Details

analyze1.0ms (0%)

Algorithm

1×

Search

Probability	Valid	Unknown	Precondition	Infinite	Domain	Can't	Iter
0%	0%	100%	0%	0%	0%	0%	0
0%	0%	100%	0%	0%	0%	0%	1
100%	50%	0%	0%	0%	50%	0%	2

Compiler

Compiled 13 to 11 computations (15.4% saved)

sample2.3s (20%)

Results

848.0ms	1044×	body	512	valid
734.0ms	2290×	body	1024	valid
678.0ms	4922×	body	256	valid

Bogosity

preprocess130.0ms (1.1%)

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	171	17
9	207	17
10	233	17
11	235	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 13 to 11 computations (15.4% saved)

simplify13.0ms (0.1%)

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	171	17
9	207	17
10	233	17
11	235	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)

prune1.0ms (0%)

Pruning

2 alts after pruning (2 fresh and 0 done)

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

Error

21.2b

Counts

3 → 1

Alt Table

Click to see full alt table

Status	Error	Program
▶	21.2b	(-.f64 (/.f64 1 (sqrt.f64 x)) (/.f64 1 (sqrt.f64 (+.f64 x 1))))

Compiler

Compiled 12 to 10 computations (16.7% saved)

localize16.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(sqrt.f64 (+.f64 x 1))
✓	0.2b	(/.f64 1 (sqrt.f64 (+.f64 x 1)))
✓	0.3b	(/.f64 1 (sqrt.f64 x))
✓	2.4b	(-.f64 (/.f64 1 (sqrt.f64 x)) (/.f64 1 (sqrt.f64 (+.f64 x 1))))

Compiler

Compiled 33 to 23 computations (30.3% saved)

series10.0ms (0.1%)

Counts

4 → 8

Calls

12 calls:

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

rewrite95.0ms (0.8%)

Algorithm

1×	batch-egg-rewrite

Rules

776×	`prod-diff_binary64`
445×	`log-prod_binary64`
351×	`fma-def_binary64`
252×	`pow2_binary64`
205×	`fma-neg_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	9	38
1	207	30
2	2979	30

Stop Event

1×	node limit

Counts

4 → 229

Calls

Call 1

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

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

simplify173.0ms (1.5%)

Algorithm

1×	egg-herbie

Rules

1216×	`fma-def_binary64`
750×	`sqr-pow_binary64`
605×	`cube-prod_binary64`
427×	`fabs-mul_binary64`
370×	`pow-sqr_binary64`

Iterations

Useful iterations: 10 (0.0ms)

Iter	Nodes	Cost
0	30	80
1	75	76
2	180	74
3	546	62
4	1395	58
5	2423	58
6	2945	58
7	3078	58
8	3232	58
9	3419	58
10	3672	56
11	4323	56
12	4730	56
13	5258	56
14	5926	56
15	6754	56
16	7157	56
17	7523	56
18	7867	56

Stop Event

1×	node limit

Counts

237 → 242

Calls

Call 1

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

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

eval173.0ms (1.5%)

Compiler: Compiled 4484 to 3575 computations (20.3% saved)

prune69.0ms (0.6%)

Pruning

26 alts after pruning (25 fresh and 1 done)

	Pruned	Kept	Total
New	217	25	242
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	217	26	243

Error

20.4b

Counts

243 → 26

Alt Table

Click to see full alt table

Status	Error	Program
	29.6b	(fma.f64 (pow.f64 (+.f64 1 x) -1/4) (neg.f64 (pow.f64 (+.f64 1 x) -1/4)) (pow.f64 x -1/2))
	29.4b	(fma.f64 (pow.f64 (cbrt.f64 (/.f64 -1 (sqrt.f64 (+.f64 1 x)))) 2) (cbrt.f64 (/.f64 -1 (sqrt.f64 (+.f64 1 x)))) (pow.f64 x -1/2))
▶	31.5b	(fma.f64 (pow.f64 x -1/6) (cbrt.f64 (/.f64 1 x)) (/.f64 -1 (sqrt.f64 (+.f64 1 x))))
	29.9b	(fma.f64 (pow.f64 x -1/4) (pow.f64 x -1/4) (/.f64 -1 (sqrt.f64 (+.f64 1 x))))
	30.5b	(fma.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))) (fma.f64 (neg.f64 (pow.f64 (+.f64 1 x) -1/6)) (cbrt.f64 (/.f64 1 (+.f64 1 x))) (pow.f64 (+.f64 1 x) -1/2)))
	32.1b	(/.f64 (-.f64 (pow.f64 x -3/2) (pow.f64 (+.f64 1 x) -3/2)) (+.f64 (/.f64 1 x) (+.f64 (/.f64 1 (+.f64 1 x)) (pow.f64 (*.f64 x (+.f64 1 x)) -1/2))))
	26.3b	(/.f64 (-.f64 (/.f64 1 x) (pow.f64 (/.f64 -1 (sqrt.f64 (+.f64 1 x))) 2)) (-.f64 (pow.f64 x -1/2) (/.f64 -1 (sqrt.f64 (+.f64 1 x)))))
	21.4b	(/.f64 (-.f64 (/.f64 1 x) (/.f64 1 (+.f64 1 x))) (+.f64 (pow.f64 x -1/2) (pow.f64 (+.f64 1 x) -1/2)))
▶	21.1b	(/.f64 (-.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)) (sqrt.f64 (*.f64 x (+.f64 1 x))))
	32.2b	(/.f64 (+.f64 (pow.f64 x -3/2) (pow.f64 (/.f64 -1 (sqrt.f64 (+.f64 1 x))) 3)) (+.f64 (/.f64 1 x) (-.f64 (pow.f64 (/.f64 -1 (sqrt.f64 (+.f64 1 x))) 2) (*.f64 (pow.f64 x -1/2) (/.f64 -1 (sqrt.f64 (+.f64 1 x)))))))
	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)))))
	32.1b	(/.f64 1 (/.f64 (+.f64 (/.f64 1 x) (+.f64 (/.f64 1 (+.f64 1 x)) (pow.f64 (*.f64 x (+.f64 1 x)) -1/2))) (-.f64 (pow.f64 x -3/2) (pow.f64 (+.f64 1 x) -3/2))))
	26.7b	(-.f64 (pow.f64 (pow.f64 x 1/4) -2) (/.f64 1 (sqrt.f64 (+.f64 x 1))))
	45.8b	(-.f64 (pow.f64 (*.f64 x x) -1/4) (/.f64 1 (sqrt.f64 (+.f64 x 1))))
	23.4b	(-.f64 (pow.f64 x -1/2) (/.f64 1 (sqrt.f64 (+.f64 x 1))))
	26.0b	(-.f64 (/.f64 1 (sqrt.f64 x)) (pow.f64 (pow.f64 (+.f64 1 x) -1/4) 2))
	23.6b	(-.f64 (/.f64 1 (sqrt.f64 x)) (pow.f64 (+.f64 1 x) -1/2))
▶	26.3b	(-.f64 (/.f64 1 (sqrt.f64 x)) (pow.f64 (cbrt.f64 (+.f64 1 x)) -3/2))
	30.7b	(-.f64 (/.f64 1 (sqrt.f64 x)) (/.f64 1 (+.f64 (*.f64 1/2 x) 1)))
✓	21.2b	(-.f64 (/.f64 1 (sqrt.f64 x)) (/.f64 1 (sqrt.f64 (+.f64 x 1))))
	31.4b	(-.f64 (/.f64 1 (sqrt.f64 x)) (+.f64 (*.f64 -1/2 x) 1))
▶	24.2b	(-.f64 (/.f64 1 (sqrt.f64 x)) (sqrt.f64 (/.f64 1 (+.f64 1 x))))
	29.7b	(-.f64 (/.f64 1 (sqrt.f64 x)) (exp.f64 (*.f64 -1/2 (log1p.f64 x))))
	29.5b	(-.f64 (/.f64 1 (sqrt.f64 x)) (cbrt.f64 (pow.f64 (+.f64 1 x) -3/2)))
▶	31.9b	(-.f64 (/.f64 1 (sqrt.f64 x)) 1)
	24.5b	(-.f64 (sqrt.f64 (/.f64 1 x)) (/.f64 1 (sqrt.f64 (+.f64 x 1))))

Compiler

Compiled 878 to 718 computations (18.2% saved)

localize21.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(sqrt.f64 (+.f64 1 x))
✓	0.2b	(/.f64 (-.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)) (sqrt.f64 (*.f64 x (+.f64 1 x))))
✓	2.4b	(-.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x))
✓	13.0b	(sqrt.f64 (*.f64 x (+.f64 1 x)))

Compiler

Compiled 44 to 28 computations (36.4% saved)

series12.0ms (0.1%)

Counts

4 → 13

Calls

12 calls:

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

rewrite100.0ms (0.9%)

Algorithm

1×	batch-egg-rewrite

Rules

558×	`log-prod_binary64`
546×	`fma-def_binary64`
430×	`pow-prod-down_binary64`
275×	`pow2_binary64`
267×	`fma-neg_binary64`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	10	48
1	224	42
2	3303	41

Stop Event

1×	node limit

Counts

4 → 221

Calls

Call 1

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

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

simplify51.0ms (0.4%)

Algorithm

1×	egg-herbie

Rules

671×	`fma-neg_binary64`
642×	`times-frac_binary64`
433×	`cancel-sign-sub-inv_binary64`
393×	`fma-def_binary64`
385×	`associate-l_binary64`

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	45	108
1	129	106
2	371	106
3	920	100
4	3432	100

Stop Event

1×	node limit

Counts

234 → 239

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

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

localize7.0ms (0.1%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.0b	(-.f64 (/.f64 1 (sqrt.f64 x)) 1)
	0.3b	(/.f64 1 (sqrt.f64 x))

Compiler

Compiled 15 to 9 computations (40% saved)

series1.0ms (0%)

Counts

1 → 2

Calls

3 calls:

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

rewrite53.0ms (0.5%)

Algorithm

1×	batch-egg-rewrite

Rules

588×	`pow1_binary64`
551×	`add-log-exp_binary64`
550×	`log1p-expm1-u_binary64`
550×	`expm1-log1p-u_binary64`
538×	`add-exp-log_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	6	9
1	129	7
2	1623	7

Stop Event

1×	node limit

Counts

1 → 31

Calls

Call 1

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

Outputs

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

simplify7.0ms (0.1%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	1	2

Stop Event

1×

saturated

Counts

33 → 32

Calls

Call 1

Inputs
-1
-1

Outputs
-1
-1

localize16.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(/.f64 1 (+.f64 1 x))
✓	0.1b	(sqrt.f64 (/.f64 1 (+.f64 1 x)))
	0.3b	(/.f64 1 (sqrt.f64 x))
✓	10.3b	(-.f64 (/.f64 1 (sqrt.f64 x)) (sqrt.f64 (/.f64 1 (+.f64 1 x))))

Compiler

Compiled 34 to 24 computations (29.4% saved)

series6.0ms (0.1%)

Counts

3 → 16

Calls

9 calls:

Time	Variable		Point	Expression
3.0ms	x	@	inf	(/.f64 1 (+.f64 1 x))
1.0ms	x	@	inf	(-.f64 (/.f64 1 (sqrt.f64 x)) (sqrt.f64 (/.f64 1 (+.f64 1 x))))
1.0ms	x	@	-inf	(-.f64 (/.f64 1 (sqrt.f64 x)) (sqrt.f64 (/.f64 1 (+.f64 1 x))))
0.0ms	x	@	0	(-.f64 (/.f64 1 (sqrt.f64 x)) (sqrt.f64 (/.f64 1 (+.f64 1 x))))
0.0ms	x	@	inf	(sqrt.f64 (/.f64 1 (+.f64 1 x)))

rewrite82.0ms (0.7%)

Algorithm

1×	batch-egg-rewrite

Rules

721×	`prod-diff_binary64`
429×	`log-prod_binary64`
368×	`fma-def_binary64`
293×	`pow-prod-down_binary64`
245×	`pow2_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	9	33
1	203	27
2	2817	27

Stop Event

1×	node limit

Counts

3 → 180

Calls

Call 1

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

Outputs

((#(struct:change #<rule egg-rr> (2) ((x +.f64 (pow.f64 x -1/2) (/.f64 -1 (sqrt.f64 (+.f64 1 x))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (pow.f64 x -1/2) (*.f64 (/.f64 -1 (sqrt.f64 (+.f64 1 x))) 1))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (-.f64 (pow.f64 x -1/2) (pow.f64 (+.f64 1 x) -1/2)) (fma.f64 (/.f64 -1 (sqrt.f64 (+.f64 1 x))) 1 (pow.f64 (+.f64 1 x) -1/2)))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (-.f64 (pow.f64 x -1/2) (pow.f64 (+.f64 1 x) -1/2)) (fma.f64 (neg.f64 (pow.f64 (+.f64 1 x) -1/6)) (/.f64 1 (cbrt.f64 (+.f64 1 x))) (pow.f64 (+.f64 1 x) -1/2)))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (-.f64 (pow.f64 x -1/2) (pow.f64 (+.f64 1 x) -1/2)) (+.f64 (/.f64 -1 (sqrt.f64 (+.f64 1 x))) (pow.f64 (+.f64 1 x) -1/2)))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (-.f64 (pow.f64 x -1/2) (pow.f64 (+.f64 1 x) -1/2)) (fma.f64 -1 (pow.f64 (+.f64 1 x) -1/2) (pow.f64 (+.f64 1 x) -1/2)))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (-.f64 (pow.f64 x 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(pow.f64 x -1/4) (pow.f64 (+.f64 1 x) -1/4)) (-.f64 (pow.f64 x -1/4) (pow.f64 (+.f64 1 x) -1/4)) (fma.f64 (neg.f64 (pow.f64 (+.f64 1 x) -1/6)) (/.f64 1 (cbrt.f64 (+.f64 1 x))) (pow.f64 (+.f64 1 x) -1/2)))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (+.f64 (pow.f64 x -1/4) (pow.f64 (+.f64 1 x) -1/4)) (-.f64 (pow.f64 x -1/4) (pow.f64 (+.f64 1 x) -1/4)) (+.f64 (/.f64 -1 (sqrt.f64 (+.f64 1 x))) (pow.f64 (+.f64 1 x) -1/2)))))))

