368) (*.f64 1/500 y) x))
(if (<=.f64 x -442250137131625/38685626227668133590597632) x (if (<=.f64 x 4429080322189317/34359738368) (*.f64 y 1/500) x))
x

Compiler

Compiled 32 to 22 computations (31.3% saved)

soundness0.0ms (0%)

end64.0ms (1.8%)

Compiler: Compiled 26 to 16 computations (38.5% saved)

Details

analyze113.0ms (3.1%)

sample1.5s (40.8%)

preprocess15.0ms (0.4%)

simplify26.0ms (0.7%)

eval0.0ms (0%)

prune1.0ms (0%)

localize5.0ms (0.1%)

series3.0ms (0.1%)

rewrite72.0ms (2%)

simplify17.0ms (0.5%)

eval23.0ms (0.6%)

prune14.0ms (0.4%)

localize6.0ms (0.2%)

series3.0ms (0.1%)

rewrite384.0ms (10.6%)

simplify14.0ms (0.4%)

localize12.0ms (0.3%)

series3.0ms (0.1%)

rewrite438.0ms (12.1%)

simplify16.0ms (0.4%)

localize9.0ms (0.3%)

series5.0ms (0.1%)

rewrite205.0ms (5.6%)

simplify34.0ms (0.9%)

localize21.0ms (0.6%)

series17.0ms (0.5%)

rewrite93.0ms (2.6%)

simplify169.0ms (4.7%)

eval86.0ms (2.4%)

prune41.0ms (1.1%)

eval0.0ms (0%)

prune5.0ms (0.1%)

eval0.0ms (0%)

prune5.0ms (0.1%)

regimes68.0ms (1.9%)

regimes20.0ms (0.6%)

regimes64.0ms (1.8%)

bsearch53.0ms (1.5%)

regimes15.0ms (0.4%)

simplify9.0ms (0.2%)

soundness0.0ms (0%)

end64.0ms (1.8%)

Profiling