Details

analyze0.0ms (0%)

Algorithm

1×

Search

True	Other	False	Iter
0%	100%	0%	0
0%	100%	0%	1
50%	0%	50%	2

Compiler

Compiled 13 to 11 computations (15.4% saved)

sample2.1s (40.6%)

Results

1.0s	2301×	body	1024	valid
442.0ms	4118×	body	64	valid
391.0ms	1046×	body	512	valid
149.0ms	528×	body	256	valid
52.0ms	263×	body	128	valid

preprocess38.0ms (0.7%)

Algorithm

2×	egg-herbie

Rules

39×	`fma-def_binary64`
32×	`fma-neg_binary64`
15×	`cancel-sign-sub-inv_binary64`
12×	`sub-neg_binary64`
10×	`distribute-rgt-in_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	9	17
1	14	17
2	20	17
3	28	17
4	38	17
5	56	17
6	93	17
7	127	17
8	174	17
9	210	17
10	236	17
11	238	17
0	1	1

Stop Event

1×	saturated
1×	saturated

Calls

Call 1

Inputs
0

Outputs
0

Call 2

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

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

Compiler

Compiled 12 to 10 computations (16.7% saved)

simplify10.0ms (0.2%)

Algorithm

1×	egg-herbie

Rules

39×	`fma-def_binary64`
32×	`fma-neg_binary64`
15×	`cancel-sign-sub-inv_binary64`
12×	`sub-neg_binary64`
10×	`distribute-rgt-in_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	9	17
1	14	17
2	20	17
3	28	17
4	38	17
5	56	17
6	93	17
7	127	17
8	174	17
9	210	17
10	236	17
11	238	17

Stop Event

1×

saturated

Counts

1 → 2

Calls

Call 1

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

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

prune5.0ms (0.1%)

Pruning

1 alts after pruning (1 fresh and 0 done)

	Pruned	Kept	Total
New	1	1	2
Fresh	1	0	1
Picked	0	0	0
Done	0	0	0
Total	2	1	3

Error

21.5b

Counts

3 → 1

Alt Table

Status	Error	Program
▶	21.5b	(+.f64 (/.f64 1 (sqrt.f64 x)) (/.f64 -1 (sqrt.f64 (+.f64 1 x))))

Compiler

Compiled 47 to 38 computations (19.1% saved)

localize7.0ms (0.1%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.1b	(/.f64 -1 (sqrt.f64 (+.f64 1 x)))
✓	0.3b	(/.f64 1 (sqrt.f64 x))
✓	2.9b	(+.f64 (/.f64 1 (sqrt.f64 x)) (/.f64 -1 (sqrt.f64 (+.f64 1 x))))

series7.0ms (0.1%)

Counts

3 → 4

Calls

9 calls:

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

rewrite98.0ms (1.9%)

Algorithm

1×	batch-egg-rewrite

Rules

462×	`log-prod_binary64`
443×	`fma-def_binary64`
344×	`pow-prod-down_binary64`
269×	`pow2_binary64`
205×	`fma-neg_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	10	32
1	221	27
2	3099	27

Stop Event

1×	node limit

Counts

3 → 145

Calls

Call 1

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

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

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((#(struct:change #<rule egg-rr> (2) ((x +.f64 0 (pow.f64 x -1/2))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (log.f64 (pow.f64 (cbrt.f64 (exp.f64 (pow.f64 x -1/2))) 2)) (log.f64 (cbrt.f64 (exp.f64 (pow.f64 x -1/2)))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (log.f64 (sqrt.f64 (exp.f64 (pow.f64 x -1/2)))) (log.f64 (sqrt.f64 (exp.f64 (pow.f64 x -1/2)))))))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (exp.f64 (log1p.f64 (pow.f64 x -1/2))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 1 (pow.f64 x -1/2))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 x -1/2) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 -1 (/.f64 1 (neg.f64 (sqrt.f64 x))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 x -1/6) (cbrt.f64 (/.f64 1 x)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 (/.f64 1 x)) (pow.f64 x -1/6))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 x -1/4) (pow.f64 x -1/4))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 1 (cbrt.f64 x)) (pow.f64 x -1/6))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 x -1/2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (sqrt.f64 x) -1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 x -1/2) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (/.f64 1 x) 1/2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (*.f64 x x) -1/4)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 x 3/2) -1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 x -1/6) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (cbrt.f64 x) -3/2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 x 1/6) -3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 x -1/4) 2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 x 1/4) -2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 x -3/2) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 x 3) -1/6)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (neg.f64 (neg.f64 (sqrt.f64 x))) -1)))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f64 (/.f64 1 x))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (exp.f64 (pow.f64 x -1/2)))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (+.f64 1 (expm1.f64 (pow.f64 x -1/2))))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (pow.f64 x -3/2))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (pow.f64 x -1/2)))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 -1/2 (log.f64 x)))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (log.f64 (sqrt.f64 x)) -1))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (*.f64 -1/2 (log.f64 x)) 1))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (log.f64 x) -1/2))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (log.f64 (pow.f64 x -1/6)) 3))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (log.f64 (pow.f64 x -1/4)) 2))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (log.f64 (pow.f64 x -3/2)) 1/3))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (*.f64 (log.f64 x) 1) -1/2))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (*.f64 (log.f64 x) 1/2) -1))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (*.f64 (log.f64 (sqrt.f64 x)) 1) -1))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (*.f64 (log.f64 (sqrt.f64 x)) -1) 1))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (*.f64 (*.f64 -1/2 (log.f64 x)) 1) 1))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (*.f64 (*.f64 -1/2 (log.f64 x)) 3) 1/3))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (pow.f64 x -1/2)))))))