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

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

simplify73.0ms (0.6%)

Algorithm

1×	egg-herbie

Rules

431×	`fma-def_binary64`
428×	`fma-neg_binary64`
418×	`cancel-sign-sub-inv_binary64`
400×	`difference-of-squares_binary64`
346×	`associate-/r*_binary64`

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	37	217
1	93	210
2	246	204
3	767	196
4	2458	195
5	6425	195

Stop Event

1×	node limit

Counts

196 → 200

Calls

Call 1

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

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

localize26.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.2b	(pow.f64 (cbrt.f64 (+.f64 1 x)) -3/2)
✓	0.2b	(cbrt.f64 (+.f64 1 x))
	0.3b	(/.f64 1 (sqrt.f64 x))
✓	14.6b	(-.f64 (/.f64 1 (sqrt.f64 x)) (pow.f64 (cbrt.f64 (+.f64 1 x)) -3/2))

Compiler

Compiled 34 to 24 computations (29.4% saved)

series8.0ms (0.1%)

Counts

3 → 8

Calls

9 calls:

Time	Variable		Point	Expression
2.0ms	x	@	-inf	(-.f64 (/.f64 1 (sqrt.f64 x)) (pow.f64 (cbrt.f64 (+.f64 1 x)) -3/2))
2.0ms	x	@	inf	(-.f64 (/.f64 1 (sqrt.f64 x)) (pow.f64 (cbrt.f64 (+.f64 1 x)) -3/2))
1.0ms	x	@	0	(-.f64 (/.f64 1 (sqrt.f64 x)) (pow.f64 (cbrt.f64 (+.f64 1 x)) -3/2))
1.0ms	x	@	-inf	(pow.f64 (cbrt.f64 (+.f64 1 x)) -3/2)
1.0ms	x	@	inf	(pow.f64 (cbrt.f64 (+.f64 1 x)) -3/2)

rewrite96.0ms (0.8%)

Algorithm

1×	batch-egg-rewrite

Rules

595×	`prod-diff_binary64`
442×	`log-prod_binary64`
311×	`fma-def_binary64`
286×	`pow-prod-down_binary64`
267×	`pow2_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	10	32
1	224	26
2	2916	26

Stop Event

1×	node limit

Counts

3 → 157

Calls

Call 1

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

Outputs

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((#(struct:change #<rule egg-rr> (2) ((x +.f64 0 (cbrt.f64 (+.f64 1 x)))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (log.f64 (pow.f64 (cbrt.f64 (exp.f64 (cbrt.f64 (+.f64 1 x)))) 2)) (log.f64 (cbrt.f64 (exp.f64 (cbrt.f64 (+.f64 1 x))))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (log.f64 (sqrt.f64 (exp.f64 (cbrt.f64 (+.f64 1 x))))) (log.f64 (sqrt.f64 (exp.f64 (cbrt.f64 (+.f64 1 x))))))))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (exp.f64 (log1p.f64 (cbrt.f64 (+.f64 1 x)))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 1 (cbrt.f64 (+.f64 1 x)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 (+.f64 1 x)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 (cbrt.f64 (+.f64 1 x))) (cbrt.f64 (exp.f64 (*.f64 2/3 (log1p.f64 x)))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 (exp.f64 (*.f64 2/3 (log1p.f64 x)))) (cbrt.f64 (cbrt.f64 (+.f64 1 x))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (+.f64 1 x) 1/6) (pow.f64 (+.f64 1 x) 1/6))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 1 1/3) (cbrt.f64 (+.f64 1 x)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (cbrt.f64 (+.f64 1 (pow.f64 x 3))) (cbrt.f64 (fma.f64 x (-.f64 x 1) 1)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (cbrt.f64 (-.f64 1 (*.f64 x x))) (cbrt.f64 (-.f64 1 x)))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (+.f64 1 x) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (cbrt.f64 (+.f64 1 x)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (+.f64 1 x) 2) 1/6)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (+.f64 1 x) 3) 1/9)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (exp.f64 (*.f64 2/3 (log1p.f64 x))) 1/2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (cbrt.f64 (cbrt.f64 (+.f64 1 x))) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (hypot.f64 1 (sqrt.f64 x)) 2/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (+.f64 1 x) 1/6) 2)))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f64 (exp.f64 (*.f64 2/3 (log1p.f64 x))))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (exp.f64 (cbrt.f64 (+.f64 1 x))))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (+.f64 1 (expm1.f64 (cbrt.f64 (+.f64 1 x)))))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (cbrt.f64 (+.f64 1 x))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 1/3 (log1p.f64 x)))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (log1p.f64 x) 1/3))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (*.f64 1/3 (log1p.f64 x)) 1))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (cbrt.f64 (+.f64 1 x))))))))

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

simplify165.0ms (1.4%)

Algorithm

1×	egg-herbie

Rules

1215×	`fma-def_binary64`
750×	`sqr-pow_binary64`
605×	`cube-prod_binary64`
420×	`fabs-mul_binary64`
370×	`pow-sqr_binary64`

Iterations

Useful iterations: 10 (0.0ms)

Iter	Nodes	Cost
0	30	84
1	75	78
2	182	74
3	528	62
4	1364	58
5	2415	58
6	2942	58
7	3076	58
8	3230	58
9	3420	58
10	3673	56
11	4333	56
12	4740	56
13	5270	56
14	5928	56
15	6752	56
16	7153	56
17	7519	56
18	7857	56

Stop Event

1×	node limit

Counts

165 → 170

Calls

Call 1

Inputs
1
(+.f64 1 (*.f64 1/3 x))
(+.f64 (.f64 -1/9 (pow.f64 x 2)) (+.f64 1 (.f64 1/3 x)))
(+.f64 (.f64 -1/9 (pow.f64 x 2)) (+.f64 1 (+.f64 (.f64 5/81 (pow.f64 x 3)) (*.f64 1/3 x))))
1
(+.f64 (*.f64 -1/2 x) 1)
(+.f64 (.f64 -1/2 x) (+.f64 1 (.f64 3/8 (pow.f64 x 2))))
(+.f64 (.f64 -1/2 x) (+.f64 1 (+.f64 (.f64 3/8 (pow.f64 x 2)) (*.f64 -5/16 (pow.f64 x 3)))))

Outputs
1
(+.f64 1 (*.f64 1/3 x))
(fma.f64 1/3 x 1)
(+.f64 (.f64 -1/9 (pow.f64 x 2)) (+.f64 1 (.f64 1/3 x)))
(fma.f64 -1/9 (.f64 x x) (+.f64 1 (.f64 1/3 x)))
(fma.f64 -1/9 (*.f64 x x) (fma.f64 1/3 x 1))
(fma.f64 x (*.f64 x -1/9) (fma.f64 1/3 x 1))
(fma.f64 x (fma.f64 x -1/9 1/3) 1)
(+.f64 (.f64 -1/9 (pow.f64 x 2)) (+.f64 1 (+.f64 (.f64 5/81 (pow.f64 x 3)) (*.f64 1/3 x))))
(fma.f64 -1/9 (.f64 x x) (+.f64 1 (fma.f64 5/81 (pow.f64 x 3) (.f64 1/3 x))))
(+.f64 (fma.f64 -1/9 (.f64 x x) (fma.f64 1/3 x 1)) (.f64 5/81 (pow.f64 x 3)))
(fma.f64 x (*.f64 x -1/9) (fma.f64 5/81 (pow.f64 x 3) (fma.f64 1/3 x 1)))
(fma.f64 5/81 (pow.f64 x 3) (fma.f64 x (fma.f64 x -1/9 1/3) 1))
(fma.f64 x (+.f64 1/3 (*.f64 x (fma.f64 x 5/81 -1/9))) 1)
(fma.f64 x (fma.f64 x (fma.f64 x 5/81 -1/9) 1/3) 1)
1
(+.f64 (*.f64 -1/2 x) 1)
(fma.f64 -1/2 x 1)
(fma.f64 x -1/2 1)
(+.f64 (.f64 -1/2 x) (+.f64 1 (.f64 3/8 (pow.f64 x 2))))
(+.f64 (fma.f64 -1/2 x 1) (.f64 (.f64 x x) 3/8))
(fma.f64 x -1/2 (fma.f64 (*.f64 x x) 3/8 1))
(fma.f64 x -1/2 (fma.f64 x (*.f64 x 3/8) 1))
(fma.f64 x (fma.f64 x 3/8 -1/2) 1)
(+.f64 (.f64 -1/2 x) (+.f64 1 (+.f64 (.f64 3/8 (pow.f64 x 2)) (*.f64 -5/16 (pow.f64 x 3)))))
(+.f64 (fma.f64 -1/2 x 1) (fma.f64 3/8 (.f64 x x) (.f64 (pow.f64 x 3) -5/16)))
(+.f64 (fma.f64 x -1/2 1) (fma.f64 (.f64 x x) 3/8 (.f64 (pow.f64 x 3) -5/16)))
(fma.f64 x -1/2 (fma.f64 x (*.f64 x 3/8) (fma.f64 (pow.f64 x 3) -5/16 1)))
(fma.f64 x -1/2 (fma.f64 x (*.f64 x (fma.f64 x -5/16 3/8)) 1))
(fma.f64 x (fma.f64 x (fma.f64 x -5/16 3/8) -1/2) 1)

localize28.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.2b	(/.f64 -1 (sqrt.f64 (+.f64 1 x)))
✓	0.9b	(cbrt.f64 (/.f64 1 x))
✓	4.1b	(pow.f64 x -1/6)
✓	29.3b	(fma.f64 (pow.f64 x -1/6) (cbrt.f64 (/.f64 1 x)) (/.f64 -1 (sqrt.f64 (+.f64 1 x))))

Compiler

Compiled 42 to 32 computations (23.8% saved)

series87.0ms (0.8%)

Counts

4 → 17

Calls

12 calls:

Time	Variable		Point	Expression
41.0ms	x	@	-inf	(pow.f64 x -1/6)
20.0ms	x	@	0	(pow.f64 x -1/6)
16.0ms	x	@	inf	(pow.f64 x -1/6)
2.0ms	x	@	-inf	(fma.f64 (pow.f64 x -1/6) (cbrt.f64 (/.f64 1 x)) (/.f64 -1 (sqrt.f64 (+.f64 1 x))))
1.0ms	x	@	inf	(fma.f64 (pow.f64 x -1/6) (cbrt.f64 (/.f64 1 x)) (/.f64 -1 (sqrt.f64 (+.f64 1 x))))

rewrite89.0ms (0.8%)

Algorithm

1×	batch-egg-rewrite

Rules

468×	`log-prod_binary64`
291×	`pow-prod-down_binary64`
287×	`prod-diff_binary64`
286×	`pow2_binary64`
203×	`pow-to-exp_binary64`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	12	40
1	255	34
2	3060	33

Stop Event

1×	node limit

Counts

4 → 136

Calls

Call 1

Inputs
(fma.f64 (pow.f64 x -1/6) (cbrt.f64 (/.f64 1 x)) (/.f64 -1 (sqrt.f64 (+.f64 1 x))))
(pow.f64 x -1/6)
(cbrt.f64 (/.f64 1 x))
(/.f64 -1 (sqrt.f64 (+.f64 1 x)))

