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)

sample1.7s (53.1%)

Results

888.0ms	2301×	body	1024	valid
463.0ms	4381×	body	128	valid
284.0ms	1046×	body	512	valid
100.0ms	528×	body	256	valid

preprocess17.0ms (0.5%)

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)

simplify11.0ms (0.3%)

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))))

eval1.0ms (0%)

Compiler: Compiled 23 to 18 computations (21.7% saved)

prune2.0ms (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

Click to see full alt table

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

Compiler

Compiled 24 to 20 computations (16.7% saved)

localize7.0ms (0.2%)

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 (0.2%)

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)))

rewrite54.0ms (1.6%)

Algorithm

1×	batch-egg-rewrite

Rules

443×	`fma-def_binary64`
205×	`fma-neg_binary64`
181×	`log-div_binary64`
181×	`expm1-udef_binary64`
181×	`log1p-udef_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 → 113

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

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

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

simplify23.0ms (0.7%)

Algorithm

1×	egg-herbie

Rules

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

Stop Event

1×	node limit

Counts

117 → 120

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)

eval46.0ms (1.4%)

Compiler: Compiled 1889 to 1469 computations (22.2% saved)

prune169.0ms (5.1%)

Pruning

14 alts after pruning (14 fresh and 0 done)

	Pruned	Kept	Total
New	106	14	120
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	107	14	121

Error

20.9b

Counts

121 → 14

Alt Table

Click to see full alt table

Status	Error	Program
	32.0b	(+.f64 (/.f64 1 (sqrt.f64 x)) (cbrt.f64 (/.f64 -1 (pow.f64 (+.f64 1 x) 3/2))))
	21.5b	(/.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)))))
	32.6b	(fma.f64 (cbrt.f64 (/.f64 1 x)) (cbrt.f64 (pow.f64 x -1/2)) (/.f64 -1 (sqrt.f64 (+.f64 1 x))))
	31.7b	(/.f64 1 (/.f64 (+.f64 (/.f64 1 x) (-.f64 (/.f64 1 (+.f64 1 x)) (/.f64 -1 (sqrt.f64 (*.f64 x (+.f64 1 x)))))) (+.f64 (pow.f64 (sqrt.f64 x) -3) (/.f64 -1 (pow.f64 (+.f64 1 x) 3/2)))))
	34.5b	(+.f64 (exp.f64 (*.f64 -1/2 (log.f64 x))) (/.f64 -1 (sqrt.f64 (+.f64 1 x))))
	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))))
	23.6b	(exp.f64 (log.f64 (fma.f64 -1 (pow.f64 (+.f64 1 x) -1/2) (pow.f64 x -1/2))))
	32.8b	(fma.f64 (pow.f64 (cbrt.f64 x) -1) (pow.f64 (cbrt.f64 (sqrt.f64 x)) -1) (/.f64 -1 (sqrt.f64 (+.f64 1 x))))
	31.8b	(/.f64 (+.f64 (pow.f64 (sqrt.f64 x) -3) (/.f64 -1 (pow.f64 (+.f64 1 x) 3/2))) (+.f64 (/.f64 1 (+.f64 1 x)) (-.f64 (/.f64 1 x) (/.f64 -1 (sqrt.f64 (*.f64 x (+.f64 1 x)))))))
	32.4b	(fma.f64 (pow.f64 (sqrt.f64 x) -1/2) (pow.f64 (sqrt.f64 x) -1/2) (/.f64 -1 (sqrt.f64 (+.f64 1 x))))
	32.0b	(fma.f64 (cbrt.f64 (/.f64 1 (+.f64 1 x))) (cbrt.f64 (/.f64 -1 (sqrt.f64 (+.f64 1 x)))) (pow.f64 x -1/2))
▶	21.5b	(.f64 (fma.f64 (sqrt.f64 x) -1 (sqrt.f64 (+.f64 1 x))) (/.f64 1 (sqrt.f64 (.f64 x (+.f64 1 x)))))
	29.4b	(+.f64 (/.f64 1 (sqrt.f64 x)) (*.f64 (cbrt.f64 (/.f64 1 (+.f64 1 x))) (cbrt.f64 (/.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)