((#(struct:change #<rule egg-rr> (2) ((x +.f64 0 (neg.f64 (pow.f64 (+.f64 1 x) -1/2)))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (log.f64 (pow.f64 (cbrt.f64 (exp.f64 (neg.f64 (pow.f64 (+.f64 1 x) -1/2)))) 2)) (log.f64 (cbrt.f64 (exp.f64 (neg.f64 (pow.f64 (+.f64 1 x) -1/2))))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (log.f64 (sqrt.f64 (exp.f64 (neg.f64 (pow.f64 (+.f64 1 x) -1/2))))) (log.f64 (sqrt.f64 (exp.f64 (neg.f64 (pow.f64 (+.f64 1 x) -1/2))))))))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (exp.f64 (log1p.f64 (neg.f64 (pow.f64 (+.f64 1 x) -1/2)))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 1 (neg.f64 (pow.f64 (+.f64 1 x) -1/2)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 -1 (pow.f64 (+.f64 1 x) -1/2))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (neg.f64 (pow.f64 (+.f64 1 x) -1/2)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 -1 (pow.f64 (+.f64 1 x) 1/6)) (cbrt.f64 (/.f64 1 (+.f64 1 x))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 (/.f64 1 (+.f64 1 x))) (/.f64 -1 (pow.f64 (+.f64 1 x) 1/6)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (sqrt.f64 (neg.f64 (pow.f64 (+.f64 1 x) -1/2))) (sqrt.f64 (neg.f64 (pow.f64 (+.f64 1 x) -1/2))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (+.f64 1 x) -1/2) -1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (neg.f64 (pow.f64 (+.f64 1 x) -1/2)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (/.f64 1 (+.f64 1 x)) 1/2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (/.f64 -1 (pow.f64 (+.f64 1 x) 1/6)) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (sqrt.f64 (neg.f64 (pow.f64 (+.f64 1 x) -1/2))) 2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (neg.f64 (sqrt.f64 (+.f64 1 x))) -1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (*.f64 -1 (pow.f64 (+.f64 1 x) -3/2)) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x neg.f64 (pow.f64 (+.f64 1 x) -1/2))))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f64 (/.f64 1 (+.f64 1 x)))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (exp.f64 (neg.f64 (pow.f64 (+.f64 1 x) -1/2))))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (+.f64 1 (expm1.f64 (neg.f64 (pow.f64 (+.f64 1 x) -1/2)))))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (/.f64 1 (exp.f64 (pow.f64 (+.f64 1 x) -1/2))))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (*.f64 -1 (pow.f64 (+.f64 1 x) -3/2)))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (neg.f64 (pow.f64 (+.f64 1 x) -1/2))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (+.f64 (log.f64 -1) (*.f64 -1/2 (log1p.f64 x))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (+.f64 (log.f64 -1) (*.f64 -1/2 (log1p.f64 x))) 1))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (log.f64 (/.f64 -1 (pow.f64 (+.f64 1 x) 1/6))) 3))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (log.f64 (sqrt.f64 (neg.f64 (pow.f64 (+.f64 1 x) -1/2)))) 2))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (log.f64 (neg.f64 (sqrt.f64 (+.f64 1 x)))) -1))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (-.f64 (log.f64 -1) (*.f64 3/2 (log1p.f64 x))) 1/3))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (*.f64 (+.f64 (log.f64 -1) (*.f64 -1/2 (log1p.f64 x))) 1) 1))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (*.f64 (+.f64 (log.f64 -1) (*.f64 -1/2 (log1p.f64 x))) 3) 1/3))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (neg.f64 (pow.f64 (+.f64 1 x) -1/2))))))))

simplify45.0ms (0.9%)

Algorithm

1×	egg-herbie

Rules

572×	`fma-neg_binary64`
536×	`unswap-sqr_binary64`
533×	`distribute-rgt-neg-in_binary64`
493×	`associate-l_binary64`
484×	`distribute-lft-neg-in_binary64`

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	20	41
1	53	39
2	113	37
3	321	31
4	814	28
5	2691	28
6	6351	28

Stop Event

1×	node limit

Counts

149 → 152

Calls

Call 1

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

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

prune347.0ms (6.7%)

Pruning

16 alts after pruning (16 fresh and 0 done)

	Pruned	Kept	Total
New	136	16	152
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	137	16	153

Error

20.9b

Counts

153 → 16

Alt Table

Status	Error	Program
	21.5b	(*.f64 (-.f64 (/.f64 1 x) (/.f64 1 (+.f64 1 x))) (/.f64 1 (+.f64 (pow.f64 x -1/2) (pow.f64 (+.f64 1 x) -1/2))))
	28.0b	(+.f64 (pow.f64 (cbrt.f64 x) -3/2) (/.f64 -1 (sqrt.f64 (+.f64 1 x))))
▶	21.3b	(.f64 (fma.f64 (sqrt.f64 x) -1 (sqrt.f64 (+.f64 1 x))) (pow.f64 (.f64 x (+.f64 1 x)) -1/2))
	32.3b	(fma.f64 (pow.f64 x -1/4) (pow.f64 x -1/4) (neg.f64 (pow.f64 (+.f64 1 x) -1/2)))
	31.9b	(+.f64 (/.f64 1 (sqrt.f64 x)) (cbrt.f64 (*.f64 -1 (pow.f64 (+.f64 1 x) -3/2))))
	32.5b	(fma.f64 (cbrt.f64 (/.f64 1 (+.f64 1 x))) (/.f64 -1 (pow.f64 (+.f64 1 x) 1/6)) (pow.f64 x -1/2))
	34.5b	(+.f64 (exp.f64 (*.f64 (log.f64 x) -1/2)) (/.f64 -1 (sqrt.f64 (+.f64 1 x))))
	31.1b	(/.f64 (fma.f64 -1 (pow.f64 (+.f64 1 x) -3/2) (pow.f64 x -3/2)) (+.f64 (/.f64 1 (+.f64 1 x)) (-.f64 (/.f64 1 x) (/.f64 -1 (sqrt.f64 (*.f64 x (+.f64 1 x)))))))
	33.7b	(fma.f64 (pow.f64 x -1/6) (cbrt.f64 (/.f64 1 x)) (neg.f64 (pow.f64 (+.f64 1 x) -1/2)))
	25.0b	(+.f64 (/.f64 1 (sqrt.f64 x)) (neg.f64 (pow.f64 (+.f64 1 x) -1/2)))
	21.5b	(-.f64 (/.f64 (/.f64 1 x) (+.f64 (pow.f64 x -1/2) (pow.f64 (+.f64 1 x) -1/2))) (/.f64 (/.f64 1 (+.f64 1 x)) (+.f64 (pow.f64 x -1/2) (pow.f64 (+.f64 1 x) -1/2))))
	24.9b	(+.f64 (pow.f64 x -1/2) (/.f64 -1 (sqrt.f64 (+.f64 1 x))))
	21.9b	(pow.f64 (cbrt.f64 (fma.f64 -1 (pow.f64 (+.f64 1 x) -1/2) (pow.f64 x -1/2))) 3)
	31.1b	(.f64 (fma.f64 -1 (pow.f64 (+.f64 1 x) -3/2) (pow.f64 x -3/2)) (/.f64 1 (-.f64 (+.f64 (/.f64 1 x) (/.f64 1 (+.f64 1 x))) (/.f64 -1 (sqrt.f64 (.f64 x (+.f64 1 x)))))))
	27.6b	(+.f64 (pow.f64 (pow.f64 x 1/4) -2) (/.f64 -1 (sqrt.f64 (+.f64 1 x))))
	33.6b	(+.f64 (*.f64 (/.f64 1 (cbrt.f64 x)) (pow.f64 x -1/6)) (/.f64 -1 (sqrt.f64 (+.f64 1 x))))

Compiler

Compiled 2902 to 2312 computations (20.3% saved)

localize10.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(*.f64 x (+.f64 1 x))
✓	0.0b	(.f64 (fma.f64 (sqrt.f64 x) -1 (sqrt.f64 (+.f64 1 x))) (pow.f64 (.f64 x (+.f64 1 x)) -1/2))
✓	2.9b	(fma.f64 (sqrt.f64 x) -1 (sqrt.f64 (+.f64 1 x)))
✓	16.5b	(pow.f64 (*.f64 x (+.f64 1 x)) -1/2)

series14.0ms (0.3%)

Counts

4 → 25

Calls

12 calls:

Time	Variable		Point	Expression
3.0ms	x	@	0	(fma.f64 (sqrt.f64 x) -1 (sqrt.f64 (+.f64 1 x)))
2.0ms	x	@	0	(.f64 (fma.f64 (sqrt.f64 x) -1 (sqrt.f64 (+.f64 1 x))) (pow.f64 (.f64 x (+.f64 1 x)) -1/2))
1.0ms	x	@	inf	(.f64 (fma.f64 (sqrt.f64 x) -1 (sqrt.f64 (+.f64 1 x))) (pow.f64 (.f64 x (+.f64 1 x)) -1/2))
1.0ms	x	@	-inf	(.f64 (fma.f64 (sqrt.f64 x) -1 (sqrt.f64 (+.f64 1 x))) (pow.f64 (.f64 x (+.f64 1 x)) -1/2))
1.0ms	x	@	-inf	(*.f64 x (+.f64 1 x))

rewrite71.0ms (1.4%)