Outputs
((#(struct:change #<rule egg-rr> (2) ((x +.f64 (/.f64 -1 (sqrt.f64 (+.f64 x 1))) (pow.f64 x -1/2))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 0 (fma.f64 -1 (pow.f64 (+.f64 x 1) -1/2) (pow.f64 x -1/2)))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (pow.f64 x -1/2) (/.f64 -1 (sqrt.f64 (+.f64 x 1))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (.f64 (pow.f64 x -1/2) 1) (/.f64 -1 (sqrt.f64 (+.f64 x 1))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (log.f64 (pow.f64 (cbrt.f64 (exp.f64 (fma.f64 -1 (pow.f64 (+.f64 x 1) -1/2) (pow.f64 x -1/2)))) 2)) (log.f64 (cbrt.f64 (exp.f64 (fma.f64 -1 (pow.f64 (+.f64 x 1) -1/2) (pow.f64 x -1/2))))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (log.f64 (sqrt.f64 (exp.f64 (fma.f64 -1 (pow.f64 (+.f64 x 1) -1/2) (pow.f64 x -1/2))))) (log.f64 (sqrt.f64 (exp.f64 (fma.f64 -1 (pow.f64 (+.f64 x 1) -1/2) (pow.f64 x -1/2))))))))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (exp.f64 (log1p.f64 (fma.f64 -1 (pow.f64 (+.f64 x 1) -1/2) (pow.f64 x -1/2)))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x .f64 1 (fma.f64 -1 (pow.f64 (+.f64 x 1) -1/2) (pow.f64 x -1/2)))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (fma.f64 -1 (pow.f64 (+.f64 x 1) -1/2) (pow.f64 x -1/2)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (cbrt.f64 (fma.f64 -1 (pow.f64 (+.f64 x 1) -1/2) (pow.f64 x -1/2))) (pow.f64 (cbrt.f64 (fma.f64 -1 (pow.f64 (+.f64 x 1) -1/2) (pow.f64 x -1/2))) 2))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (pow.f64 (cbrt.f64 (fma.f64 -1 (pow.f64 (+.f64 x 1) -1/2) (pow.f64 x -1/2))) 2) (cbrt.f64 (fma.f64 -1 (pow.f64 (+.f64 x 1) -1/2) (pow.f64 x -1/2))))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (sqrt.f64 (fma.f64 -1 (pow.f64 (+.f64 x 1) -1/2) (pow.f64 x -1/2))) (sqrt.f64 (fma.f64 -1 (pow.f64 (+.f64 x 1) -1/2) (pow.f64 x -1/2))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (+.f64 (pow.f64 x -3/2) (pow.f64 (neg.f64 (sqrt.f64 (+.f64 x 1))) -3)) (+.f64 (/.f64 1 x) (-.f64 (/.f64 1 (+.f64 x 1)) (.f64 (pow.f64 x -1/2) (/.f64 -1 (sqrt.f64 (+.f64 x 1)))))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (-.f64 (/.f64 1 x) (/.f64 1 (+.f64 x 1))) (-.f64 (pow.f64 x -1/2) (/.f64 -1 (sqrt.f64 (+.f64 x 1)))))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (fma.f64 -1 (pow.f64 (+.f64 x 1) -1/2) (pow.f64 x -1/2)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (fma.f64 -1 (pow.f64 (+.f64 x 1) -1/2) (pow.f64 x -1/2)) 2) 1/2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (fma.f64 -1 (pow.f64 (+.f64 x 1) -1/2) (pow.f64 x -1/2)) 3) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (cbrt.f64 (fma.f64 -1 (pow.f64 (+.f64 x 1) -1/2) (pow.f64 x -1/2))) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (sqrt.f64 (fma.f64 -1 (pow.f64 (+.f64 x 1) -1/2) (pow.f64 x -1/2))) 2)))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f64 (pow.f64 (fma.f64 -1 (pow.f64 (+.f64 x 1) -1/2) (pow.f64 x -1/2)) 2))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (exp.f64 (fma.f64 -1 (pow.f64 (+.f64 x 1) -1/2) (pow.f64 x -1/2))))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (+.f64 1 (expm1.f64 (fma.f64 -1 (pow.f64 (+.f64 x 1) -1/2) (pow.f64 x -1/2)))))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (.f64 (exp.f64 (/.f64 -1 (sqrt.f64 (+.f64 x 1)))) (exp.f64 (pow.f64 x -1/2))))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (.f64 (+.f64 1 (expm1.f64 (/.f64 -1 (sqrt.f64 (+.f64 x 1))))) (exp.f64 (pow.f64 x -1/2))))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (.f64 (exp.f64 (pow.f64 x -1/2)) (+.f64 1 (expm1.f64 (/.f64 -1 (sqrt.f64 (+.f64 x 1)))))))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (pow.f64 (fma.f64 -1 (pow.f64 (+.f64 x 1) -1/2) (pow.f64 x -1/2)) 3))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (fma.f64 -1 (pow.f64 (+.f64 x 1) -1/2) (pow.f64 x -1/2))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (log.f64 (fma.f64 -1 (pow.f64 (+.f64 x 1) -1/2) (pow.f64 x -1/2))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (.f64 (log.f64 (fma.f64 -1 (pow.f64 (+.f64 x 1) -1/2) (pow.f64 x -1/2))) 1))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (.f64 (.f64 3 (log.f64 (fma.f64 -1 (pow.f64 (+.f64 x 1) -1/2) (pow.f64 x -1/2)))) 1/3))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (.f64 (log.f64 (cbrt.f64 (fma.f64 -1 (pow.f64 (+.f64 x 1) -1/2) (pow.f64 x -1/2)))) 3))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (log.f64 (sqrt.f64 (fma.f64 -1 (pow.f64 (+.f64 x 1) -1/2) (pow.f64 x -1/2)))) 2))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (fma.f64 -1 (pow.f64 (+.f64 x 1) -1/2) (pow.f64 x -1/2))))))))
((#(struct:change #<rule egg-rr> (2) ((x +.f64 0 (pow.f64 x -1/6))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (log.f64 (pow.f64 (cbrt.f64 (exp.f64 (pow.f64 x -1/6))) 2)) (log.f64 (cbrt.f64 (exp.f64 (pow.f64 x -1/6)))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (log.f64 (sqrt.f64 (exp.f64 (pow.f64 x -1/6)))) (log.f64 (sqrt.f64 (exp.f64 (pow.f64 x -1/6)))))))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (exp.f64 (log1p.f64 (pow.f64 x -1/6))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (pow.f64 x -1/6) 1)))) (#(struct:change #<rule egg-rr> (2) ((x .f64 1 (pow.f64 x -1/6))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (pow.f64 (.f64 x x) -1/18) (pow.f64 x -1/18))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (pow.f64 x -1/18) (pow.f64 (.f64 x x) -1/18))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (pow.f64 x -1/12) (pow.f64 x -1/12))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (sqrt.f64 (pow.f64 (pow.f64 x -1/18) 4)) (sqrt.f64 (pow.f64 (.f64 x x) -1/18)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 1 (sqrt.f64 (cbrt.f64 x)))))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f64 (/.f64 1 (cbrt.f64 x)))))) (#(struct:change #<rule egg-rr> (2) ((x fabs.f64 (pow.f64 x -1/6))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (exp.f64 (pow.f64 x -1/6)))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (+.f64 1 (expm1.f64 (pow.f64 x -1/6))))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (pow.f64 x -1/2))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (pow.f64 x -1/6)))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (log.f64 (pow.f64 x -1/6)))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (.f64 (log.f64 (pow.f64 x -1/6)) 1))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (.f64 (neg.f64 (log.f64 x)) 1/6))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (.f64 (.f64 -1/3 (log.f64 x)) 1/2))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (.f64 (.f64 2 (log.f64 x)) -1/12))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (.f64 (log.f64 (pow.f64 x -1/18)) 3))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (.f64 (.f64 -1/2 (log.f64 x)) 1/3))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (.f64 (.f64 -1/12 (log.f64 x)) 2))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (pow.f64 x -1/6)))))))
((#(struct:change #<rule egg-rr> (2) ((x +.f64 0 (/.f64 1 (cbrt.f64 x)))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (log.f64 (pow.f64 (cbrt.f64 (exp.f64 (/.f64 1 (cbrt.f64 x)))) 2)) (log.f64 (cbrt.f64 (exp.f64 (/.f64 1 (cbrt.f64 x))))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (log.f64 (sqrt.f64 (exp.f64 (/.f64 1 (cbrt.f64 x))))) (log.f64 (sqrt.f64 (exp.f64 (/.f64 1 (cbrt.f64 x))))))))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (exp.f64 (log1p.f64 (/.f64 1 (cbrt.f64 x)))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (pow.f64 x -1/6) (pow.f64 x -1/6))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 1 (/.f64 1 (cbrt.f64 x)))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (/.f64 1 (cbrt.f64 x)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (pow.f64 (.f64 x x) -1/18) (pow.f64 (pow.f64 x -1/18) 4))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (pow.f64 (pow.f64 x -1/18) 4) (pow.f64 (.f64 x x) -1/18))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (pow.f64 x -1/12) (pow.f64 x -1/4))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (pow.f64 x -1/4) (pow.f64 x -1/12))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (pow.f64 (pow.f64 x -1/18) 5) (pow.f64 x -1/18))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 1 (cbrt.f64 x))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 1 (/.f64 (cbrt.f64 x) 1))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 -1 (cbrt.f64 (neg.f64 x)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 -1 (neg.f64 (cbrt.f64 x)))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 x -1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 x -1/6) 2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (/.f64 1 x) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (/.f64 1 (cbrt.f64 x)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (.f64 x x) -1/6)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 x -2) 1/6)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 x -3) 1/9)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (cbrt.f64 x) -2) 1/2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (cbrt.f64 x) -1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (.f64 x x) -1/18) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 x -1/18) 6)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (sqrt.f64 x) -2/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 x -1/2) 2/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 x 3) -1/9)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 x -1/12) 4)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 x 4) -1/12)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (/.f64 (cbrt.f64 x) 1) -1)))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f64 (pow.f64 (cbrt.f64 x) -2))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (exp.f64 (/.f64 1 (cbrt.f64 x))))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (+.f64 1 (expm1.f64 (/.f64 1 (cbrt.f64 x)))))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (/.f64 1 (cbrt.f64 x))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (.f64 -1/3 (log.f64 x)))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (.f64 (neg.f64 (log.f64 x)) 1/3))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (.f64 (.f64 -1/3 (log.f64 x)) 1))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (.f64 (log.f64 x) -1/3))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (.f64 (log.f64 (pow.f64 x -1/6)) 2))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (.f64 (.f64 2 (log.f64 x)) -1/6))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (.f64 (log.f64 (cbrt.f64 x)) -1))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (.f64 (*.f64 2 (log.f64 (pow.f64 x -1/18))) 3))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (/.f64 1 (cbrt.f64 x))))))))
((#(struct:change #<rule egg-rr> (2) ((x +.f64 0 (/.f64 -1 (sqrt.f64 (+.f64 x 1))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (log.f64 (pow.f64 (cbrt.f64 (exp.f64 (/.f64 -1 (sqrt.f64 (+.f64 x 1))))) 2)) (log.f64 (cbrt.f64 (exp.f64 (/.f64 -1 (sqrt.f64 (+.f64 x 1)))))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (log.f64 (sqrt.f64 (exp.f64 (/.f64 -1 (sqrt.f64 (+.f64 x 1)))))) (log.f64 (sqrt.f64 (exp.f64 (/.f64 -1 (sqrt.f64 (+.f64 x 1)))))))))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (exp.f64 (log1p.f64 (/.f64 -1 (sqrt.f64 (+.f64 x 1))))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x .f64 1 (/.f64 -1 (sqrt.f64 (+.f64 x 1))))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 -1 (pow.f64 (+.f64 x 1) -1/2))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (/.f64 -1 (sqrt.f64 (+.f64 x 1))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (/.f64 -1 (pow.f64 (+.f64 x 1) 1/6)) (cbrt.f64 (/.f64 1 (+.f64 x 1))))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (cbrt.f64 (/.f64 1 (+.f64 x 1))) (/.f64 -1 (pow.f64 (+.f64 x 1) 1/6)))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (pow.f64 (neg.f64 (sqrt.f64 (+.f64 x 1))) -1/2) (pow.f64 (neg.f64 (sqrt.f64 (+.f64 x 1))) -1/2))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (pow.f64 (+.f64 x 1) -1/2) -1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (/.f64 -1 (sqrt.f64 (+.f64 x 1))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (/.f64 1 (+.f64 x 1)) 1/2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (neg.f64 (sqrt.f64 (+.f64 x 1))) -3) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (/.f64 -1 (pow.f64 (+.f64 x 1) 1/6)) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (neg.f64 (sqrt.f64 (+.f64 x 1))) -1/2) 2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (neg.f64 (sqrt.f64 (+.f64 x 1))) -1)))) (#(struct:change #<rule egg-rr> (2) ((x neg.f64 (pow.f64 (+.f64 x 1) -1/2))))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f64 (/.f64 1 (+.f64 x 1)))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (exp.f64 (/.f64 -1 (sqrt.f64 (+.f64 x 1)))))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (+.f64 1 (expm1.f64 (/.f64 -1 (sqrt.f64 (+.f64 x 1))))))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (/.f64 1 (exp.f64 (pow.f64 (+.f64 x 1) -1/2))))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (pow.f64 (neg.f64 (sqrt.f64 (+.f64 x 1))) -3))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (/.f64 -1 (sqrt.f64 (+.f64 x 1)))))))) (#(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 (pow.f64 (neg.f64 (sqrt.f64 (+.f64 x 1))) -3)) 1/3))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (.f64 (log.f64 (/.f64 -1 (pow.f64 (+.f64 x 1) 1/6))) 3))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (.f64 (-.f64 (log.f64 (sqrt.f64 -1)) (.f64 1/4 (log1p.f64 x))) 2))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (log.f64 (neg.f64 (sqrt.f64 (+.f64 x 1)))) -1))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (/.f64 -1 (sqrt.f64 (+.f64 x 1)))))))))

simplify48.0ms (0.4%)

Algorithm

1×	egg-herbie

Rules

713×	`fma-neg_binary64`
562×	`distribute-rgt-neg-in_binary64`
561×	`associate-l_binary64`
467×	`cancel-sign-sub-inv_binary64`
465×	`fma-def_binary64`

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	31	126
1	83	124
2	180	122
3	485	116
4	1321	77
5	4430	77

Stop Event

1×	node limit

Counts

153 → 146

Calls

Call 1

Inputs
-1
(pow.f64 (/.f64 1 x) 1/6)
(pow.f64 (/.f64 1 x) 1/6)
(pow.f64 (/.f64 1 x) 1/6)
(pow.f64 (/.f64 1 x) 1/6)
(pow.f64 (/.f64 1 x) 1/6)
(pow.f64 (/.f64 1 x) 1/6)
(pow.f64 (/.f64 1 x) 1/6)
(pow.f64 (/.f64 1 x) 1/6)
(exp.f64 (.f64 -1/6 (+.f64 (.f64 -1 (log.f64 (/.f64 -1 x))) (log.f64 -1))))
(exp.f64 (.f64 -1/6 (+.f64 (.f64 -1 (log.f64 (/.f64 -1 x))) (log.f64 -1))))
(exp.f64 (.f64 -1/6 (+.f64 (.f64 -1 (log.f64 (/.f64 -1 x))) (log.f64 -1))))
(exp.f64 (.f64 -1/6 (+.f64 (.f64 -1 (log.f64 (/.f64 -1 x))) (log.f64 -1))))
-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
(pow.f64 (/.f64 1 x) 1/6)
(pow.f64 x -1/6)
(pow.f64 (/.f64 1 x) 1/6)
(pow.f64 x -1/6)
(pow.f64 (/.f64 1 x) 1/6)
(pow.f64 x -1/6)
(pow.f64 (/.f64 1 x) 1/6)
(pow.f64 x -1/6)
(pow.f64 (/.f64 1 x) 1/6)
(pow.f64 x -1/6)
(pow.f64 (/.f64 1 x) 1/6)
(pow.f64 x -1/6)
(pow.f64 (/.f64 1 x) 1/6)
(pow.f64 x -1/6)
(pow.f64 (/.f64 1 x) 1/6)
(pow.f64 x -1/6)
(exp.f64 (.f64 -1/6 (+.f64 (.f64 -1 (log.f64 (/.f64 -1 x))) (log.f64 -1))))
(pow.f64 (/.f64 1 x) 1/6)
(pow.f64 x -1/6)
(exp.f64 (.f64 -1/6 (+.f64 (.f64 -1 (log.f64 (/.f64 -1 x))) (log.f64 -1))))
(pow.f64 (/.f64 1 x) 1/6)
(pow.f64 x -1/6)
(exp.f64 (.f64 -1/6 (+.f64 (.f64 -1 (log.f64 (/.f64 -1 x))) (log.f64 -1))))
(pow.f64 (/.f64 1 x) 1/6)
(pow.f64 x -1/6)
(exp.f64 (.f64 -1/6 (+.f64 (.f64 -1 (log.f64 (/.f64 -1 x))) (log.f64 -1))))
(pow.f64 (/.f64 1 x) 1/6)
(pow.f64 x -1/6)
-1
(-.f64 (*.f64 1/2 x) 1)
(fma.f64 1/2 x -1)
(fma.f64 x 1/2 -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 x 1/2 (fma.f64 -3/8 (*.f64 x x) -1))
(fma.f64 x 1/2 (fma.f64 x (*.f64 x -3/8) -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 -1 (fma.f64 x 1/2 (fma.f64 -3/8 (.f64 x x) (.f64 5/16 (pow.f64 x 3)))))
(fma.f64 x 1/2 (fma.f64 x (*.f64 x -3/8) (fma.f64 5/16 (pow.f64 x 3) -1)))
(fma.f64 x 1/2 (fma.f64 x (*.f64 x (fma.f64 x 5/16 -3/8)) -1))
(fma.f64 x (fma.f64 x (fma.f64 x 5/16 -3/8) 1/2) -1)

eval599.0ms (5.3%)