Compiler

Compiled 538 to 442 computations (17.8% saved)

localize9.0ms (0.3%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(.f64 (fma.f64 (sqrt.f64 x) -1 (sqrt.f64 (+.f64 1 x))) (/.f64 1 (sqrt.f64 (.f64 x (+.f64 1 x)))))
✓	0.1b	(/.f64 1 (sqrt.f64 (*.f64 x (+.f64 1 x))))
✓	2.9b	(fma.f64 (sqrt.f64 x) -1 (sqrt.f64 (+.f64 1 x)))
✓	16.5b	(sqrt.f64 (*.f64 x (+.f64 1 x)))

series27.0ms (0.8%)

Counts

4 → 17

Calls

12 calls:

Time	Variable		Point	Expression
18.0ms	x	@	-inf	(.f64 (fma.f64 (sqrt.f64 x) -1 (sqrt.f64 (+.f64 1 x))) (/.f64 1 (sqrt.f64 (.f64 x (+.f64 1 x)))))
2.0ms	x	@	inf	(.f64 (fma.f64 (sqrt.f64 x) -1 (sqrt.f64 (+.f64 1 x))) (/.f64 1 (sqrt.f64 (.f64 x (+.f64 1 x)))))
2.0ms	x	@	0	(.f64 (fma.f64 (sqrt.f64 x) -1 (sqrt.f64 (+.f64 1 x))) (/.f64 1 (sqrt.f64 (.f64 x (+.f64 1 x)))))
1.0ms	x	@	0	(sqrt.f64 (*.f64 x (+.f64 1 x)))
1.0ms	x	@	inf	(fma.f64 (sqrt.f64 x) -1 (sqrt.f64 (+.f64 1 x)))

rewrite57.0ms (1.7%)

Algorithm

1×	batch-egg-rewrite

Rules

347×	`prod-diff_binary64`
254×	`fma-def_binary64`
191×	`expm1-udef_binary64`
191×	`log1p-udef_binary64`
175×	`log-pow_binary64`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	12	56
1	248	47
2	3040	46

Stop Event

1×	node limit

Counts

4 → 122

Calls

Call 1

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

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

simplify29.0ms (0.9%)

Algorithm

1×	egg-herbie

Rules

758×	`times-frac_binary64`
653×	`fma-def_binary64`
474×	`fma-neg_binary64`
399×	`cancel-sign-sub-inv_binary64`
267×	`sub-neg_binary64`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	44	214
1	137	212
2	350	211
3	895	211
4	2662	211

Stop Event

1×	node limit

Counts

139 → 152

Calls

Call 1

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

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

eval54.0ms (1.6%)

Compiler: Compiled 3032 to 1943 computations (35.9% saved)

prune352.0ms (10.7%)

Pruning

11 alts after pruning (11 fresh and 0 done)

	Pruned	Kept	Total
New	146	6	152
Fresh	8	5	13
Picked	1	0	1
Done	0	0	0
Total	155	11	166