Algorithm

1×	batch-egg-rewrite

Rules

524×	`log-prod_binary64`
395×	`pow-prod-down_binary64`
335×	`prod-diff_binary64`
294×	`pow2_binary64`
242×	`fma-def_binary64`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	12	53
1	250	53
2	2939	47

Stop Event

1×	node limit

Counts

4 → 138

Calls

Call 1

Inputs
(pow.f64 (*.f64 x (+.f64 1 x)) -1/2)
(fma.f64 (sqrt.f64 x) -1 (sqrt.f64 (+.f64 1 x)))
(.f64 (fma.f64 (sqrt.f64 x) -1 (sqrt.f64 (+.f64 1 x))) (pow.f64 (.f64 x (+.f64 1 x)) -1/2))
(*.f64 x (+.f64 1 x))

Outputs
((#(struct:change #<rule egg-rr> (2) ((x +.f64 0 (pow.f64 (fma.f64 x x x) -1/2))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (log.f64 (pow.f64 (cbrt.f64 (exp.f64 (pow.f64 (fma.f64 x x x) -1/2))) 2)) (log.f64 (cbrt.f64 (exp.f64 (pow.f64 (fma.f64 x x x) -1/2)))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (log.f64 (sqrt.f64 (exp.f64 (pow.f64 (fma.f64 x x x) -1/2)))) (log.f64 (sqrt.f64 (exp.f64 (pow.f64 (fma.f64 x x x) -1/2)))))))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (exp.f64 (log1p.f64 (pow.f64 (fma.f64 x x x) -1/2))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x .f64 1 (pow.f64 (fma.f64 x x x) -1/2))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (pow.f64 (fma.f64 x x x) -1/2) 1)))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (pow.f64 (fma.f64 x x x) -1/6) (cbrt.f64 (pow.f64 (fma.f64 x x x) -1)))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (cbrt.f64 (pow.f64 (fma.f64 x x x) -1)) (pow.f64 (fma.f64 x x x) -1/6))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (pow.f64 x -1/2) (pow.f64 (+.f64 x 1) -1/2))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (pow.f64 (+.f64 x 1) -1/2) (pow.f64 x -1/2))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (pow.f64 (fma.f64 x x x) -1/4) (pow.f64 (fma.f64 x x x) -1/4))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (pow.f64 (cbrt.f64 (fma.f64 x x x)) -1) (pow.f64 (fma.f64 x x x) -1/6))))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f64 (pow.f64 (fma.f64 x x x) -1))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (exp.f64 (pow.f64 (fma.f64 x x x) -1/2)))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (+.f64 1 (expm1.f64 (pow.f64 (fma.f64 x x x) -1/2))))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (pow.f64 (fma.f64 x x x) -3/2))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (pow.f64 (fma.f64 x x x) -1/2)))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (log.f64 (pow.f64 (fma.f64 x x x) -1/2)))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (.f64 (log.f64 (pow.f64 (fma.f64 x x x) -1/2)) 1))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (.f64 (.f64 2 (log.f64 (fma.f64 x x x))) -1/4))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (.f64 (log.f64 (pow.f64 (fma.f64 x x x) -3/2)) 1/3))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (.f64 (log.f64 (pow.f64 (fma.f64 x x x) -1/6)) 3))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (.f64 (*.f64 -1/4 (log.f64 (fma.f64 x x x))) 2))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (pow.f64 (fma.f64 x x x) -1/2)))))))
((#(struct:change #<rule egg-rr> (2) ((x +.f64 (sqrt.f64 (+.f64 x 1)) (.f64 (sqrt.f64 x) -1))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 0 (fma.f64 (sqrt.f64 x) -1 (sqrt.f64 (+.f64 x 1))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (.f64 (sqrt.f64 x) -1) (sqrt.f64 (+.f64 x 1)))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (.f64 (.f64 (sqrt.f64 x) -1) 1) (sqrt.f64 (+.f64 x 1)))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (log.f64 (pow.f64 (cbrt.f64 (exp.f64 (fma.f64 (sqrt.f64 x) -1 (sqrt.f64 (+.f64 x 1))))) 2)) (log.f64 (cbrt.f64 (exp.f64 (fma.f64 (sqrt.f64 x) -1 (sqrt.f64 (+.f64 x 1)))))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (log.f64 (sqrt.f64 (exp.f64 (fma.f64 (sqrt.f64 x) -1 (sqrt.f64 (+.f64 x 1)))))) (log.f64 (sqrt.f64 (exp.f64 (fma.f64 (sqrt.f64 x) -1 (sqrt.f64 (+.f64 x 1)))))))))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (exp.f64 (log1p.f64 (fma.f64 (sqrt.f64 x) -1 (sqrt.f64 (+.f64 x 1))))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x .f64 1 (fma.f64 (sqrt.f64 x) -1 (sqrt.f64 (+.f64 x 1))))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (fma.f64 (sqrt.f64 x) -1 (sqrt.f64 (+.f64 x 1))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (cbrt.f64 (fma.f64 (sqrt.f64 x) -1 (sqrt.f64 (+.f64 x 1)))) (cbrt.f64 (pow.f64 (fma.f64 (sqrt.f64 x) -1 (sqrt.f64 (+.f64 x 1))) 2)))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (cbrt.f64 (pow.f64 (fma.f64 (sqrt.f64 x) -1 (sqrt.f64 (+.f64 x 1))) 2)) (cbrt.f64 (fma.f64 (sqrt.f64 x) -1 (sqrt.f64 (+.f64 x 1)))))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (sqrt.f64 (fma.f64 (sqrt.f64 x) -1 (sqrt.f64 (+.f64 x 1)))) (sqrt.f64 (fma.f64 (sqrt.f64 x) -1 (sqrt.f64 (+.f64 x 1)))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (+.f64 (pow.f64 (.f64 (sqrt.f64 x) -1) 3) (pow.f64 (+.f64 x 1) 3/2)) (+.f64 (pow.f64 (.f64 (sqrt.f64 x) -1) 2) (-.f64 (+.f64 x 1) (.f64 (.f64 (sqrt.f64 x) -1) (sqrt.f64 (+.f64 x 1))))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (-.f64 (pow.f64 (.f64 (sqrt.f64 x) -1) 2) (+.f64 x 1)) (-.f64 (.f64 (sqrt.f64 x) -1) (sqrt.f64 (+.f64 x 1))))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (fma.f64 (sqrt.f64 x) -1 (sqrt.f64 (+.f64 x 1))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (fma.f64 (sqrt.f64 x) -1 (sqrt.f64 (+.f64 x 1))) 2) 1/2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (fma.f64 (sqrt.f64 x) -1 (sqrt.f64 (+.f64 x 1))) 3) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (cbrt.f64 (fma.f64 (sqrt.f64 x) -1 (sqrt.f64 (+.f64 x 1)))) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (sqrt.f64 (fma.f64 (sqrt.f64 x) -1 (sqrt.f64 (+.f64 x 1)))) 2)))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f64 (pow.f64 (fma.f64 (sqrt.f64 x) -1 (sqrt.f64 (+.f64 x 1))) 2))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (exp.f64 (fma.f64 (sqrt.f64 x) -1 (sqrt.f64 (+.f64 x 1)))))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (+.f64 1 (expm1.f64 (fma.f64 (sqrt.f64 x) -1 (sqrt.f64 (+.f64 x 1))))))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (.f64 (exp.f64 (sqrt.f64 (+.f64 x 1))) (exp.f64 (.f64 (sqrt.f64 x) -1))))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (.f64 (+.f64 1 (expm1.f64 (sqrt.f64 (+.f64 x 1)))) (exp.f64 (.f64 (sqrt.f64 x) -1))))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (.f64 (exp.f64 (.f64 (sqrt.f64 x) -1)) (+.f64 1 (expm1.f64 (sqrt.f64 (+.f64 x 1))))))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (pow.f64 (fma.f64 (sqrt.f64 x) -1 (sqrt.f64 (+.f64 x 1))) 3))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (fma.f64 (sqrt.f64 x) -1 (sqrt.f64 (+.f64 x 1)))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (log.f64 (fma.f64 (sqrt.f64 x) -1 (sqrt.f64 (+.f64 x 1)))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (.f64 (log.f64 (fma.f64 (sqrt.f64 x) -1 (sqrt.f64 (+.f64 x 1)))) 1))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (.f64 (.f64 3 (log.f64 (fma.f64 (sqrt.f64 x) -1 (sqrt.f64 (+.f64 x 1))))) 1/3))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (.f64 (log.f64 (cbrt.f64 (fma.f64 (sqrt.f64 x) -1 (sqrt.f64 (+.f64 x 1))))) 3))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (.f64 (log.f64 (sqrt.f64 (fma.f64 (sqrt.f64 x) -1 (sqrt.f64 (+.f64 x 1))))) 2))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (fma.f64 (sqrt.f64 x) -1 (sqrt.f64 (+.f64 x 1)))))))))