Compiler: Compiled 16018 to 12120 computations (24.3% saved)

prune393.0ms (3.5%)

Pruning

27 alts after pruning (25 fresh and 2 done)

	Pruned	Kept	Total
New	873	16	889
Fresh	11	9	20
Picked	0	1	1
Done	4	1	5
Total	888	27	915

Error

19.9b

Counts

915 → 27

Alt Table

Click to see full alt table

Status	Error	Program
	29.6b	(fma.f64 (pow.f64 (+.f64 1 x) -1/4) (neg.f64 (pow.f64 (+.f64 1 x) -1/4)) (pow.f64 x -1/2))
✓	31.5b	(fma.f64 (pow.f64 x -1/6) (cbrt.f64 (/.f64 1 x)) (/.f64 -1 (sqrt.f64 (+.f64 1 x))))
	31.9b	(fma.f64 (pow.f64 x -1/6) (cbrt.f64 (/.f64 1 x)) (*.f64 (/.f64 -1 (pow.f64 (+.f64 x 1) 1/6)) (cbrt.f64 (/.f64 1 (+.f64 x 1)))))
	29.9b	(fma.f64 (pow.f64 x -1/4) (pow.f64 x -1/4) (/.f64 -1 (sqrt.f64 (+.f64 1 x))))
	29.8b	(fma.f64 (/.f64 (pow.f64 (+.f64 x 1) 1/4) 1) (/.f64 (pow.f64 (+.f64 x 1) 1/4) (hypot.f64 x (sqrt.f64 x))) (neg.f64 (/.f64 1 (sqrt.f64 (+.f64 x 1)))))
	31.4b	(fma.f64 (/.f64 (cbrt.f64 (+.f64 x 1)) (cbrt.f64 (fma.f64 x x x))) (/.f64 (pow.f64 (+.f64 x 1) 1/6) (pow.f64 (fma.f64 x x x) 1/6)) (neg.f64 (/.f64 1 (sqrt.f64 (+.f64 x 1)))))
▶	30.3b	(fma.f64 (/.f64 1 (sqrt.f64 (cbrt.f64 x))) (cbrt.f64 (/.f64 1 x)) (/.f64 -1 (sqrt.f64 (+.f64 1 x))))
	21.2b	(/.f64 (fma.f64 (pow.f64 (+.f64 x 1) 1/4) (pow.f64 (+.f64 x 1) 1/4) (neg.f64 (sqrt.f64 x))) (sqrt.f64 (*.f64 x (+.f64 1 x))))
▶	20.7b	(/.f64 (/.f64 (+.f64 x (-.f64 1 x)) (+.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x))) (sqrt.f64 (*.f64 x (+.f64 1 x))))
	32.1b	(/.f64 (-.f64 (pow.f64 x -3/2) (pow.f64 (+.f64 1 x) -3/2)) (+.f64 (/.f64 1 x) (+.f64 (/.f64 1 (+.f64 1 x)) (pow.f64 (*.f64 (+.f64 1 x) x) -1/2))))
	21.4b	(/.f64 (-.f64 (/.f64 1 x) (/.f64 1 (+.f64 1 x))) (+.f64 (pow.f64 x -1/2) (pow.f64 (+.f64 1 x) -1/2)))
	52.3b	(/.f64 (-.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)) (+.f64 (+.f64 x 1/2) (/.f64 -1/8 x)))
	50.8b	(/.f64 (-.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)) (+.f64 x 1/2))
	51.1b	(/.f64 (-.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)) x)
▶	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)))))
	22.7b	(/.f64 1 (sqrt.f64 (*.f64 x (+.f64 1 x))))
	26.7b	(-.f64 (pow.f64 (pow.f64 x 1/4) -2) (/.f64 1 (sqrt.f64 (+.f64 x 1))))
	22.7b	(-.f64 (pow.f64 x -1/2) (sqrt.f64 (/.f64 1 (+.f64 1 x))))
▶	31.8b	(-.f64 (pow.f64 x -1/2) 1)
▶	23.6b	(-.f64 (/.f64 1 (sqrt.f64 x)) (pow.f64 (+.f64 1 x) -1/2))
	30.7b	(-.f64 (/.f64 1 (sqrt.f64 x)) (/.f64 1 (+.f64 (*.f64 1/2 x) 1)))
	31.4b	(-.f64 (/.f64 1 (sqrt.f64 x)) (+.f64 (*.f64 -1/2 x) 1))
	56.0b	(-.f64 (/.f64 1 (sqrt.f64 x)) (sqrt.f64 (/.f64 1 x)))
	56.3b	(-.f64 (/.f64 1 (sqrt.f64 x)) (sqrt.f64 (+.f64 (/.f64 1 x) (/.f64 (/.f64 -1 x) x))))
	29.5b	(-.f64 (/.f64 1 (sqrt.f64 x)) (cbrt.f64 (pow.f64 (+.f64 1 x) -3/2)))
✓	31.9b	(-.f64 (/.f64 1 (sqrt.f64 x)) 1)
	62.8b	-1

Compiler

Compiled 804 to 632 computations (21.4% saved)

localize135.0ms (1.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(/.f64 (+.f64 x (-.f64 1 x)) (+.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x)))
✓	0.2b	(/.f64 (/.f64 (+.f64 x (-.f64 1 x)) (+.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x))) (sqrt.f64 (*.f64 x (+.f64 1 x))))
✓	1.9b	(+.f64 x (-.f64 1 x))
	13.0b	(sqrt.f64 (*.f64 x (+.f64 1 x)))

Compiler

Compiled 74 to 47 computations (36.5% saved)

series15.0ms (0.1%)

Counts

3 → 13

Calls

9 calls:

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

rewrite161.0ms (1.4%)

Algorithm

1×	batch-egg-rewrite

Rules

863×	`fma-def_binary64`
430×	`fma-neg_binary64`
326×	`log-div_binary64`
257×	`expm1-udef_binary64`
257×	`log1p-udef_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	14	58
1	334	37
2	4988	37

Stop Event

1×	node limit

Counts

3 → 293

Calls

Call 1

Inputs

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

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

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

Outputs

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

simplify12.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

1×	`1-exp_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	1	13
1	4	13

Stop Event

1×

saturated

Counts

306 → 294

Calls

Call 1

Inputs
1
1
1
1
1
1
1
1
1
1
1
1
1

Outputs
1
1
1
1
1
1
1
1
1
1
1
1
1

localize10.0ms (0.1%)

Local error

Found 1 expressions with local error:

New	Error	Program
✓	0.0b	(-.f64 (pow.f64 x -1/2) 1)

Compiler

Compiled 12 to 9 computations (25% saved)

series2.0ms (0%)

Counts

1 → 8

Calls

3 calls:

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

rewrite57.0ms (0.5%)

Algorithm

1×	batch-egg-rewrite

Rules

583×	`pow1_binary64`
550×	`add-log-exp_binary64`
548×	`log1p-expm1-u_binary64`
548×	`expm1-log1p-u_binary64`
539×	`add-exp-log_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	6	7
1	132	7
2	1553	7

Stop Event

1×	node limit

Counts

1 → 31

Calls

Call 1

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

Outputs

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

simplify53.0ms (0.5%)

Algorithm

1×	egg-herbie

Rules

796×	`fma-neg_binary64`
589×	`associate-l_binary64`
565×	`fma-def_binary64`
310×	`distribute-rgt-in_binary64`
280×	`distribute-lft-in_binary64`

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	17	72
1	44	72
2	89	72
3	193	72
4	528	56
5	1558	56
6	7173	56

Stop Event

1×	node limit

Counts

39 → 33

Calls

Call 1

Inputs
(-.f64 (pow.f64 (/.f64 1 x) 1/2) 1)
(-.f64 (pow.f64 (/.f64 1 x) 1/2) 1)
(-.f64 (pow.f64 (/.f64 1 x) 1/2) 1)
(-.f64 (pow.f64 (/.f64 1 x) 1/2) 1)
(-.f64 (exp.f64 (.f64 -1/2 (+.f64 (.f64 -1 (log.f64 (/.f64 -1 x))) (log.f64 -1)))) 1)
(-.f64 (exp.f64 (.f64 -1/2 (+.f64 (.f64 -1 (log.f64 (/.f64 -1 x))) (log.f64 -1)))) 1)
(-.f64 (exp.f64 (.f64 -1/2 (+.f64 (.f64 -1 (log.f64 (/.f64 -1 x))) (log.f64 -1)))) 1)
(-.f64 (exp.f64 (.f64 -1/2 (+.f64 (.f64 -1 (log.f64 (/.f64 -1 x))) (log.f64 -1)))) 1)

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

localize16.0ms (0.1%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.0b	(pow.f64 (+.f64 1 x) -1/2)
	0.3b	(/.f64 1 (sqrt.f64 x))
✓	8.6b	(-.f64 (/.f64 1 (sqrt.f64 x)) (pow.f64 (+.f64 1 x) -1/2))

Compiler

Compiled 28 to 19 computations (32.1% saved)

series4.0ms (0%)

Counts

2 → 14

Calls

6 calls:

Time	Variable		Point	Expression
1.0ms	x	@	-inf	(-.f64 (/.f64 1 (sqrt.f64 x)) (pow.f64 (+.f64 1 x) -1/2))
1.0ms	x	@	inf	(-.f64 (/.f64 1 (sqrt.f64 x)) (pow.f64 (+.f64 1 x) -1/2))
1.0ms	x	@	0	(-.f64 (/.f64 1 (sqrt.f64 x)) (pow.f64 (+.f64 1 x) -1/2))
1.0ms	x	@	-inf	(pow.f64 (+.f64 1 x) -1/2)
0.0ms	x	@	inf	(pow.f64 (+.f64 1 x) -1/2)

rewrite96.0ms (0.8%)

Algorithm

1×	batch-egg-rewrite

Rules

595×	`prod-diff_binary64`
409×	`log-prod_binary64`
301×	`fma-def_binary64`
266×	`pow-prod-down_binary64`
250×	`pow2_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	9	22
1	206	20
2	2709	20

Stop Event

1×	node limit

Counts

2 → 133

Calls

Call 1

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

Outputs

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

simplify78.0ms (0.7%)

Algorithm

1×	egg-herbie

Rules

469×	`distribute-rgt-out_binary64`
452×	`fma-def_binary64`
309×	`times-frac_binary64`
240×	`fma-neg_binary64`
236×	`associate-/l*_binary64`

Iterations

Useful iterations: 5 (0.0ms)

Iter	Nodes	Cost
0	60	373
1	155	354
2	369	289
3	1025	237
4	3828	215
5	5828	193

Stop Event

1×	node limit

Counts

147 → 157

Calls

Call 1

Inputs
(*.f64 -1 (sqrt.f64 (/.f64 1 x)))
(.f64 -1 (exp.f64 (.f64 -1/2 (+.f64 (*.f64 -1 (log.f64 (/.f64 -1 x))) (log.f64 -1)))))
1
(+.f64 (*.f64 -1/2 x) 1)
(+.f64 (.f64 -1/2 x) (+.f64 1 (.f64 3/8 (pow.f64 x 2))))
(+.f64 (.f64 -1/2 x) (+.f64 1 (+.f64 (.f64 3/8 (pow.f64 x 2)) (*.f64 -5/16 (pow.f64 x 3)))))
(sqrt.f64 (/.f64 1 x))
(+.f64 (sqrt.f64 (/.f64 1 x)) (*.f64 -1/2 (sqrt.f64 (/.f64 1 (pow.f64 x 3)))))
(+.f64 (.f64 3/8 (sqrt.f64 (/.f64 1 (pow.f64 x 5)))) (+.f64 (sqrt.f64 (/.f64 1 x)) (.f64 -1/2 (sqrt.f64 (/.f64 1 (pow.f64 x 3))))))
(+.f64 (.f64 3/8 (sqrt.f64 (/.f64 1 (pow.f64 x 5)))) (+.f64 (.f64 -5/16 (sqrt.f64 (/.f64 1 (pow.f64 x 7)))) (+.f64 (sqrt.f64 (/.f64 1 x)) (*.f64 -1/2 (sqrt.f64 (/.f64 1 (pow.f64 x 3)))))))
(exp.f64 (.f64 -1/2 (+.f64 (.f64 -1 (log.f64 (/.f64 -1 x))) (log.f64 -1))))
(+.f64 (exp.f64 (.f64 -1/2 (+.f64 (.f64 -1 (log.f64 (/.f64 -1 x))) (log.f64 -1)))) (.f64 -1/2 (/.f64 (exp.f64 (.f64 -1/2 (+.f64 (*.f64 -1 (log.f64 (/.f64 -1 x))) (log.f64 -1)))) x)))
(+.f64 (exp.f64 (.f64 -1/2 (+.f64 (.f64 -1 (log.f64 (/.f64 -1 x))) (log.f64 -1)))) (+.f64 (.f64 3/8 (/.f64 (exp.f64 (.f64 -1/2 (+.f64 (.f64 -1 (log.f64 (/.f64 -1 x))) (log.f64 -1)))) (pow.f64 x 2))) (.f64 -1/2 (/.f64 (exp.f64 (.f64 -1/2 (+.f64 (.f64 -1 (log.f64 (/.f64 -1 x))) (log.f64 -1)))) x))))
(+.f64 (exp.f64 (.f64 -1/2 (+.f64 (.f64 -1 (log.f64 (/.f64 -1 x))) (log.f64 -1)))) (+.f64 (.f64 3/8 (/.f64 (exp.f64 (.f64 -1/2 (+.f64 (.f64 -1 (log.f64 (/.f64 -1 x))) (log.f64 -1)))) (pow.f64 x 2))) (+.f64 (.f64 -5/16 (/.f64 (exp.f64 (.f64 -1/2 (+.f64 (.f64 -1 (log.f64 (/.f64 -1 x))) (log.f64 -1)))) (pow.f64 x 3))) (.f64 -1/2 (/.f64 (exp.f64 (.f64 -1/2 (+.f64 (*.f64 -1 (log.f64 (/.f64 -1 x))) (log.f64 -1)))) x)))))