Error

20.7b

Counts

166 → 11

Alt Table

Click to see full alt table

Status	Error	Program
	31.8b	(/.f64 (+.f64 (pow.f64 (sqrt.f64 x) -3) (/.f64 -1 (pow.f64 (+.f64 1 x) 3/2))) (+.f64 (/.f64 1 (+.f64 1 x)) (-.f64 (/.f64 1 x) (/.f64 -1 (sqrt.f64 (*.f64 x (+.f64 1 x)))))))
	21.4b	(.f64 (/.f64 (fma.f64 (.f64 (sqrt.f64 x) -1) (.f64 (sqrt.f64 x) -1) (neg.f64 (+.f64 x 1))) (-.f64 (.f64 (sqrt.f64 x) -1) (sqrt.f64 (+.f64 x 1)))) (/.f64 1 (sqrt.f64 (*.f64 x (+.f64 1 x)))))
	32.0b	(fma.f64 (cbrt.f64 (/.f64 1 (+.f64 1 x))) (cbrt.f64 (/.f64 -1 (sqrt.f64 (+.f64 1 x)))) (pow.f64 x -1/2))
	23.6b	(*.f64 (fma.f64 (sqrt.f64 x) -1 (sqrt.f64 (+.f64 1 x))) (-.f64 (exp.f64 (log1p.f64 (pow.f64 (fma.f64 x x x) -1/2))) 1))
	32.4b	(.f64 (/.f64 (+.f64 (pow.f64 (.f64 (sqrt.f64 x) -1) 3) (pow.f64 (+.f64 x 1) 3/2)) (fma.f64 (.f64 (sqrt.f64 x) -1) (.f64 (sqrt.f64 x) -1) (-.f64 (+.f64 x 1) (.f64 (.f64 (sqrt.f64 x) -1) (sqrt.f64 (+.f64 x 1)))))) (/.f64 1 (sqrt.f64 (*.f64 x (+.f64 1 x)))))
	21.9b	(*.f64 (fma.f64 (sqrt.f64 x) -1 (sqrt.f64 (+.f64 1 x))) (pow.f64 (cbrt.f64 (pow.f64 (fma.f64 x x x) -1/2)) 3))
	32.8b	(fma.f64 (pow.f64 (cbrt.f64 x) -1) (pow.f64 (cbrt.f64 (sqrt.f64 x)) -1) (/.f64 -1 (sqrt.f64 (+.f64 1 x))))
	23.0b	(.f64 1 (/.f64 1 (sqrt.f64 (.f64 x (+.f64 1 x)))))
	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))))
▶	21.3b	(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))))
	21.9b	(pow.f64 (cbrt.f64 (fma.f64 -1 (pow.f64 (+.f64 1 x) -1/2) (pow.f64 x -1/2))) 3)

Compiler

Compiled 508 to 388 computations (23.6% saved)

localize13.0ms (0.4%)

Local error

Found 3 expressions with local error:

New

Error

Program

✓

0.2b

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

✓

16.5b

(pow.f64 (fma.f64 x x x) -1/2)

✓

32.2b

(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))))

series8.0ms (0.2%)

Counts

3 → 12

Calls

9 calls:

Time	Variable		Point	Expression
2.0ms	x	@	inf	(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))))
2.0ms	x	@	-inf	(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))))
2.0ms	x	@	0	(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))))
0.0ms	x	@	-inf	(*.f64 (pow.f64 (fma.f64 x x x) -1/2) (sqrt.f64 (+.f64 x 1)))
0.0ms	x	@	0	(pow.f64 (fma.f64 x x x) -1/2)

rewrite48.0ms (1.5%)

Algorithm

1×	batch-egg-rewrite

Rules

383×	`prod-diff_binary64`
216×	`fma-def_binary64`
195×	`log1p-udef_binary64`
194×	`expm1-udef_binary64`
168×	`log-pow_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	13	56
1	265	45
2	3078	45

Stop Event

1×	node limit

Counts

3 → 59

Calls

Call 1

Inputs

(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))))

(pow.f64 (fma.f64 x x x) -1/2)

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

Outputs

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

simplify24.0ms (0.7%)

Algorithm

1×	egg-herbie

Rules

712×	`times-frac_binary64`
503×	`fma-def_binary64`
332×	`associate-/l/_binary64`
315×	`fma-neg_binary64`
255×	`cancel-sign-sub-inv_binary64`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	44	209
1	117	209
2	279	203
3	684	203
4	1992	203

Stop Event

1×	node limit

Counts

71 → 80

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)))

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

eval55.0ms (1.7%)

Compiler: Compiled 3177 to 1877 computations (40.9% saved)

prune139.0ms (4.2%)

Pruning

11 alts after pruning (10 fresh and 1 done)

	Pruned	Kept	Total
New	118	0	118
Fresh	0	10	10
Picked	0	1	1
Done	0	0	0
Total	118	11	129