((#(struct:change #<rule egg-rr> (2) ((x +.f64 0 (.f64 (pow.f64 (fma.f64 x x x) -1/2) (fma.f64 (sqrt.f64 x) -1 (sqrt.f64 (+.f64 x 1)))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (.f64 (.f64 (sqrt.f64 x) -1) (pow.f64 (fma.f64 x x x) -1/2)) (.f64 (sqrt.f64 (+.f64 x 1)) (pow.f64 (fma.f64 x x x) -1/2)))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (.f64 (pow.f64 (fma.f64 x x x) -1/2) (.f64 (sqrt.f64 x) -1)) (.f64 (pow.f64 (fma.f64 x x x) -1/2) (sqrt.f64 (+.f64 x 1))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (log.f64 (pow.f64 (cbrt.f64 (pow.f64 (exp.f64 (fma.f64 (sqrt.f64 x) -1 (sqrt.f64 (+.f64 x 1)))) (pow.f64 (fma.f64 x x x) -1/2))) 2)) (log.f64 (cbrt.f64 (pow.f64 (exp.f64 (fma.f64 (sqrt.f64 x) -1 (sqrt.f64 (+.f64 x 1)))) (pow.f64 (fma.f64 x x x) -1/2)))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (log.f64 (sqrt.f64 (pow.f64 (exp.f64 (fma.f64 (sqrt.f64 x) -1 (sqrt.f64 (+.f64 x 1)))) (pow.f64 (fma.f64 x x x) -1/2)))) (log.f64 (sqrt.f64 (pow.f64 (exp.f64 (fma.f64 (sqrt.f64 x) -1 (sqrt.f64 (+.f64 x 1)))) (pow.f64 (fma.f64 x x x) -1/2)))))))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (exp.f64 (log1p.f64 (.f64 (pow.f64 (fma.f64 x x x) -1/2) (fma.f64 (sqrt.f64 x) -1 (sqrt.f64 (+.f64 x 1)))))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (.f64 (pow.f64 (fma.f64 x x x) -1/2) (fma.f64 (sqrt.f64 x) -1 (sqrt.f64 (+.f64 x 1)))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (.f64 (pow.f64 (fma.f64 (sqrt.f64 x) -1 (sqrt.f64 (+.f64 x 1))) 2) (pow.f64 (fma.f64 x x x) -1)) 1/2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (.f64 (pow.f64 (fma.f64 (sqrt.f64 x) -1 (sqrt.f64 (+.f64 x 1))) 3) (pow.f64 (fma.f64 x x x) -3/2)) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (cbrt.f64 (.f64 (pow.f64 (fma.f64 x x x) -1/2) (fma.f64 (sqrt.f64 x) -1 (sqrt.f64 (+.f64 x 1))))) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (.f64 (sqrt.f64 (fma.f64 (sqrt.f64 x) -1 (sqrt.f64 (+.f64 x 1)))) (pow.f64 (fma.f64 x x x) -1/4)) 2)))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f64 (.f64 (pow.f64 (fma.f64 (sqrt.f64 x) -1 (sqrt.f64 (+.f64 x 1))) 2) (pow.f64 (fma.f64 x x x) -1)))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (pow.f64 (exp.f64 (fma.f64 (sqrt.f64 x) -1 (sqrt.f64 (+.f64 x 1)))) (pow.f64 (fma.f64 x x x) -1/2)))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (+.f64 1 (expm1.f64 (.f64 (pow.f64 (fma.f64 x x x) -1/2) (fma.f64 (sqrt.f64 x) -1 (sqrt.f64 (+.f64 x 1)))))))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (.f64 (pow.f64 (fma.f64 (sqrt.f64 x) -1 (sqrt.f64 (+.f64 x 1))) 3) (pow.f64 (fma.f64 x x x) -3/2)))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (.f64 (pow.f64 (fma.f64 x x x) -1/2) (fma.f64 (sqrt.f64 x) -1 (sqrt.f64 (+.f64 x 1))))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (fma.f64 -1/2 (log.f64 (fma.f64 x x x)) (log.f64 (fma.f64 (sqrt.f64 x) -1 (sqrt.f64 (+.f64 x 1))))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (.f64 (fma.f64 -1/2 (log.f64 (fma.f64 x x x)) (log.f64 (fma.f64 (sqrt.f64 x) -1 (sqrt.f64 (+.f64 x 1))))) 1))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (.f64 (.f64 3 (fma.f64 -1/2 (log.f64 (fma.f64 x x x)) (log.f64 (fma.f64 (sqrt.f64 x) -1 (sqrt.f64 (+.f64 x 1)))))) 1/3))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (.f64 (log.f64 (cbrt.f64 (.f64 (pow.f64 (fma.f64 x x x) -1/2) (fma.f64 (sqrt.f64 x) -1 (sqrt.f64 (+.f64 x 1)))))) 3))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (.f64 (log.f64 (.f64 (sqrt.f64 (fma.f64 (sqrt.f64 x) -1 (sqrt.f64 (+.f64 x 1)))) (pow.f64 (fma.f64 x x x) -1/4))) 2))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (pow.f64 (fma.f64 x x x) -1/2) (.f64 (sqrt.f64 x) -1) (.f64 (pow.f64 (fma.f64 x x x) -1/2) (sqrt.f64 (+.f64 x 1))))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (.f64 (sqrt.f64 x) -1) (pow.f64 (fma.f64 x x x) -1/2) (.f64 (sqrt.f64 (+.f64 x 1)) (pow.f64 (fma.f64 x x x) -1/2)))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (*.f64 (pow.f64 (fma.f64 x x x) -1/2) (fma.f64 (sqrt.f64 x) -1 (sqrt.f64 (+.f64 x 1))))))))))
((#(struct:change #<rule egg-rr> (2) ((x +.f64 x (.f64 x x))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 x (.f64 (.f64 x x) 1))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 0 (fma.f64 x x x))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (.f64 x x) x)))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (log.f64 (pow.f64 (cbrt.f64 (exp.f64 (fma.f64 x x x))) 2)) (log.f64 (cbrt.f64 (exp.f64 (fma.f64 x x x)))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (log.f64 (sqrt.f64 (exp.f64 (fma.f64 x x x)))) (log.f64 (sqrt.f64 (exp.f64 (fma.f64 x x x)))))))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (exp.f64 (log1p.f64 (fma.f64 x x x))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (+.f64 (pow.f64 x 3) (pow.f64 x 6)) (fma.f64 x x (-.f64 (pow.f64 x 4) (pow.f64 x 3))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (.f64 (+.f64 1 (pow.f64 x 3)) x) (fma.f64 x (-.f64 x 1) 1))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (.f64 (-.f64 1 (.f64 x x)) x) (-.f64 1 x))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (.f64 x (+.f64 1 (pow.f64 x 3))) (fma.f64 x (-.f64 x 1) 1))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (.f64 x (-.f64 1 (.f64 x x))) (-.f64 1 x))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (-.f64 (.f64 x x) (pow.f64 x 4)) (-.f64 x (.f64 x x)))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (fma.f64 x x x) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (fma.f64 x x x) 2) 1/2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (fma.f64 x x x) 3) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (cbrt.f64 (fma.f64 x x x)) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (hypot.f64 x (sqrt.f64 x)) 2)))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f64 (pow.f64 (fma.f64 x x x) 2))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (exp.f64 (fma.f64 x x x)))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (+.f64 1 (expm1.f64 (fma.f64 x x x))))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (.f64 (+.f64 1 (expm1.f64 x)) (exp.f64 (.f64 x x))))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (.f64 (exp.f64 (.f64 x x)) (exp.f64 x)))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (.f64 (exp.f64 (.f64 x x)) (+.f64 1 (expm1.f64 x))))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (pow.f64 (fma.f64 x x x) 3))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (fma.f64 x x x)))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (log.f64 (fma.f64 x x x)))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (.f64 (log.f64 (fma.f64 x x x)) 1))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (.f64 (.f64 3 (log.f64 (fma.f64 x x x))) 1/3))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (.f64 (log.f64 (cbrt.f64 (fma.f64 x x x))) 3))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (.f64 (log.f64 (hypot.f64 x (sqrt.f64 x))) 2))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 x x x)))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 x 1 (.f64 x x))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 x 1 (.f64 (.f64 x x) 1))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 1 x (.f64 x x))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 1 x (.f64 (.f64 x x) 1))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 1 (.f64 x x) x)))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (sqrt.f64 x) (sqrt.f64 x) (.f64 x x))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (sqrt.f64 x) (sqrt.f64 x) (.f64 (.f64 x x) 1))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (sqrt.f64 x) (pow.f64 x 3/2) x)))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (pow.f64 x 3/2) (sqrt.f64 x) x)))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (cbrt.f64 x) (cbrt.f64 (.f64 x x)) (.f64 x x))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (cbrt.f64 x) (cbrt.f64 (.f64 x x)) (.f64 (.f64 x x) 1))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (cbrt.f64 (.f64 x x)) (cbrt.f64 x) (.f64 x x))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (cbrt.f64 (.f64 x x)) (cbrt.f64 x) (.f64 (.f64 x x) 1))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (cbrt.f64 (.f64 x x)) (.f64 x (cbrt.f64 x)) x)))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (cbrt.f64 (.f64 x x)) (.f64 (cbrt.f64 x) 1) (.f64 x x))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (cbrt.f64 (.f64 x x)) (.f64 (cbrt.f64 x) 1) (.f64 (.f64 x x) 1))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (pow.f64 x 1/4) (pow.f64 x 3/4) (.f64 x x))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (pow.f64 x 1/4) (pow.f64 x 3/4) (.f64 (.f64 x x) 1))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (.f64 x (cbrt.f64 x)) (cbrt.f64 (.f64 x x)) x)))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (pow.f64 x 3/4) (pow.f64 x 1/4) (.f64 x x))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (pow.f64 x 3/4) (pow.f64 x 1/4) (.f64 (.f64 x x) 1))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (pow.f64 x 5/6) (pow.f64 x 1/6) (.f64 x x))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (pow.f64 x 5/6) (pow.f64 x 1/6) (.f64 (*.f64 x x) 1))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (pow.f64 (cbrt.f64 x) 5) (cbrt.f64 x) x)))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (fma.f64 x x x)))))))