Outputs
(*.f64 -1 (sqrt.f64 (/.f64 1 x)))
(neg.f64 (sqrt.f64 (/.f64 1 x)))
(pow.f64 x -1/2)
(.f64 -1 (exp.f64 (.f64 -1/2 (+.f64 (*.f64 -1 (log.f64 (/.f64 -1 x))) (log.f64 -1)))))
(neg.f64 (sqrt.f64 (/.f64 1 x)))
(pow.f64 x -1/2)
1
(+.f64 (*.f64 -1/2 x) 1)
(fma.f64 -1/2 x 1)
(fma.f64 x -1/2 1)
(+.f64 (.f64 -1/2 x) (+.f64 1 (.f64 3/8 (pow.f64 x 2))))
(+.f64 (fma.f64 -1/2 x 1) (.f64 3/8 (.f64 x x)))
(fma.f64 x -1/2 (fma.f64 3/8 (*.f64 x x) 1))
(fma.f64 x -1/2 (fma.f64 x (*.f64 x 3/8) 1))
(fma.f64 x (fma.f64 x 3/8 -1/2) 1)
(+.f64 (.f64 -1/2 x) (+.f64 1 (+.f64 (.f64 3/8 (pow.f64 x 2)) (*.f64 -5/16 (pow.f64 x 3)))))
(+.f64 (fma.f64 -1/2 x 1) (fma.f64 3/8 (.f64 x x) (.f64 -5/16 (pow.f64 x 3))))
(+.f64 (fma.f64 x -1/2 1) (fma.f64 -5/16 (pow.f64 x 3) (.f64 (.f64 3/8 x) x)))
(fma.f64 x -1/2 (fma.f64 x (*.f64 x 3/8) (fma.f64 -5/16 (pow.f64 x 3) 1)))
(fma.f64 x -1/2 (fma.f64 x (*.f64 x (fma.f64 x -5/16 3/8)) 1))
(fma.f64 x (*.f64 x (fma.f64 x -5/16 3/8)) (fma.f64 x -1/2 1))
(sqrt.f64 (/.f64 1 x))
(neg.f64 (sqrt.f64 (/.f64 1 x)))
(pow.f64 x -1/2)
(+.f64 (sqrt.f64 (/.f64 1 x)) (*.f64 -1/2 (sqrt.f64 (/.f64 1 (pow.f64 x 3)))))
(fma.f64 -1/2 (sqrt.f64 (/.f64 1 (pow.f64 x 3))) (sqrt.f64 (/.f64 1 x)))
(fma.f64 -1/2 (sqrt.f64 (/.f64 1 (pow.f64 x 3))) (pow.f64 x -1/2))
(+.f64 (.f64 3/8 (sqrt.f64 (/.f64 1 (pow.f64 x 5)))) (+.f64 (sqrt.f64 (/.f64 1 x)) (.f64 -1/2 (sqrt.f64 (/.f64 1 (pow.f64 x 3))))))
(fma.f64 3/8 (sqrt.f64 (/.f64 1 (pow.f64 x 5))) (+.f64 (sqrt.f64 (/.f64 1 x)) (*.f64 -1/2 (sqrt.f64 (/.f64 1 (pow.f64 x 3))))))
(fma.f64 3/8 (sqrt.f64 (/.f64 1 (pow.f64 x 5))) (fma.f64 -1/2 (sqrt.f64 (/.f64 1 (pow.f64 x 3))) (sqrt.f64 (/.f64 1 x))))
(fma.f64 -1/2 (sqrt.f64 (/.f64 1 (pow.f64 x 3))) (fma.f64 3/8 (sqrt.f64 (/.f64 1 (pow.f64 x 5))) (sqrt.f64 (/.f64 1 x))))
(fma.f64 3/8 (sqrt.f64 (/.f64 1 (pow.f64 x 5))) (fma.f64 -1/2 (sqrt.f64 (/.f64 1 (pow.f64 x 3))) (pow.f64 x -1/2)))
(+.f64 (.f64 3/8 (sqrt.f64 (/.f64 1 (pow.f64 x 5)))) (+.f64 (.f64 -5/16 (sqrt.f64 (/.f64 1 (pow.f64 x 7)))) (+.f64 (sqrt.f64 (/.f64 1 x)) (*.f64 -1/2 (sqrt.f64 (/.f64 1 (pow.f64 x 3)))))))
(fma.f64 3/8 (sqrt.f64 (/.f64 1 (pow.f64 x 5))) (fma.f64 -5/16 (sqrt.f64 (/.f64 1 (pow.f64 x 7))) (+.f64 (sqrt.f64 (/.f64 1 x)) (*.f64 -1/2 (sqrt.f64 (/.f64 1 (pow.f64 x 3)))))))
(fma.f64 3/8 (sqrt.f64 (/.f64 1 (pow.f64 x 5))) (fma.f64 -5/16 (sqrt.f64 (/.f64 1 (pow.f64 x 7))) (fma.f64 -1/2 (sqrt.f64 (/.f64 1 (pow.f64 x 3))) (sqrt.f64 (/.f64 1 x)))))
(fma.f64 3/8 (sqrt.f64 (/.f64 1 (pow.f64 x 5))) (fma.f64 -1/2 (sqrt.f64 (/.f64 1 (pow.f64 x 3))) (fma.f64 -5/16 (sqrt.f64 (/.f64 1 (pow.f64 x 7))) (sqrt.f64 (/.f64 1 x)))))
(fma.f64 -1/2 (sqrt.f64 (/.f64 1 (pow.f64 x 3))) (fma.f64 3/8 (sqrt.f64 (/.f64 1 (pow.f64 x 5))) (fma.f64 -5/16 (sqrt.f64 (/.f64 1 (pow.f64 x 7))) (sqrt.f64 (/.f64 1 x)))))
(fma.f64 -1/2 (sqrt.f64 (/.f64 1 (pow.f64 x 3))) (fma.f64 3/8 (sqrt.f64 (/.f64 1 (pow.f64 x 5))) (fma.f64 -5/16 (sqrt.f64 (/.f64 1 (pow.f64 x 7))) (pow.f64 x -1/2))))
(exp.f64 (.f64 -1/2 (+.f64 (.f64 -1 (log.f64 (/.f64 -1 x))) (log.f64 -1))))
(neg.f64 (sqrt.f64 (/.f64 1 x)))
(pow.f64 x -1/2)
(+.f64 (exp.f64 (.f64 -1/2 (+.f64 (.f64 -1 (log.f64 (/.f64 -1 x))) (log.f64 -1)))) (.f64 -1/2 (/.f64 (exp.f64 (.f64 -1/2 (+.f64 (*.f64 -1 (log.f64 (/.f64 -1 x))) (log.f64 -1)))) x)))
(+.f64 (pow.f64 (exp.f64 -1/2) (fma.f64 -1 (log.f64 (/.f64 -1 x)) (log.f64 -1))) (*.f64 -1/2 (/.f64 (pow.f64 (exp.f64 -1/2) (fma.f64 -1 (log.f64 (/.f64 -1 x)) (log.f64 -1))) x)))
(fma.f64 -1/2 (/.f64 (pow.f64 (exp.f64 -1/2) (-.f64 (log.f64 -1) (log.f64 (/.f64 -1 x)))) x) (pow.f64 (exp.f64 -1/2) (-.f64 (log.f64 -1) (log.f64 (/.f64 -1 x)))))
(fma.f64 (pow.f64 (/.f64 -1 x) 1/2) (pow.f64 -1 -1/2) (.f64 (/.f64 -1/2 x) (.f64 (pow.f64 (/.f64 -1 x) 1/2) (pow.f64 -1 -1/2))))
(*.f64 (+.f64 (/.f64 -1/2 x) 1) (pow.f64 (exp.f64 -1/2) (log.f64 x)))
(*.f64 (+.f64 1 (/.f64 -1/2 x)) (pow.f64 x -1/2))
(+.f64 (/.f64 -1/2 (pow.f64 x 3/2)) (pow.f64 x -1/2))
(+.f64 (exp.f64 (.f64 -1/2 (+.f64 (.f64 -1 (log.f64 (/.f64 -1 x))) (log.f64 -1)))) (+.f64 (.f64 3/8 (/.f64 (exp.f64 (.f64 -1/2 (+.f64 (.f64 -1 (log.f64 (/.f64 -1 x))) (log.f64 -1)))) (pow.f64 x 2))) (.f64 -1/2 (/.f64 (exp.f64 (.f64 -1/2 (+.f64 (.f64 -1 (log.f64 (/.f64 -1 x))) (log.f64 -1)))) x))))
(+.f64 (pow.f64 (exp.f64 -1/2) (fma.f64 -1 (log.f64 (/.f64 -1 x)) (log.f64 -1))) (fma.f64 3/8 (/.f64 (pow.f64 (exp.f64 -1/2) (fma.f64 -1 (log.f64 (/.f64 -1 x)) (log.f64 -1))) (.f64 x x)) (.f64 -1/2 (/.f64 (pow.f64 (exp.f64 -1/2) (fma.f64 -1 (log.f64 (/.f64 -1 x)) (log.f64 -1))) x))))
(+.f64 (pow.f64 (exp.f64 -1/2) (-.f64 (log.f64 -1) (log.f64 (/.f64 -1 x)))) (fma.f64 3/8 (/.f64 (pow.f64 (exp.f64 -1/2) (-.f64 (log.f64 -1) (log.f64 (/.f64 -1 x)))) (*.f64 x x)) (/.f64 -1/2 (/.f64 x (pow.f64 (exp.f64 -1/2) (-.f64 (log.f64 -1) (log.f64 (/.f64 -1 x))))))))
(fma.f64 (pow.f64 (/.f64 -1 x) 1/2) (pow.f64 -1 -1/2) (.f64 (/.f64 (.f64 (pow.f64 (/.f64 -1 x) 1/2) (pow.f64 -1 -1/2)) x) (+.f64 -1/2 (/.f64 3/8 x))))
(fma.f64 (/.f64 (pow.f64 (exp.f64 -1/2) (log.f64 x)) x) (+.f64 -1/2 (/.f64 3/8 x)) (pow.f64 (exp.f64 -1/2) (log.f64 x)))
(fma.f64 (/.f64 (pow.f64 x -1/2) x) (+.f64 -1/2 (/.f64 3/8 x)) (pow.f64 x -1/2))
(fma.f64 (/.f64 1 (pow.f64 x 3/2)) (+.f64 -1/2 (/.f64 3/8 x)) (pow.f64 x -1/2))
(+.f64 (exp.f64 (.f64 -1/2 (+.f64 (.f64 -1 (log.f64 (/.f64 -1 x))) (log.f64 -1)))) (+.f64 (.f64 3/8 (/.f64 (exp.f64 (.f64 -1/2 (+.f64 (.f64 -1 (log.f64 (/.f64 -1 x))) (log.f64 -1)))) (pow.f64 x 2))) (+.f64 (.f64 -5/16 (/.f64 (exp.f64 (.f64 -1/2 (+.f64 (.f64 -1 (log.f64 (/.f64 -1 x))) (log.f64 -1)))) (pow.f64 x 3))) (.f64 -1/2 (/.f64 (exp.f64 (.f64 -1/2 (+.f64 (*.f64 -1 (log.f64 (/.f64 -1 x))) (log.f64 -1)))) x)))))
(+.f64 (pow.f64 (exp.f64 -1/2) (fma.f64 -1 (log.f64 (/.f64 -1 x)) (log.f64 -1))) (fma.f64 3/8 (/.f64 (pow.f64 (exp.f64 -1/2) (fma.f64 -1 (log.f64 (/.f64 -1 x)) (log.f64 -1))) (.f64 x x)) (fma.f64 -5/16 (/.f64 (pow.f64 (exp.f64 -1/2) (fma.f64 -1 (log.f64 (/.f64 -1 x)) (log.f64 -1))) (pow.f64 x 3)) (.f64 -1/2 (/.f64 (pow.f64 (exp.f64 -1/2) (fma.f64 -1 (log.f64 (/.f64 -1 x)) (log.f64 -1))) x)))))
(+.f64 (pow.f64 (exp.f64 -1/2) (-.f64 (log.f64 -1) (log.f64 (/.f64 -1 x)))) (fma.f64 3/8 (/.f64 (pow.f64 (exp.f64 -1/2) (-.f64 (log.f64 -1) (log.f64 (/.f64 -1 x)))) (*.f64 x x)) (fma.f64 -1/2 (/.f64 (pow.f64 (exp.f64 -1/2) (-.f64 (log.f64 -1) (log.f64 (/.f64 -1 x)))) x) (/.f64 -5/16 (/.f64 (pow.f64 x 3) (pow.f64 (exp.f64 -1/2) (-.f64 (log.f64 -1) (log.f64 (/.f64 -1 x)))))))))
(fma.f64 (pow.f64 (/.f64 -1 x) 1/2) (pow.f64 -1 -1/2) (fma.f64 -1/2 (/.f64 (.f64 (pow.f64 (/.f64 -1 x) 1/2) (pow.f64 -1 -1/2)) x) (.f64 (*.f64 (/.f64 (pow.f64 (/.f64 -1 x) 1/2) x) (/.f64 (pow.f64 -1 -1/2) x)) (+.f64 3/8 (/.f64 -5/16 x)))))
(+.f64 (pow.f64 (exp.f64 -1/2) (log.f64 x)) (.f64 (/.f64 (pow.f64 (exp.f64 -1/2) (log.f64 x)) x) (+.f64 -1/2 (+.f64 (/.f64 3/8 x) (/.f64 -5/16 (.f64 x x))))))
(fma.f64 (/.f64 1 (pow.f64 x 5/2)) (+.f64 3/8 (/.f64 -5/16 x)) (*.f64 (+.f64 1 (/.f64 -1/2 x)) (pow.f64 x -1/2)))
(fma.f64 (/.f64 1 (pow.f64 x 5/2)) (+.f64 3/8 (/.f64 -5/16 x)) (+.f64 (/.f64 -1/2 (pow.f64 x 3/2)) (pow.f64 x -1/2)))