Error

20.7b

Counts

129 → 11

Alt Table

Click to see full alt table

Status	Error	Program
	31.8b	(/.f64 (+.f64 (pow.f64 (sqrt.f64 x) -3) (/.f64 -1 (pow.f64 (+.f64 1 x) 3/2))) (+.f64 (/.f64 1 (+.f64 1 x)) (-.f64 (/.f64 1 x) (/.f64 -1 (sqrt.f64 (*.f64 x (+.f64 1 x)))))))
▶	21.4b	(.f64 (/.f64 (fma.f64 (.f64 (sqrt.f64 x) -1) (.f64 (sqrt.f64 x) -1) (neg.f64 (+.f64 x 1))) (-.f64 (.f64 (sqrt.f64 x) -1) (sqrt.f64 (+.f64 x 1)))) (/.f64 1 (sqrt.f64 (*.f64 x (+.f64 1 x)))))
	32.0b	(fma.f64 (cbrt.f64 (/.f64 1 (+.f64 1 x))) (cbrt.f64 (/.f64 -1 (sqrt.f64 (+.f64 1 x)))) (pow.f64 x -1/2))
	23.6b	(*.f64 (fma.f64 (sqrt.f64 x) -1 (sqrt.f64 (+.f64 1 x))) (-.f64 (exp.f64 (log1p.f64 (pow.f64 (fma.f64 x x x) -1/2))) 1))
	32.4b	(.f64 (/.f64 (+.f64 (pow.f64 (.f64 (sqrt.f64 x) -1) 3) (pow.f64 (+.f64 x 1) 3/2)) (fma.f64 (.f64 (sqrt.f64 x) -1) (.f64 (sqrt.f64 x) -1) (-.f64 (+.f64 x 1) (.f64 (.f64 (sqrt.f64 x) -1) (sqrt.f64 (+.f64 x 1)))))) (/.f64 1 (sqrt.f64 (*.f64 x (+.f64 1 x)))))
	21.9b	(*.f64 (fma.f64 (sqrt.f64 x) -1 (sqrt.f64 (+.f64 1 x))) (pow.f64 (cbrt.f64 (pow.f64 (fma.f64 x x x) -1/2)) 3))
	32.8b	(fma.f64 (pow.f64 (cbrt.f64 x) -1) (pow.f64 (cbrt.f64 (sqrt.f64 x)) -1) (/.f64 -1 (sqrt.f64 (+.f64 1 x))))
	23.0b	(.f64 1 (/.f64 1 (sqrt.f64 (.f64 x (+.f64 1 x)))))
	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))))
✓	21.3b	(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))))
	21.9b	(pow.f64 (cbrt.f64 (fma.f64 -1 (pow.f64 (+.f64 1 x) -1/2) (pow.f64 x -1/2))) 3)

Compiler

Compiled 485 to 374 computations (22.9% saved)

localize15.0ms (0.4%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.1b	(/.f64 1 (sqrt.f64 (*.f64 x (+.f64 1 x))))
✓	0.1b	(.f64 (/.f64 (fma.f64 (.f64 (sqrt.f64 x) -1) (.f64 (sqrt.f64 x) -1) (neg.f64 (+.f64 x 1))) (-.f64 (.f64 (sqrt.f64 x) -1) (sqrt.f64 (+.f64 x 1)))) (/.f64 1 (sqrt.f64 (*.f64 x (+.f64 1 x)))))
	16.5b	(sqrt.f64 (*.f64 x (+.f64 1 x)))
✓	32.2b	(fma.f64 (.f64 (sqrt.f64 x) -1) (.f64 (sqrt.f64 x) -1) (neg.f64 (+.f64 x 1)))

series18.0ms (0.5%)

Counts

2 → 4

Calls

6 calls:

Time	Variable		Point	Expression
8.0ms	x	@	-inf	(.f64 (/.f64 (fma.f64 (.f64 (sqrt.f64 x) -1) (.f64 (sqrt.f64 x) -1) (neg.f64 (+.f64 x 1))) (-.f64 (.f64 (sqrt.f64 x) -1) (sqrt.f64 (+.f64 x 1)))) (/.f64 1 (sqrt.f64 (*.f64 x (+.f64 1 x)))))
4.0ms	x	@	inf	(.f64 (/.f64 (fma.f64 (.f64 (sqrt.f64 x) -1) (.f64 (sqrt.f64 x) -1) (neg.f64 (+.f64 x 1))) (-.f64 (.f64 (sqrt.f64 x) -1) (sqrt.f64 (+.f64 x 1)))) (/.f64 1 (sqrt.f64 (*.f64 x (+.f64 1 x)))))
2.0ms	x	@	0	(.f64 (/.f64 (fma.f64 (.f64 (sqrt.f64 x) -1) (.f64 (sqrt.f64 x) -1) (neg.f64 (+.f64 x 1))) (-.f64 (.f64 (sqrt.f64 x) -1) (sqrt.f64 (+.f64 x 1)))) (/.f64 1 (sqrt.f64 (*.f64 x (+.f64 1 x)))))
1.0ms	x	@	-inf	(fma.f64 (.f64 (sqrt.f64 x) -1) (.f64 (sqrt.f64 x) -1) (neg.f64 (+.f64 x 1)))
1.0ms	x	@	0	(fma.f64 (.f64 (sqrt.f64 x) -1) (.f64 (sqrt.f64 x) -1) (neg.f64 (+.f64 x 1)))

rewrite33.0ms (1%)

Algorithm

1×	batch-egg-rewrite

Rules

179×	`add-sqr-sqrt_binary64`
175×	`*-un-lft-identity_binary64`
175×	`pow1_binary64`
165×	`add-cbrt-cube_binary64`
164×	`add-exp-log_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	17	67
1	383	26

Stop Event

1×	node limit

Counts

2 → 84

Calls

Call 1

Inputs

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

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

Outputs

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

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

simplify8.0ms (0.3%)

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

88 → 89

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)

eval90.0ms (2.7%)

Compiler: Compiled 5278 to 3427 computations (35.1% saved)

prune176.0ms (5.3%)

Pruning

2 alts after pruning (1 fresh and 1 done)

	Pruned	Kept	Total
New	180	1	181
Fresh	9	0	9
Picked	1	0	1
Done	0	1	1
Total	190	2	192

Error

6.3b

Counts

192 → 2

Alt Table

Click to see full alt table

Status

Error

Program

6.5b

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

✓

21.3b

(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))))

Compiler

Compiled 44 to 31 computations (29.5% saved)

regimes30.0ms (0.9%)

Accuracy

Total -39.4b remaining (-610.4%)

Threshold costs -39.4b (-610.4%)

Counts

23 → 1

Calls

Call 1

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

Results

Time	Error	Segments	Branch
11.0ms	6.5b	1	`x`
7.0ms	6.5b	1	`(-.f64 (/.f64 1 (sqrt.f64 x)) (/.f64 1 (sqrt.f64 (+.f64 x 1))))`

Compiler

Compiled 457 to 340 computations (25.6% 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	31
1	23	30
2	27	30
3	35	30
4	41	30
5	44	30
6	45	30

Stop Event

1×

saturated

Calls

Call 1

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

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

end19.0ms (0.6%)

Stop Event

1×

fuel

Compiler

Compiled 40 to 32 computations (20% 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%)

sample1.7s (53.1%)

preprocess17.0ms (0.5%)

simplify11.0ms (0.3%)

eval1.0ms (0%)

prune2.0ms (0.1%)

localize7.0ms (0.2%)

series7.0ms (0.2%)

rewrite54.0ms (1.6%)

simplify23.0ms (0.7%)

eval46.0ms (1.4%)

prune169.0ms (5.1%)

localize9.0ms (0.3%)

series27.0ms (0.8%)

rewrite57.0ms (1.7%)

simplify29.0ms (0.9%)

eval54.0ms (1.6%)

prune352.0ms (10.7%)

localize13.0ms (0.4%)

series8.0ms (0.2%)

rewrite48.0ms (1.5%)

simplify24.0ms (0.7%)

eval55.0ms (1.7%)

prune139.0ms (4.2%)

localize15.0ms (0.4%)

series18.0ms (0.5%)

rewrite33.0ms (1%)

simplify8.0ms (0.3%)

eval90.0ms (2.7%)

prune176.0ms (5.3%)

regimes30.0ms (0.9%)

simplify3.0ms (0.1%)

end19.0ms (0.6%)

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