simplify33.0ms (0.6%)

Algorithm

1×	egg-herbie

Rules

712×	`times-frac_binary64`
552×	`fma-def_binary64`
452×	`associate-l_binary64`
371×	`associate-*r/_binary64`
365×	`associate-*l/_binary64`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	45	282
1	119	264
2	285	258
3	697	258
4	2024	258

Stop Event

1×	node limit

Counts

163 → 164

Calls

Call 1

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

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

prune670.0ms (13%)

Pruning

9 alts after pruning (9 fresh and 0 done)

	Pruned	Kept	Total
New	160	4	164
Fresh	10	5	15
Picked	1	0	1
Done	0	0	0
Total	171	9	180

Error

20.2b

Counts

180 → 9

Alt Table

Status	Error	Program
▶	20.8b	(.f64 (/.f64 (-.f64 (pow.f64 (.f64 (sqrt.f64 x) -1) 2) (+.f64 x 1)) (-.f64 (.f64 (sqrt.f64 x) -1) (sqrt.f64 (+.f64 x 1)))) (pow.f64 (.f64 x (+.f64 1 x)) -1/2))
	21.3b	(fma.f64 (.f64 (sqrt.f64 x) -1) (pow.f64 (fma.f64 x x x) -1/2) (.f64 (sqrt.f64 (+.f64 x 1)) (pow.f64 (fma.f64 x x x) -1/2)))
	21.5b	(-.f64 (/.f64 (/.f64 1 x) (+.f64 (pow.f64 x -1/2) (pow.f64 (+.f64 1 x) -1/2))) (/.f64 (/.f64 1 (+.f64 1 x)) (+.f64 (pow.f64 x -1/2) (pow.f64 (+.f64 1 x) -1/2))))
	21.9b	(pow.f64 (cbrt.f64 (fma.f64 -1 (pow.f64 (+.f64 1 x) -1/2) (pow.f64 x -1/2))) 3)
	21.5b	(*.f64 (-.f64 (/.f64 1 x) (/.f64 1 (+.f64 1 x))) (/.f64 1 (+.f64 (pow.f64 x -1/2) (pow.f64 (+.f64 1 x) -1/2))))
	31.1b	(.f64 (fma.f64 -1 (pow.f64 (+.f64 1 x) -3/2) (pow.f64 x -3/2)) (/.f64 1 (-.f64 (+.f64 (/.f64 1 x) (/.f64 1 (+.f64 1 x))) (/.f64 -1 (sqrt.f64 (.f64 x (+.f64 1 x)))))))
	32.3b	(fma.f64 (pow.f64 x -1/4) (pow.f64 x -1/4) (neg.f64 (pow.f64 (+.f64 1 x) -1/2)))
	32.3b	(.f64 (/.f64 (+.f64 (pow.f64 (.f64 (sqrt.f64 x) -1) 3) (pow.f64 (+.f64 x 1) 3/2)) (+.f64 (pow.f64 (.f64 (sqrt.f64 x) -1) 2) (-.f64 (+.f64 x 1) (.f64 (.f64 (sqrt.f64 x) -1) (sqrt.f64 (+.f64 x 1)))))) (pow.f64 (.f64 x (+.f64 1 x)) -1/2))
	22.8b	(.f64 1 (pow.f64 (.f64 x (+.f64 1 x)) -1/2))