localize80.0ms (0.7%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.0b	(/.f64 1 (+.f64 1 x))
✓	0.1b	(/.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)))))
✓	0.4b	(/.f64 (+.f64 (pow.f64 x -1/2) (pow.f64 (+.f64 1 x) -1/2)) (-.f64 (/.f64 1 x) (/.f64 1 (+.f64 1 x))))
✓	2.3b	(-.f64 (/.f64 1 x) (/.f64 1 (+.f64 1 x)))

Compiler

Compiled 81 to 63 computations (22.2% saved)

series12.0ms (0.1%)

Counts

3 → 36

Calls

9 calls:

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

rewrite183.0ms (1.6%)

Algorithm

1×	batch-egg-rewrite

Rules

723×	`log-prod_binary64`
662×	`fma-def_binary64`
326×	`fma-neg_binary64`
281×	`log-div_binary64`
259×	`expm1-udef_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	13	72
1	319	42
2	4928	42

Stop Event

1×	node limit

Counts

3 → 329

Calls

Call 1

Inputs

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

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

Outputs

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

simplify78.0ms (0.7%)

Algorithm

1×	egg-herbie

Rules

909×	`fma-def_binary64`
347×	`associate--l+_binary64`
338×	`distribute-rgt-in_binary64`
321×	`associate-/r*_binary64`
303×	`associate-l_binary64`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	214	1907
1	731	1795
2	2349	1505

Stop Event

1×	node limit

Counts

365 → 391

Calls

Call 1

Inputs
(/.f64 1 x)
(-.f64 (/.f64 1 x) 1)
(-.f64 (+.f64 (/.f64 1 x) x) 1)
(-.f64 (+.f64 (*.f64 -1 (pow.f64 x 2)) (+.f64 (/.f64 1 x) x)) 1)
(/.f64 1 (pow.f64 x 2))
(-.f64 (/.f64 1 (pow.f64 x 2)) (/.f64 1 (pow.f64 x 3)))
(-.f64 (+.f64 (/.f64 1 (pow.f64 x 4)) (/.f64 1 (pow.f64 x 2))) (/.f64 1 (pow.f64 x 3)))
(-.f64 (+.f64 (/.f64 1 (pow.f64 x 4)) (/.f64 1 (pow.f64 x 2))) (+.f64 (/.f64 1 (pow.f64 x 5)) (/.f64 1 (pow.f64 x 3))))
(/.f64 1 (pow.f64 x 2))
(-.f64 (/.f64 1 (pow.f64 x 2)) (/.f64 1 (pow.f64 x 3)))
(-.f64 (+.f64 (/.f64 1 (pow.f64 x 4)) (/.f64 1 (pow.f64 x 2))) (/.f64 1 (pow.f64 x 3)))
(-.f64 (+.f64 (/.f64 1 (pow.f64 x 4)) (/.f64 1 (pow.f64 x 2))) (+.f64 (/.f64 1 (pow.f64 x 5)) (/.f64 1 (pow.f64 x 3))))
(*.f64 (+.f64 (pow.f64 x -1/2) 1) x)
(+.f64 (.f64 (+.f64 (pow.f64 x -1/2) 1) x) (.f64 -1 (.f64 (+.f64 1/2 (.f64 -1 (+.f64 1 (pow.f64 x -1/2)))) (pow.f64 x 2))))
(+.f64 (.f64 -1 (.f64 (+.f64 9/8 (+.f64 (pow.f64 x -1/2) (.f64 -1 (+.f64 (pow.f64 x -1/2) 1)))) (pow.f64 x 3))) (+.f64 (.f64 (+.f64 (pow.f64 x -1/2) 1) x) (.f64 -1 (.f64 (+.f64 1/2 (*.f64 -1 (+.f64 1 (pow.f64 x -1/2)))) (pow.f64 x 2)))))
(+.f64 (.f64 -1 (.f64 (+.f64 (pow.f64 x -1/2) (+.f64 23/16 (+.f64 (.f64 -1 (+.f64 1/2 (.f64 -1 (+.f64 (pow.f64 x -1/2) 1)))) (.f64 -2 (+.f64 1 (pow.f64 x -1/2)))))) (pow.f64 x 4))) (+.f64 (.f64 -1 (.f64 (+.f64 9/8 (+.f64 (pow.f64 x -1/2) (.f64 -1 (+.f64 (pow.f64 x -1/2) 1)))) (pow.f64 x 3))) (+.f64 (.f64 (+.f64 (pow.f64 x -1/2) 1) x) (.f64 -1 (.f64 (+.f64 1/2 (.f64 -1 (+.f64 1 (pow.f64 x -1/2)))) (pow.f64 x 2))))))
(*.f64 2 (sqrt.f64 (pow.f64 x 3)))
(+.f64 (.f64 (-.f64 (.f64 -1/2 (sqrt.f64 (/.f64 1 x))) (.f64 -2 (sqrt.f64 (/.f64 1 x)))) x) (.f64 2 (sqrt.f64 (pow.f64 x 3))))
(-.f64 (+.f64 (.f64 3/8 (sqrt.f64 (/.f64 1 x))) (+.f64 (.f64 (-.f64 (.f64 -1/2 (sqrt.f64 (/.f64 1 x))) (.f64 -2 (sqrt.f64 (/.f64 1 x)))) x) (.f64 2 (sqrt.f64 (pow.f64 x 3))))) (+.f64 (.f64 -1 (-.f64 (.f64 -1/2 (sqrt.f64 (/.f64 1 x))) (.f64 -2 (sqrt.f64 (/.f64 1 x))))) (*.f64 2 (sqrt.f64 (/.f64 1 x)))))
(-.f64 (+.f64 (.f64 3/8 (sqrt.f64 (/.f64 1 x))) (+.f64 (.f64 (-.f64 (.f64 -1/2 (sqrt.f64 (/.f64 1 x))) (.f64 -2 (sqrt.f64 (/.f64 1 x)))) x) (+.f64 (.f64 -5/16 (sqrt.f64 (/.f64 1 (pow.f64 x 3)))) (.f64 2 (sqrt.f64 (pow.f64 x 3)))))) (+.f64 (.f64 -1 (-.f64 (.f64 -1/2 (sqrt.f64 (/.f64 1 x))) (.f64 -2 (sqrt.f64 (/.f64 1 x))))) (+.f64 (.f64 -1 (/.f64 (-.f64 (.f64 3/8 (sqrt.f64 (/.f64 1 x))) (+.f64 (.f64 -1 (-.f64 (.f64 -1/2 (sqrt.f64 (/.f64 1 x))) (.f64 -2 (sqrt.f64 (/.f64 1 x))))) (.f64 2 (sqrt.f64 (/.f64 1 x))))) x)) (+.f64 (.f64 -1/2 (sqrt.f64 (/.f64 1 (pow.f64 x 3)))) (*.f64 2 (sqrt.f64 (/.f64 1 x)))))))
(.f64 2 (.f64 (exp.f64 (.f64 -1/2 (+.f64 (.f64 -1 (log.f64 (/.f64 -1 x))) (log.f64 -1)))) (pow.f64 x 2)))
(+.f64 (.f64 -1 (.f64 (-.f64 (.f64 1/2 (exp.f64 (.f64 -1/2 (+.f64 (.f64 -1 (log.f64 (/.f64 -1 x))) (log.f64 -1))))) (.f64 2 (exp.f64 (.f64 -1/2 (+.f64 (.f64 -1 (log.f64 (/.f64 -1 x))) (log.f64 -1)))))) x)) (.f64 2 (.f64 (exp.f64 (.f64 -1/2 (+.f64 (.f64 -1 (log.f64 (/.f64 -1 x))) (log.f64 -1)))) (pow.f64 x 2))))
(-.f64 (+.f64 (.f64 -1 (.f64 (-.f64 (.f64 1/2 (exp.f64 (.f64 -1/2 (+.f64 (.f64 -1 (log.f64 (/.f64 -1 x))) (log.f64 -1))))) (.f64 2 (exp.f64 (.f64 -1/2 (+.f64 (.f64 -1 (log.f64 (/.f64 -1 x))) (log.f64 -1)))))) x)) (+.f64 (.f64 3/8 (exp.f64 (.f64 -1/2 (+.f64 (.f64 -1 (log.f64 (/.f64 -1 x))) (log.f64 -1))))) (.f64 2 (.f64 (exp.f64 (.f64 -1/2 (+.f64 (.f64 -1 (log.f64 (/.f64 -1 x))) (log.f64 -1)))) (pow.f64 x 2))))) (.f64 1/2 (exp.f64 (.f64 -1/2 (+.f64 (.f64 -1 (log.f64 (/.f64 -1 x))) (log.f64 -1))))))
(-.f64 (+.f64 (.f64 -1 (/.f64 (-.f64 (.f64 5/16 (exp.f64 (.f64 -1/2 (+.f64 (.f64 -1 (log.f64 (/.f64 -1 x))) (log.f64 -1))))) (.f64 3/8 (exp.f64 (.f64 -1/2 (+.f64 (.f64 -1 (log.f64 (/.f64 -1 x))) (log.f64 -1)))))) x)) (+.f64 (.f64 -1 (.f64 (-.f64 (.f64 1/2 (exp.f64 (.f64 -1/2 (+.f64 (.f64 -1 (log.f64 (/.f64 -1 x))) (log.f64 -1))))) (.f64 2 (exp.f64 (.f64 -1/2 (+.f64 (.f64 -1 (log.f64 (/.f64 -1 x))) (log.f64 -1)))))) x)) (+.f64 (.f64 3/8 (exp.f64 (.f64 -1/2 (+.f64 (.f64 -1 (log.f64 (/.f64 -1 x))) (log.f64 -1))))) (.f64 2 (.f64 (exp.f64 (.f64 -1/2 (+.f64 (.f64 -1 (log.f64 (/.f64 -1 x))) (log.f64 -1)))) (pow.f64 x 2)))))) (.f64 1/2 (exp.f64 (.f64 -1/2 (+.f64 (*.f64 -1 (log.f64 (/.f64 -1 x))) (log.f64 -1))))))
(/.f64 1 (*.f64 (+.f64 (pow.f64 x -1/2) 1) x))
(-.f64 (+.f64 (/.f64 1 (.f64 (+.f64 (pow.f64 x -1/2) 1) x)) (.f64 1/2 (/.f64 1 (*.f64 (+.f64 1 (pow.f64 x -1/2)) (+.f64 (pow.f64 x -1/2) 1))))) (/.f64 1 (+.f64 (pow.f64 x -1/2) 1)))
(-.f64 (+.f64 (/.f64 1 (.f64 (+.f64 (pow.f64 x -1/2) 1) x)) (+.f64 (.f64 (-.f64 (/.f64 1 (+.f64 (pow.f64 x -1/2) 1)) (+.f64 (.f64 3/8 (/.f64 1 (.f64 (+.f64 1 (pow.f64 x -1/2)) (+.f64 (pow.f64 x -1/2) 1)))) (.f64 -1/2 (/.f64 (-.f64 (.f64 1/2 (/.f64 1 (.f64 (+.f64 1 (pow.f64 x -1/2)) (+.f64 (pow.f64 x -1/2) 1)))) (/.f64 1 (+.f64 1 (pow.f64 x -1/2)))) (+.f64 (pow.f64 x -1/2) 1))))) x) (.f64 1/2 (/.f64 1 (*.f64 (+.f64 1 (pow.f64 x -1/2)) (+.f64 (pow.f64 x -1/2) 1)))))) (/.f64 1 (+.f64 (pow.f64 x -1/2) 1)))
(-.f64 (+.f64 (/.f64 1 (.f64 (+.f64 (pow.f64 x -1/2) 1) x)) (+.f64 (.f64 (-.f64 (.f64 5/16 (/.f64 1 (.f64 (+.f64 1 (pow.f64 x -1/2)) (+.f64 (pow.f64 x -1/2) 1)))) (+.f64 (.f64 -1/2 (/.f64 (-.f64 (/.f64 1 (+.f64 1 (pow.f64 x -1/2))) (+.f64 (.f64 -1/2 (/.f64 (-.f64 (.f64 1/2 (/.f64 1 (.f64 (+.f64 1 (pow.f64 x -1/2)) (+.f64 (pow.f64 x -1/2) 1)))) (/.f64 1 (+.f64 (pow.f64 x -1/2) 1))) (+.f64 1 (pow.f64 x -1/2)))) (.f64 3/8 (/.f64 1 (.f64 (+.f64 1 (pow.f64 x -1/2)) (+.f64 (pow.f64 x -1/2) 1)))))) (+.f64 (pow.f64 x -1/2) 1))) (+.f64 (.f64 3/8 (/.f64 (-.f64 (.f64 1/2 (/.f64 1 (.f64 (+.f64 1 (pow.f64 x -1/2)) (+.f64 (pow.f64 x -1/2) 1)))) (/.f64 1 (+.f64 1 (pow.f64 x -1/2)))) (+.f64 (pow.f64 x -1/2) 1))) (/.f64 1 (+.f64 (pow.f64 x -1/2) 1))))) (pow.f64 x 2)) (+.f64 (.f64 (-.f64 (/.f64 1 (+.f64 (pow.f64 x -1/2) 1)) (+.f64 (.f64 3/8 (/.f64 1 (.f64 (+.f64 1 (pow.f64 x -1/2)) (+.f64 (pow.f64 x -1/2) 1)))) (.f64 -1/2 (/.f64 (-.f64 (.f64 1/2 (/.f64 1 (.f64 (+.f64 1 (pow.f64 x -1/2)) (+.f64 (pow.f64 x -1/2) 1)))) (/.f64 1 (+.f64 1 (pow.f64 x -1/2)))) (+.f64 (pow.f64 x -1/2) 1))))) x) (.f64 1/2 (/.f64 1 (*.f64 (+.f64 1 (pow.f64 x -1/2)) (+.f64 (pow.f64 x -1/2) 1))))))) (/.f64 1 (+.f64 (pow.f64 x -1/2) 1)))
(*.f64 1/2 (sqrt.f64 (/.f64 1 (pow.f64 x 3))))
(-.f64 (+.f64 (.f64 1/2 (sqrt.f64 (/.f64 1 (pow.f64 x 3)))) (.f64 -1/2 (sqrt.f64 (/.f64 1 (pow.f64 x 5))))) (*.f64 -1/8 (sqrt.f64 (/.f64 1 (pow.f64 x 5)))))
(-.f64 (+.f64 (.f64 1/2 (sqrt.f64 (/.f64 1 (pow.f64 x 7)))) (+.f64 (.f64 1/2 (sqrt.f64 (/.f64 1 (pow.f64 x 3)))) (.f64 -1/2 (sqrt.f64 (/.f64 1 (pow.f64 x 5)))))) (+.f64 (.f64 -1/8 (sqrt.f64 (/.f64 1 (pow.f64 x 5)))) (+.f64 (.f64 -1/4 (/.f64 (-.f64 (.f64 -1/2 (sqrt.f64 x)) (.f64 -1/8 (sqrt.f64 x))) (pow.f64 x 4))) (.f64 3/32 (sqrt.f64 (/.f64 1 (pow.f64 x 7)))))))
(-.f64 (+.f64 (.f64 -1/2 (sqrt.f64 (/.f64 1 (pow.f64 x 9)))) (+.f64 (.f64 1/2 (sqrt.f64 (/.f64 1 (pow.f64 x 7)))) (+.f64 (.f64 -1/2 (sqrt.f64 (/.f64 1 (pow.f64 x 5)))) (.f64 1/2 (sqrt.f64 (/.f64 1 (pow.f64 x 3))))))) (+.f64 (.f64 -1/8 (sqrt.f64 (/.f64 1 (pow.f64 x 5)))) (+.f64 (.f64 3/16 (/.f64 (-.f64 (.f64 -1/2 (sqrt.f64 x)) (.f64 -1/8 (sqrt.f64 x))) (pow.f64 x 5))) (+.f64 (.f64 -1/4 (/.f64 (-.f64 (.f64 1/2 (sqrt.f64 x)) (+.f64 (.f64 3/32 (sqrt.f64 x)) (.f64 -1/4 (-.f64 (.f64 -1/2 (sqrt.f64 x)) (.f64 -1/8 (sqrt.f64 x)))))) (pow.f64 x 5))) (+.f64 (.f64 -5/64 (sqrt.f64 (/.f64 1 (pow.f64 x 9)))) (+.f64 (.f64 -1/4 (/.f64 (-.f64 (.f64 -1/2 (sqrt.f64 x)) (.f64 -1/8 (sqrt.f64 x))) (pow.f64 x 4))) (*.f64 3/32 (sqrt.f64 (/.f64 1 (pow.f64 x 7))))))))))
(/.f64 1/2 (.f64 (exp.f64 (.f64 -1/2 (+.f64 (*.f64 -1 (log.f64 (/.f64 -1 x))) (log.f64 -1)))) (pow.f64 x 2)))
(-.f64 (.f64 1/2 (/.f64 1 (.f64 (exp.f64 (.f64 -1/2 (+.f64 (.f64 -1 (log.f64 (/.f64 -1 x))) (log.f64 -1)))) (pow.f64 x 2)))) (.f64 3/8 (/.f64 1 (.f64 (exp.f64 (.f64 -1/2 (+.f64 (.f64 -1 (log.f64 (/.f64 -1 x))) (log.f64 -1)))) (pow.f64 x 3)))))
(-.f64 (+.f64 (.f64 1/2 (/.f64 1 (.f64 (exp.f64 (.f64 -1/2 (+.f64 (.f64 -1 (log.f64 (/.f64 -1 x))) (log.f64 -1)))) (pow.f64 x 2)))) (.f64 5/16 (/.f64 1 (.f64 (exp.f64 (.f64 -1/2 (+.f64 (.f64 -1 (log.f64 (/.f64 -1 x))) (log.f64 -1)))) (pow.f64 x 4))))) (.f64 3/8 (/.f64 1 (.f64 (exp.f64 (.f64 -1/2 (+.f64 (.f64 -1 (log.f64 (/.f64 -1 x))) (log.f64 -1)))) (pow.f64 x 3)))))
(-.f64 (+.f64 (.f64 1/2 (/.f64 1 (.f64 (exp.f64 (.f64 -1/2 (+.f64 (.f64 -1 (log.f64 (/.f64 -1 x))) (log.f64 -1)))) (pow.f64 x 2)))) (.f64 5/16 (/.f64 1 (.f64 (exp.f64 (.f64 -1/2 (+.f64 (.f64 -1 (log.f64 (/.f64 -1 x))) (log.f64 -1)))) (pow.f64 x 4))))) (+.f64 (.f64 3/8 (/.f64 1 (.f64 (exp.f64 (.f64 -1/2 (+.f64 (.f64 -1 (log.f64 (/.f64 -1 x))) (log.f64 -1)))) (pow.f64 x 3)))) (.f64 35/128 (/.f64 1 (.f64 (exp.f64 (.f64 -1/2 (+.f64 (.f64 -1 (log.f64 (/.f64 -1 x))) (log.f64 -1)))) (pow.f64 x 5))))))

