Details

analyze5.0ms (0.4%)

Algorithm

1×

Search

True	Other	False	Iter
0%	100%	0%	0
0%	100%	0%	1
0%	100%	0%	2
0%	50%	50%	3
12.5%	25%	62.5%	4
18.7%	12.5%	68.8%	5
21.9%	6.2%	71.9%	6
23.4%	3.1%	73.5%	7
24.2%	1.6%	74.2%	8
24.6%	0.8%	74.6%	9
24.8%	0.4%	74.8%	10
24.9%	0.2%	74.9%	11
24.9%	0.1%	75%	12
25%	0%	75%	13
25%	0%	75%	14

Compiler

Compiled 15 to 11 computations (26.7% saved)

sample994.0ms (76.9%)

Results

979.0ms	8256×	body	128	valid
1.0ms	5×	body	128	invalid

Compiler

Compiled 30 to 22 computations (26.7% saved)

preprocess38.0ms (3%)

Algorithm

2×	egg-herbie

Rules

492×	`fma-neg_binary64`
454×	`unsub-neg_binary64`
411×	`distribute-rgt-in_binary64`
374×	`fma-def_binary64`
353×	`distribute-neg-in_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	10	20
1	18	20
2	25	20
3	36	20
4	53	20
5	81	20
6	128	20
7	323	20
8	664	20
9	1447	20
10	2776	20
11	4161	20
0	1	1

Stop Event

1×	saturated
1×	node limit

Calls

Call 1

Inputs
0

Outputs
0

Call 2

Inputs
(log.f64 (+.f64 (/.f64 1 x) (/.f64 (sqrt.f64 (-.f64 1 (*.f64 x x))) x)))

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

Compiler

Compiled 14 to 10 computations (28.6% saved)

simplify34.0ms (2.6%)

Algorithm

1×	egg-herbie

Rules

492×	`fma-neg_binary64`
454×	`unsub-neg_binary64`
411×	`distribute-rgt-in_binary64`
374×	`fma-def_binary64`
353×	`distribute-neg-in_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	10	20
1	18	20
2	25	20
3	36	20
4	53	20
5	81	20
6	128	20
7	323	20
8	664	20
9	1447	20
10	2776	20
11	4161	20

Stop Event

1×	node limit

Counts

1 → 1

Calls

Call 1

Inputs
(log.f64 (+.f64 (/.f64 1 x) (/.f64 (sqrt.f64 (-.f64 1 (*.f64 x x))) x)))

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

prune2.0ms (0.1%)

Pruning

2 alts after pruning (2 fresh and 0 done)

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

Error

Counts

2 → 1

Alt Table

Status	Error	Program
▶	0b	(log.f64 (+.f64 (/.f64 1 x) (/.f64 (sqrt.f64 (-.f64 1 (*.f64 x x))) x)))

Compiler

Compiled 42 to 30 computations (28.6% saved)

localize8.0ms (0.6%)

Local error

Found 1 expressions with local error:

New	Error	Program
✓	0.0b	(+.f64 (/.f64 1 x) (/.f64 (sqrt.f64 (-.f64 1 (*.f64 x x))) x))

series3.0ms (0.2%)

Counts

1 → 12

Calls

3 calls:

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

rewrite54.0ms (4.2%)

Algorithm

1×	batch-egg-rewrite

Rules

481×	`log-prod_binary64`
394×	`fma-def_binary64`
192×	`fma-neg_binary64`
182×	`log-div_binary64`
175×	`expm1-udef_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	9	18
1	208	18
2	3106	18

Stop Event

1×	node limit

Counts

1 → 82

Calls

Call 1

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

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

Outputs

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

simplify22.0ms (1.7%)

Algorithm

1×	egg-herbie

Rules

619×	`associate-/r*_binary64`
435×	`fma-def_binary64`
375×	`associate-l_binary64`
304×	`associate-r_binary64`
184×	`times-frac_binary64`

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	47	209
1	134	199
2	351	195
3	1154	191

Stop Event

1×	node limit

Counts

94 → 104

Calls

Call 1

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

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

prune55.0ms (4.2%)

Pruning

1 alts after pruning (0 fresh and 1 done)

	Pruned	Kept	Total
New	104	0	104
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	104	1	105

Error

Counts

105 → 1

Alt Table

Status	Error	Program
✓	0b	(log.f64 (+.f64 (/.f64 1 x) (/.f64 (sqrt.f64 (-.f64 1 (*.f64 x x))) x)))

Compiler

Compiled 2011 to 1330 computations (33.9% saved)

regimes17.0ms (1.3%)

Accuracy

Total 0.0b remaining (0%)

Threshold costs 0.0b (0%)

Counts

5 → 1

Compiler

Compiled 76 to 55 computations (27.6% saved)

simplify2.0ms (0.2%)

Algorithm

1×	egg-herbie

Rules

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

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	10	20
1	18	20
2	25	20
3	29	20
4	31	20

Stop Event

1×

saturated

Calls

Call 1

Inputs
(log.f64 (+.f64 (/.f64 1 x) (/.f64 (sqrt.f64 (-.f64 1 (*.f64 x x))) x)))

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

end57.0ms (4.4%)

Stop Event

1×

done

Compiler

Compiled 42 to 30 computations (28.6% saved)

Details

analyze5.0ms (0.4%)

sample994.0ms (76.9%)

preprocess38.0ms (3%)

simplify34.0ms (2.6%)

prune2.0ms (0.1%)

localize8.0ms (0.6%)

series3.0ms (0.2%)

rewrite54.0ms (4.2%)

simplify22.0ms (1.7%)

prune55.0ms (4.2%)

regimes17.0ms (1.3%)

simplify2.0ms (0.2%)

end57.0ms (4.4%)

Profiling