Compiler

Compiled 3821 to 2507 computations (34.4% saved)

localize18.0ms (0.3%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.1b	(.f64 (/.f64 (-.f64 (pow.f64 (.f64 (sqrt.f64 x) -1) 2) (+.f64 x 1)) (-.f64 (.f64 (sqrt.f64 x) -1) (sqrt.f64 (+.f64 x 1)))) (pow.f64 (.f64 x (+.f64 1 x)) -1/2))
✓	0.5b	(pow.f64 (*.f64 (sqrt.f64 x) -1) 2)
	16.5b	(pow.f64 (*.f64 x (+.f64 1 x)) -1/2)
✓	17.8b	(-.f64 (pow.f64 (*.f64 (sqrt.f64 x) -1) 2) (+.f64 x 1))

series19.0ms (0.4%)

Counts

3 → 4

Calls

9 calls:

Time	Variable		Point	Expression
5.0ms	x	@	-inf	(.f64 (/.f64 (-.f64 (pow.f64 (.f64 (sqrt.f64 x) -1) 2) (+.f64 x 1)) (-.f64 (.f64 (sqrt.f64 x) -1) (sqrt.f64 (+.f64 x 1)))) (pow.f64 (.f64 x (+.f64 1 x)) -1/2))
5.0ms	x	@	0	(.f64 (/.f64 (-.f64 (pow.f64 (.f64 (sqrt.f64 x) -1) 2) (+.f64 x 1)) (-.f64 (.f64 (sqrt.f64 x) -1) (sqrt.f64 (+.f64 x 1)))) (pow.f64 (.f64 x (+.f64 1 x)) -1/2))
5.0ms	x	@	inf	(.f64 (/.f64 (-.f64 (pow.f64 (.f64 (sqrt.f64 x) -1) 2) (+.f64 x 1)) (-.f64 (.f64 (sqrt.f64 x) -1) (sqrt.f64 (+.f64 x 1)))) (pow.f64 (.f64 x (+.f64 1 x)) -1/2))
1.0ms	x	@	0	(-.f64 (pow.f64 (*.f64 (sqrt.f64 x) -1) 2) (+.f64 x 1))
1.0ms	x	@	inf	(-.f64 (pow.f64 (*.f64 (sqrt.f64 x) -1) 2) (+.f64 x 1))

rewrite85.0ms (1.7%)

Algorithm

1×	batch-egg-rewrite

Rules

800×	`fma-def_binary64`
454×	`fma-neg_binary64`
285×	`log1p-udef_binary64`
284×	`expm1-udef_binary64`
198×	`add-sqr-sqrt_binary64`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	18	67
1	420	31
2	5733	29

Stop Event

1×	node limit

Counts

3 → 159

Calls

Call 1

Inputs

(-.f64 (pow.f64 (*.f64 (sqrt.f64 x) -1) 2) (+.f64 x 1))

(pow.f64 (*.f64 (sqrt.f64 x) -1) 2)

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

Outputs

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

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

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

simplify12.0ms (0.2%)

Algorithm

1×	egg-herbie

Rules

9×	`sub-neg_binary64`
4×	`+-commutative_binary64`
4×	`fma-def_binary64`
3×	`associate-+l-_binary64`
2×	`*-commutative_binary64`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	6	12
1	13	12
2	18	11
3	26	11
4	36	11
5	42	11
6	51	11
7	62	11
8	65	11

Stop Event

1×

saturated

Counts

163 → 163

Calls

Call 1

Inputs
-1
(-.f64 (*.f64 -1 x) 1)
(*.f64 -1 x)
(*.f64 -1 x)

Outputs
-1
(-.f64 (*.f64 -1 x) 1)
(fma.f64 -1 x -1)
(-.f64 -1 x)
(*.f64 -1 x)
(neg.f64 x)
(*.f64 -1 x)
(neg.f64 x)

prune837.0ms (16.2%)

Pruning

4 alts after pruning (4 fresh and 0 done)

	Pruned	Kept	Total
New	205	3	208
Fresh	7	1	8
Picked	1	0	1
Done	0	0	0
Total	213	4	217

Error

6.3b

Counts

217 → 4

Alt Table

Status	Error	Program
	21.3b	(fma.f64 (.f64 (sqrt.f64 x) -1) (pow.f64 (fma.f64 x x x) -1/2) (.f64 (sqrt.f64 (+.f64 x 1)) (pow.f64 (fma.f64 x x x) -1/2)))
▶	6.4b	(.f64 (/.f64 -1 (-.f64 (.f64 (sqrt.f64 x) -1) (sqrt.f64 (+.f64 x 1)))) (pow.f64 (*.f64 x (+.f64 1 x)) -1/2))
	26.3b	(.f64 (/.f64 (-.f64 (pow.f64 (.f64 (sqrt.f64 x) -1) 2) (+.f64 x 1)) (-.f64 (.f64 (sqrt.f64 x) -1) (sqrt.f64 (+.f64 x 1)))) (.f64 (pow.f64 (+.f64 x 1) -1/2) (pow.f64 x -1/2)))
	20.1b	(/.f64 (neg.f64 (*.f64 (-.f64 (-.f64 x 1) x) (pow.f64 (fma.f64 x x x) -1/2))) (-.f64 (sqrt.f64 x) (neg.f64 (sqrt.f64 (+.f64 x 1)))))

Compiler

Compiled 6595 to 4518 computations (31.5% saved)

localize12.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(-.f64 (*.f64 (sqrt.f64 x) -1) (sqrt.f64 (+.f64 x 1)))
✓	0.1b	(.f64 (/.f64 -1 (-.f64 (.f64 (sqrt.f64 x) -1) (sqrt.f64 (+.f64 x 1)))) (pow.f64 (*.f64 x (+.f64 1 x)) -1/2))
✓	0.2b	(/.f64 -1 (-.f64 (*.f64 (sqrt.f64 x) -1) (sqrt.f64 (+.f64 x 1))))
	16.5b	(pow.f64 (*.f64 x (+.f64 1 x)) -1/2)

series15.0ms (0.3%)

Counts

3 → 2

Calls

9 calls:

Time	Variable		Point	Expression
4.0ms	x	@	inf	(.f64 (/.f64 -1 (-.f64 (.f64 (sqrt.f64 x) -1) (sqrt.f64 (+.f64 x 1)))) (pow.f64 (*.f64 x (+.f64 1 x)) -1/2))
3.0ms	x	@	-inf	(.f64 (/.f64 -1 (-.f64 (.f64 (sqrt.f64 x) -1) (sqrt.f64 (+.f64 x 1)))) (pow.f64 (*.f64 x (+.f64 1 x)) -1/2))
2.0ms	x	@	0	(.f64 (/.f64 -1 (-.f64 (.f64 (sqrt.f64 x) -1) (sqrt.f64 (+.f64 x 1)))) (pow.f64 (*.f64 x (+.f64 1 x)) -1/2))
2.0ms	x	@	inf	(/.f64 -1 (-.f64 (*.f64 (sqrt.f64 x) -1) (sqrt.f64 (+.f64 x 1))))
1.0ms	x	@	-inf	(/.f64 -1 (-.f64 (*.f64 (sqrt.f64 x) -1) (sqrt.f64 (+.f64 x 1))))

rewrite73.0ms (1.4%)

Algorithm

1×	batch-egg-rewrite

Rules

665×	`log-prod_binary64`
621×	`fma-def_binary64`
332×	`fma-neg_binary64`
237×	`log1p-udef_binary64`
236×	`expm1-udef_binary64`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	15	60
1	339	50
2	4430	48

Stop Event

1×	node limit

Counts

3 → 161

Calls

Call 1

Inputs

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

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

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

Outputs

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

simplify9.0ms (0.2%)

Algorithm

1×	egg-herbie

Rules

1×	`1-exp_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	2	2
1	5	2

Stop Event

1×

saturated

Counts

163 → 163

Calls

Call 1

Inputs
1
-1

Outputs
1
-1

prune567.0ms (11%)

Pruning

8 alts after pruning (8 fresh and 0 done)

	Pruned	Kept	Total
New	201	7	208
Fresh	2	1	3
Picked	1	0	1
Done	0	0	0
Total	204	8	212

Error

0.0b

Counts

212 → 8

Alt Table

Status	Error	Program
	29.4b	(.f64 (/.f64 -1 (-.f64 (.f64 (sqrt.f64 x) -1) (sqrt.f64 (+.f64 x 1)))) (+.f64 (/.f64 1 x) (/.f64 -1/2 (*.f64 x x))))
	21.3b	(fma.f64 (.f64 (sqrt.f64 x) -1) (pow.f64 (fma.f64 x x x) -1/2) (.f64 (sqrt.f64 (+.f64 x 1)) (pow.f64 (fma.f64 x x x) -1/2)))
	21.4b	(.f64 (/.f64 -1 (-.f64 (.f64 (sqrt.f64 x) -1) (sqrt.f64 (+.f64 x 1)))) (cbrt.f64 (pow.f64 (fma.f64 x x x) -3/2)))
	0.2b	(.f64 (/.f64 -1 (-.f64 (.f64 (sqrt.f64 x) -1) (sqrt.f64 (+.f64 x 1)))) (*.f64 (pow.f64 (+.f64 x 1) -1/2) (pow.f64 x -1/2)))
	6.3b	(/.f64 (pow.f64 (fma.f64 x x x) -1/2) (-.f64 (sqrt.f64 x) (neg.f64 (sqrt.f64 (+.f64 x 1)))))
	6.4b	(.f64 (/.f64 -1 (fma.f64 (.f64 -1 (cbrt.f64 x)) (cbrt.f64 (sqrt.f64 x)) (neg.f64 (sqrt.f64 (+.f64 x 1))))) (pow.f64 (*.f64 x (+.f64 1 x)) -1/2))
	6.6b	(pow.f64 (sqrt.f64 (/.f64 (pow.f64 (fma.f64 x x x) -1/2) (-.f64 (sqrt.f64 x) (neg.f64 (sqrt.f64 (+.f64 x 1)))))) 2)
	6.4b	(.f64 (/.f64 -1 (fma.f64 (pow.f64 x 1/4) (.f64 (pow.f64 x 1/4) -1) (neg.f64 (sqrt.f64 (+.f64 x 1))))) (pow.f64 (*.f64 x (+.f64 1 x)) -1/2))

Compiler

Compiled 5330 to 3839 computations (28% saved)

regimes38.0ms (0.7%)

Accuracy

Total -62.8b remaining (-28641.3%)

Threshold costs -62.8b (-28641.3%)