Outputs
(/.f64 1 x)
(-.f64 (/.f64 1 x) 1)
(+.f64 (/.f64 1 x) -1)
(-.f64 (+.f64 (/.f64 1 x) x) 1)
(+.f64 (/.f64 1 x) (-.f64 x 1))
(+.f64 x (+.f64 (/.f64 1 x) -1))
(-.f64 (+.f64 (*.f64 -1 (pow.f64 x 2)) (+.f64 (/.f64 1 x) x)) 1)
(+.f64 (fma.f64 -1 (*.f64 x x) (+.f64 x (/.f64 1 x))) -1)
(+.f64 -1 (-.f64 (+.f64 x (/.f64 1 x)) (*.f64 x x)))
(+.f64 (+.f64 x (/.f64 1 x)) (fma.f64 x (neg.f64 x) -1))
(/.f64 1 (pow.f64 x 2))
(/.f64 1 (*.f64 x x))
(-.f64 (/.f64 1 (pow.f64 x 2)) (/.f64 1 (pow.f64 x 3)))
(-.f64 (/.f64 1 (*.f64 x x)) (/.f64 1 (pow.f64 x 3)))
(+.f64 (/.f64 1 (*.f64 x x)) (/.f64 -1 (pow.f64 x 3)))
(-.f64 (+.f64 (/.f64 1 (pow.f64 x 4)) (/.f64 1 (pow.f64 x 2))) (/.f64 1 (pow.f64 x 3)))
(+.f64 (/.f64 1 (pow.f64 x 4)) (-.f64 (/.f64 1 (*.f64 x x)) (/.f64 1 (pow.f64 x 3))))
(+.f64 (/.f64 1 (*.f64 x x)) (+.f64 (/.f64 1 (pow.f64 x 4)) (/.f64 -1 (pow.f64 x 3))))
(-.f64 (+.f64 (/.f64 1 (pow.f64 x 4)) (/.f64 1 (pow.f64 x 2))) (+.f64 (/.f64 1 (pow.f64 x 5)) (/.f64 1 (pow.f64 x 3))))
(-.f64 (+.f64 (/.f64 1 (*.f64 x x)) (/.f64 1 (pow.f64 x 4))) (+.f64 (/.f64 1 (pow.f64 x 3)) (/.f64 1 (pow.f64 x 5))))
(-.f64 (+.f64 (/.f64 1 (*.f64 x x)) (+.f64 (/.f64 1 (pow.f64 x 4)) (/.f64 -1 (pow.f64 x 3)))) (/.f64 1 (pow.f64 x 5)))
(+.f64 (/.f64 1 (*.f64 x x)) (-.f64 (+.f64 (/.f64 1 (pow.f64 x 4)) (/.f64 -1 (pow.f64 x 3))) (/.f64 1 (pow.f64 x 5))))
(/.f64 1 (pow.f64 x 2))
(/.f64 1 (*.f64 x x))
(-.f64 (/.f64 1 (pow.f64 x 2)) (/.f64 1 (pow.f64 x 3)))
(-.f64 (/.f64 1 (*.f64 x x)) (/.f64 1 (pow.f64 x 3)))
(+.f64 (/.f64 1 (*.f64 x x)) (/.f64 -1 (pow.f64 x 3)))
(-.f64 (+.f64 (/.f64 1 (pow.f64 x 4)) (/.f64 1 (pow.f64 x 2))) (/.f64 1 (pow.f64 x 3)))
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(-.f64 (+.f64 (/.f64 1 (.f64 (+.f64 (pow.f64 x -1/2) 1) x)) (+.f64 (.f64 (-.f64 (.f64 5/16 (/.f64 1 (.f64 (+.f64 1 (pow.f64 x -1/2)) (+.f64 (pow.f64 x -1/2) 1)))) (+.f64 (.f64 -1/2 (/.f64 (-.f64 (/.f64 1 (+.f64 1 (pow.f64 x -1/2))) (+.f64 (.f64 -1/2 (/.f64 (-.f64 (.f64 1/2 (/.f64 1 (.f64 (+.f64 1 (pow.f64 x -1/2)) (+.f64 (pow.f64 x -1/2) 1)))) (/.f64 1 (+.f64 (pow.f64 x -1/2) 1))) (+.f64 1 (pow.f64 x -1/2)))) (.f64 3/8 (/.f64 1 (.f64 (+.f64 1 (pow.f64 x -1/2)) (+.f64 (pow.f64 x -1/2) 1)))))) (+.f64 (pow.f64 x -1/2) 1))) (+.f64 (.f64 3/8 (/.f64 (-.f64 (.f64 1/2 (/.f64 1 (.f64 (+.f64 1 (pow.f64 x -1/2)) (+.f64 (pow.f64 x -1/2) 1)))) (/.f64 1 (+.f64 1 (pow.f64 x -1/2)))) (+.f64 (pow.f64 x -1/2) 1))) (/.f64 1 (+.f64 (pow.f64 x -1/2) 1))))) (pow.f64 x 2)) (+.f64 (.f64 (-.f64 (/.f64 1 (+.f64 (pow.f64 x -1/2) 1)) (+.f64 (.f64 3/8 (/.f64 1 (.f64 (+.f64 1 (pow.f64 x -1/2)) (+.f64 (pow.f64 x -1/2) 1)))) (.f64 -1/2 (/.f64 (-.f64 (.f64 1/2 (/.f64 1 (.f64 (+.f64 1 (pow.f64 x -1/2)) (+.f64 (pow.f64 x -1/2) 1)))) (/.f64 1 (+.f64 1 (pow.f64 x -1/2)))) (+.f64 (pow.f64 x -1/2) 1))))) x) (.f64 1/2 (/.f64 1 (*.f64 (+.f64 1 (pow.f64 x -1/2)) (+.f64 (pow.f64 x -1/2) 1))))))) (/.f64 1 (+.f64 (pow.f64 x -1/2) 1)))
(+.f64 (/.f64 1 (.f64 x (+.f64 1 (pow.f64 x -1/2)))) (-.f64 (fma.f64 (-.f64 (/.f64 5/16 (.f64 (+.f64 1 (pow.f64 x -1/2)) (+.f64 1 (pow.f64 x -1/2)))) (fma.f64 -1/2 (/.f64 (-.f64 (/.f64 1 (+.f64 1 (pow.f64 x -1/2))) (fma.f64 -1/2 (/.f64 (-.f64 (/.f64 1/2 (.f64 (+.f64 1 (pow.f64 x -1/2)) (+.f64 1 (pow.f64 x -1/2)))) (/.f64 1 (+.f64 1 (pow.f64 x -1/2)))) (+.f64 1 (pow.f64 x -1/2))) (/.f64 3/8 (.f64 (+.f64 1 (pow.f64 x -1/2)) (+.f64 1 (pow.f64 x -1/2)))))) (+.f64 1 (pow.f64 x -1/2))) (fma.f64 3/8 (/.f64 (-.f64 (/.f64 1/2 (.f64 (+.f64 1 (pow.f64 x -1/2)) (+.f64 1 (pow.f64 x -1/2)))) (/.f64 1 (+.f64 1 (pow.f64 x -1/2)))) (+.f64 1 (pow.f64 x -1/2))) (/.f64 1 (+.f64 1 (pow.f64 x -1/2)))))) (.f64 x x) (fma.f64 (-.f64 (/.f64 1 (+.f64 1 (pow.f64 x -1/2))) (fma.f64 -1/2 (/.f64 (-.f64 (/.f64 1/2 (.f64 (+.f64 1 (pow.f64 x -1/2)) (+.f64 1 (pow.f64 x -1/2)))) (/.f64 1 (+.f64 1 (pow.f64 x -1/2)))) (+.f64 1 (pow.f64 x -1/2))) (/.f64 3/8 (.f64 (+.f64 1 (pow.f64 x -1/2)) (+.f64 1 (pow.f64 x -1/2)))))) x (/.f64 1/2 (*.f64 (+.f64 1 (pow.f64 x -1/2)) (+.f64 1 (pow.f64 x -1/2)))))) (/.f64 1 (+.f64 1 (pow.f64 x -1/2)))))
(+.f64 (/.f64 1 (.f64 x (+.f64 1 (pow.f64 x -1/2)))) (+.f64 (fma.f64 (.f64 x x) (-.f64 (/.f64 5/16 (.f64 (+.f64 1 (pow.f64 x -1/2)) (+.f64 1 (pow.f64 x -1/2)))) (fma.f64 -1/2 (/.f64 (-.f64 (/.f64 1 (+.f64 1 (pow.f64 x -1/2))) (fma.f64 -1/2 (/.f64 (+.f64 (/.f64 1/2 (.f64 (+.f64 1 (pow.f64 x -1/2)) (+.f64 1 (pow.f64 x -1/2)))) (/.f64 -1 (+.f64 1 (pow.f64 x -1/2)))) (+.f64 1 (pow.f64 x -1/2))) (/.f64 3/8 (.f64 (+.f64 1 (pow.f64 x -1/2)) (+.f64 1 (pow.f64 x -1/2)))))) (+.f64 1 (pow.f64 x -1/2))) (fma.f64 3/8 (/.f64 (+.f64 (/.f64 1/2 (.f64 (+.f64 1 (pow.f64 x -1/2)) (+.f64 1 (pow.f64 x -1/2)))) (/.f64 -1 (+.f64 1 (pow.f64 x -1/2)))) (+.f64 1 (pow.f64 x -1/2))) (/.f64 1 (+.f64 1 (pow.f64 x -1/2)))))) (fma.f64 x (-.f64 (/.f64 1 (+.f64 1 (pow.f64 x -1/2))) (fma.f64 -1/2 (/.f64 (+.f64 (/.f64 1/2 (.f64 (+.f64 1 (pow.f64 x -1/2)) (+.f64 1 (pow.f64 x -1/2)))) (/.f64 -1 (+.f64 1 (pow.f64 x -1/2)))) (+.f64 1 (pow.f64 x -1/2))) (/.f64 3/8 (.f64 (+.f64 1 (pow.f64 x -1/2)) (+.f64 1 (pow.f64 x -1/2)))))) (/.f64 1/2 (*.f64 (+.f64 1 (pow.f64 x -1/2)) (+.f64 1 (pow.f64 x -1/2)))))) (/.f64 -1 (+.f64 1 (pow.f64 x -1/2)))))