Counts

32 → 1

Calls

Call 1

Inputs
(.f64 (/.f64 -1 (-.f64 (.f64 (sqrt.f64 x) -1) (sqrt.f64 (+.f64 x 1)))) (+.f64 (/.f64 1 x) (/.f64 -1/2 (*.f64 x x))))
(.f64 (/.f64 -1 (-.f64 (.f64 (sqrt.f64 x) -1) (sqrt.f64 (+.f64 x 1)))) (cbrt.f64 (pow.f64 (fma.f64 x x x) -3/2)))
(.f64 (/.f64 -1 (-.f64 (.f64 (sqrt.f64 x) -1) (sqrt.f64 (+.f64 x 1)))) (*.f64 (pow.f64 (+.f64 x 1) -1/2) (pow.f64 x -1/2)))
(/.f64 (pow.f64 (fma.f64 x x x) -1/2) (-.f64 (sqrt.f64 x) (neg.f64 (sqrt.f64 (+.f64 x 1)))))
(.f64 (/.f64 -1 (fma.f64 (.f64 -1 (cbrt.f64 x)) (cbrt.f64 (sqrt.f64 x)) (neg.f64 (sqrt.f64 (+.f64 x 1))))) (pow.f64 (*.f64 x (+.f64 1 x)) -1/2))
(pow.f64 (sqrt.f64 (/.f64 (pow.f64 (fma.f64 x x x) -1/2) (-.f64 (sqrt.f64 x) (neg.f64 (sqrt.f64 (+.f64 x 1)))))) 2)
(.f64 (/.f64 -1 (fma.f64 (pow.f64 x 1/4) (.f64 (pow.f64 x 1/4) -1) (neg.f64 (sqrt.f64 (+.f64 x 1))))) (pow.f64 (*.f64 x (+.f64 1 x)) -1/2))
(.f64 (/.f64 -1 (-.f64 (.f64 (sqrt.f64 x) -1) (sqrt.f64 (+.f64 x 1)))) (pow.f64 (*.f64 x (+.f64 1 x)) -1/2))
(.f64 (/.f64 (-.f64 (pow.f64 (.f64 (sqrt.f64 x) -1) 2) (+.f64 x 1)) (-.f64 (.f64 (sqrt.f64 x) -1) (sqrt.f64 (+.f64 x 1)))) (.f64 (pow.f64 (+.f64 x 1) -1/2) (pow.f64 x -1/2)))
(/.f64 (neg.f64 (*.f64 (-.f64 (-.f64 x 1) x) (pow.f64 (fma.f64 x x x) -1/2))) (-.f64 (sqrt.f64 x) (neg.f64 (sqrt.f64 (+.f64 x 1)))))
(.f64 (/.f64 (-.f64 (pow.f64 (.f64 (sqrt.f64 x) -1) 2) (+.f64 x 1)) (-.f64 (.f64 (sqrt.f64 x) -1) (sqrt.f64 (+.f64 x 1)))) (pow.f64 (.f64 x (+.f64 1 x)) -1/2))
(fma.f64 (.f64 (sqrt.f64 x) -1) (pow.f64 (fma.f64 x x x) -1/2) (.f64 (sqrt.f64 (+.f64 x 1)) (pow.f64 (fma.f64 x x x) -1/2)))
(.f64 (/.f64 (+.f64 (pow.f64 (.f64 (sqrt.f64 x) -1) 3) (pow.f64 (+.f64 x 1) 3/2)) (+.f64 (pow.f64 (.f64 (sqrt.f64 x) -1) 2) (-.f64 (+.f64 x 1) (.f64 (.f64 (sqrt.f64 x) -1) (sqrt.f64 (+.f64 x 1)))))) (pow.f64 (.f64 x (+.f64 1 x)) -1/2))
(.f64 1 (pow.f64 (.f64 x (+.f64 1 x)) -1/2))
(*.f64 (-.f64 (/.f64 1 x) (/.f64 1 (+.f64 1 x))) (/.f64 1 (+.f64 (pow.f64 x -1/2) (pow.f64 (+.f64 1 x) -1/2))))
(+.f64 (pow.f64 (cbrt.f64 x) -3/2) (/.f64 -1 (sqrt.f64 (+.f64 1 x))))
(.f64 (fma.f64 (sqrt.f64 x) -1 (sqrt.f64 (+.f64 1 x))) (pow.f64 (.f64 x (+.f64 1 x)) -1/2))
(fma.f64 (pow.f64 x -1/4) (pow.f64 x -1/4) (neg.f64 (pow.f64 (+.f64 1 x) -1/2)))
(+.f64 (/.f64 1 (sqrt.f64 x)) (cbrt.f64 (*.f64 -1 (pow.f64 (+.f64 1 x) -3/2))))
(fma.f64 (cbrt.f64 (/.f64 1 (+.f64 1 x))) (/.f64 -1 (pow.f64 (+.f64 1 x) 1/6)) (pow.f64 x -1/2))
(+.f64 (exp.f64 (*.f64 (log.f64 x) -1/2)) (/.f64 -1 (sqrt.f64 (+.f64 1 x))))
(/.f64 (fma.f64 -1 (pow.f64 (+.f64 1 x) -3/2) (pow.f64 x -3/2)) (+.f64 (/.f64 1 (+.f64 1 x)) (-.f64 (/.f64 1 x) (/.f64 -1 (sqrt.f64 (*.f64 x (+.f64 1 x)))))))
(fma.f64 (pow.f64 x -1/6) (cbrt.f64 (/.f64 1 x)) (neg.f64 (pow.f64 (+.f64 1 x) -1/2)))
(+.f64 (/.f64 1 (sqrt.f64 x)) (neg.f64 (pow.f64 (+.f64 1 x) -1/2)))
(-.f64 (/.f64 (/.f64 1 x) (+.f64 (pow.f64 x -1/2) (pow.f64 (+.f64 1 x) -1/2))) (/.f64 (/.f64 1 (+.f64 1 x)) (+.f64 (pow.f64 x -1/2) (pow.f64 (+.f64 1 x) -1/2))))
(+.f64 (pow.f64 x -1/2) (/.f64 -1 (sqrt.f64 (+.f64 1 x))))
(pow.f64 (cbrt.f64 (fma.f64 -1 (pow.f64 (+.f64 1 x) -1/2) (pow.f64 x -1/2))) 3)
(.f64 (fma.f64 -1 (pow.f64 (+.f64 1 x) -3/2) (pow.f64 x -3/2)) (/.f64 1 (-.f64 (+.f64 (/.f64 1 x) (/.f64 1 (+.f64 1 x))) (/.f64 -1 (sqrt.f64 (.f64 x (+.f64 1 x)))))))
(+.f64 (pow.f64 (pow.f64 x 1/4) -2) (/.f64 -1 (sqrt.f64 (+.f64 1 x))))
(+.f64 (*.f64 (/.f64 1 (cbrt.f64 x)) (pow.f64 x -1/6)) (/.f64 -1 (sqrt.f64 (+.f64 1 x))))
(+.f64 (/.f64 1 (sqrt.f64 x)) (/.f64 -1 (sqrt.f64 (+.f64 1 x))))
(-.f64 (/.f64 1 (sqrt.f64 x)) (/.f64 1 (sqrt.f64 (+.f64 x 1))))

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

Results

15.0ms	0.2b	`x`
6.0ms	0.2b	`(-.f64 (/.f64 1 (sqrt.f64 x)) (/.f64 1 (sqrt.f64 (+.f64 x 1))))`

Compiler

Compiled 616 to 455 computations (26.1% saved)

simplify3.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

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

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	15	32
1	23	31
2	27	31
3	35	31
4	41	31
5	44	31
6	45	31

Stop Event

1×

saturated

Calls

Call 1

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

Outputs

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

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

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

end21.0ms (0.4%)

Stop Event

1×

fuel

Compiler

Compiled 42 to 34 computations (19% saved)

Iter	Nodes	Cost
0	9	17
1	14	17
2	20	17
3	28	17
4	38	17
5	56	17
6	93	17
7	127	17
8	174	17
9	210	17
10	236	17
11	238	17
0	1	1

Iter	Nodes	Cost
0	9	17
1	14	17
2	20	17
3	28	17
4	38	17
5	56	17
6	93	17
7	127	17
8	174	17
9	210	17
10	236	17
11	238	17

Iter	Nodes	Cost
0	9	17
1	14	17
2	20	17
3	28	17
4	38	17
5	56	17
6	93	17
7	127	17
8	174	17
9	210	17
10	236	17
11	238	17
0	1	1

Iter	Nodes	Cost
0	9	17
1	14	17
2	20	17
3	28	17
4	38	17
5	56	17
6	93	17
7	127	17
8	174	17
9	210	17
10	236	17
11	238	17

Details

analyze0.0ms (0%)

sample2.1s (40.6%)

preprocess38.0ms (0.7%)

simplify10.0ms (0.2%)

prune5.0ms (0.1%)

localize7.0ms (0.1%)

series7.0ms (0.1%)

rewrite98.0ms (1.9%)

simplify45.0ms (0.9%)

prune347.0ms (6.7%)

localize10.0ms (0.2%)

series14.0ms (0.3%)

rewrite71.0ms (1.4%)

simplify33.0ms (0.6%)

prune670.0ms (13%)

localize18.0ms (0.3%)

series19.0ms (0.4%)

rewrite85.0ms (1.7%)

simplify12.0ms (0.2%)

prune837.0ms (16.2%)

localize12.0ms (0.2%)

series15.0ms (0.3%)

rewrite73.0ms (1.4%)

simplify9.0ms (0.2%)

prune567.0ms (11%)

regimes38.0ms (0.7%)

simplify3.0ms (0.1%)

end21.0ms (0.4%)

Profiling

Iter	Nodes	Cost
0	9	17
1	14	17
2	20	17
3	28	17
4	38	17
5	56	17
6	93	17
7	127	17
8	174	17
9	210	17
10	236	17
11	238	17
0	1	1

Iter	Nodes	Cost
0	9	17
1	14	17
2	20	17
3	28	17
4	38	17
5	56	17
6	93	17
7	127	17
8	174	17
9	210	17
10	236	17
11	238	17