(+.f64 (/.f64 1 (+.f64 x (sqrt.f64 x))) (fma.f64 x (.f64 x (-.f64 (/.f64 5/16 (.f64 (-.f64 -1 (pow.f64 x -1/2)) (-.f64 -1 (pow.f64 x -1/2)))) (fma.f64 -1/2 (-.f64 (/.f64 (+.f64 (/.f64 1 (+.f64 1 (pow.f64 x -1/2))) (.f64 1/2 (+.f64 (/.f64 1/2 (pow.f64 (+.f64 1 (pow.f64 x -1/2)) 3)) (/.f64 -1 (.f64 (-.f64 -1 (pow.f64 x -1/2)) (-.f64 -1 (pow.f64 x -1/2))))))) (+.f64 1 (pow.f64 x -1/2))) (/.f64 3/8 (pow.f64 (+.f64 1 (pow.f64 x -1/2)) 3))) (fma.f64 3/8 (+.f64 (/.f64 1/2 (pow.f64 (+.f64 1 (pow.f64 x -1/2)) 3)) (/.f64 -1 (.f64 (-.f64 -1 (pow.f64 x -1/2)) (-.f64 -1 (pow.f64 x -1/2))))) (/.f64 1 (+.f64 1 (pow.f64 x -1/2))))))) (+.f64 (fma.f64 x (-.f64 (/.f64 1 (+.f64 1 (pow.f64 x -1/2))) (fma.f64 -1/2 (+.f64 (/.f64 1/2 (pow.f64 (+.f64 1 (pow.f64 x -1/2)) 3)) (/.f64 -1 (.f64 (-.f64 -1 (pow.f64 x -1/2)) (-.f64 -1 (pow.f64 x -1/2))))) (/.f64 3/8 (.f64 (-.f64 -1 (pow.f64 x -1/2)) (-.f64 -1 (pow.f64 x -1/2)))))) (/.f64 1/2 (.f64 (-.f64 -1 (pow.f64 x -1/2)) (-.f64 -1 (pow.f64 x -1/2))))) (/.f64 1 (-.f64 -1 (pow.f64 x -1/2))))))
(*.f64 1/2 (sqrt.f64 (/.f64 1 (pow.f64 x 3))))
(-.f64 (+.f64 (.f64 1/2 (sqrt.f64 (/.f64 1 (pow.f64 x 3)))) (.f64 -1/2 (sqrt.f64 (/.f64 1 (pow.f64 x 5))))) (*.f64 -1/8 (sqrt.f64 (/.f64 1 (pow.f64 x 5)))))
(+.f64 (fma.f64 1/2 (sqrt.f64 (/.f64 1 (pow.f64 x 3))) (.f64 -1/2 (sqrt.f64 (/.f64 1 (pow.f64 x 5))))) (.f64 1/8 (sqrt.f64 (/.f64 1 (pow.f64 x 5)))))
(fma.f64 1/2 (sqrt.f64 (/.f64 1 (pow.f64 x 3))) (*.f64 (sqrt.f64 (/.f64 1 (pow.f64 x 5))) -3/8))
(-.f64 (+.f64 (.f64 1/2 (sqrt.f64 (/.f64 1 (pow.f64 x 7)))) (+.f64 (.f64 1/2 (sqrt.f64 (/.f64 1 (pow.f64 x 3)))) (.f64 -1/2 (sqrt.f64 (/.f64 1 (pow.f64 x 5)))))) (+.f64 (.f64 -1/8 (sqrt.f64 (/.f64 1 (pow.f64 x 5)))) (+.f64 (.f64 -1/4 (/.f64 (-.f64 (.f64 -1/2 (sqrt.f64 x)) (.f64 -1/8 (sqrt.f64 x))) (pow.f64 x 4))) (.f64 3/32 (sqrt.f64 (/.f64 1 (pow.f64 x 7)))))))
(-.f64 (fma.f64 1/2 (sqrt.f64 (/.f64 1 (pow.f64 x 7))) (fma.f64 1/2 (sqrt.f64 (/.f64 1 (pow.f64 x 3))) (.f64 -1/2 (sqrt.f64 (/.f64 1 (pow.f64 x 5)))))) (fma.f64 -1/8 (sqrt.f64 (/.f64 1 (pow.f64 x 5))) (fma.f64 -1/4 (/.f64 (.f64 (sqrt.f64 x) -3/8) (pow.f64 x 4)) (*.f64 (sqrt.f64 (/.f64 1 (pow.f64 x 7))) 3/32))))
(fma.f64 1/2 (sqrt.f64 (/.f64 1 (pow.f64 x 7))) (-.f64 (fma.f64 1/2 (sqrt.f64 (/.f64 1 (pow.f64 x 3))) (.f64 (sqrt.f64 (/.f64 1 (pow.f64 x 5))) -3/8)) (fma.f64 (sqrt.f64 (/.f64 1 (pow.f64 x 7))) 3/32 (/.f64 (.f64 (sqrt.f64 x) 3/32) (pow.f64 x 4)))))
(-.f64 (fma.f64 1/2 (+.f64 (sqrt.f64 (/.f64 1 (pow.f64 x 7))) (sqrt.f64 (/.f64 1 (pow.f64 x 3)))) (*.f64 (sqrt.f64 (/.f64 1 (pow.f64 x 5))) -3/8)) (fma.f64 (sqrt.f64 (/.f64 1 (pow.f64 x 7))) 3/32 (/.f64 (sqrt.f64 x) (/.f64 (pow.f64 x 4) 3/32))))
(-.f64 (+.f64 (.f64 -1/2 (sqrt.f64 (/.f64 1 (pow.f64 x 9)))) (+.f64 (.f64 1/2 (sqrt.f64 (/.f64 1 (pow.f64 x 7)))) (+.f64 (.f64 -1/2 (sqrt.f64 (/.f64 1 (pow.f64 x 5)))) (.f64 1/2 (sqrt.f64 (/.f64 1 (pow.f64 x 3))))))) (+.f64 (.f64 -1/8 (sqrt.f64 (/.f64 1 (pow.f64 x 5)))) (+.f64 (.f64 3/16 (/.f64 (-.f64 (.f64 -1/2 (sqrt.f64 x)) (.f64 -1/8 (sqrt.f64 x))) (pow.f64 x 5))) (+.f64 (.f64 -1/4 (/.f64 (-.f64 (.f64 1/2 (sqrt.f64 x)) (+.f64 (.f64 3/32 (sqrt.f64 x)) (.f64 -1/4 (-.f64 (.f64 -1/2 (sqrt.f64 x)) (.f64 -1/8 (sqrt.f64 x)))))) (pow.f64 x 5))) (+.f64 (.f64 -5/64 (sqrt.f64 (/.f64 1 (pow.f64 x 9)))) (+.f64 (.f64 -1/4 (/.f64 (-.f64 (.f64 -1/2 (sqrt.f64 x)) (.f64 -1/8 (sqrt.f64 x))) (pow.f64 x 4))) (*.f64 3/32 (sqrt.f64 (/.f64 1 (pow.f64 x 7))))))))))
(-.f64 (fma.f64 -1/2 (sqrt.f64 (/.f64 1 (pow.f64 x 9))) (fma.f64 1/2 (sqrt.f64 (/.f64 1 (pow.f64 x 7))) (fma.f64 1/2 (sqrt.f64 (/.f64 1 (pow.f64 x 3))) (.f64 -1/2 (sqrt.f64 (/.f64 1 (pow.f64 x 5))))))) (fma.f64 -1/8 (sqrt.f64 (/.f64 1 (pow.f64 x 5))) (fma.f64 3/16 (/.f64 (.f64 (sqrt.f64 x) -3/8) (pow.f64 x 5)) (fma.f64 -1/4 (/.f64 (-.f64 (.f64 1/2 (sqrt.f64 x)) (fma.f64 3/32 (sqrt.f64 x) (.f64 -1/4 (.f64 (sqrt.f64 x) -3/8)))) (pow.f64 x 5)) (fma.f64 -5/64 (sqrt.f64 (/.f64 1 (pow.f64 x 9))) (fma.f64 -1/4 (/.f64 (.f64 (sqrt.f64 x) -3/8) (pow.f64 x 4)) (*.f64 (sqrt.f64 (/.f64 1 (pow.f64 x 7))) 3/32)))))))
(fma.f64 -1/2 (sqrt.f64 (/.f64 1 (pow.f64 x 9))) (-.f64 (+.f64 (.f64 1/2 (+.f64 (sqrt.f64 (/.f64 1 (pow.f64 x 7))) (sqrt.f64 (/.f64 1 (pow.f64 x 3))))) (.f64 (sqrt.f64 (/.f64 1 (pow.f64 x 5))) -3/8)) (fma.f64 3/16 (/.f64 (sqrt.f64 x) (/.f64 (pow.f64 x 5) -3/8)) (fma.f64 -1/4 (/.f64 (-.f64 (.f64 (sqrt.f64 x) 13/32) (.f64 (sqrt.f64 x) 3/32)) (pow.f64 x 5)) (fma.f64 (sqrt.f64 (/.f64 1 (pow.f64 x 9))) -5/64 (fma.f64 (sqrt.f64 (/.f64 1 (pow.f64 x 7))) 3/32 (/.f64 (*.f64 (sqrt.f64 x) 3/32) (pow.f64 x 4))))))))
(-.f64 (fma.f64 -1/2 (sqrt.f64 (/.f64 1 (pow.f64 x 9))) (fma.f64 1/2 (+.f64 (sqrt.f64 (/.f64 1 (pow.f64 x 7))) (sqrt.f64 (/.f64 1 (pow.f64 x 3)))) (.f64 (sqrt.f64 (/.f64 1 (pow.f64 x 5))) -3/8))) (+.f64 (fma.f64 (sqrt.f64 (/.f64 1 (pow.f64 x 7))) 3/32 (fma.f64 (sqrt.f64 (/.f64 1 (pow.f64 x 9))) -5/64 (/.f64 (sqrt.f64 x) (/.f64 (pow.f64 x 4) 3/32)))) (fma.f64 -1/4 (/.f64 (.f64 (sqrt.f64 x) 5/16) (pow.f64 x 5)) (/.f64 (*.f64 (sqrt.f64 x) -9/128) (pow.f64 x 5)))))
(/.f64 1/2 (.f64 (exp.f64 (.f64 -1/2 (+.f64 (*.f64 -1 (log.f64 (/.f64 -1 x))) (log.f64 -1)))) (pow.f64 x 2)))
(/.f64 1/2 (.f64 (.f64 x x) (pow.f64 (exp.f64 -1/2) (fma.f64 -1 (log.f64 (/.f64 -1 x)) (log.f64 -1)))))
(/.f64 (/.f64 1/2 (pow.f64 (exp.f64 -1/2) (-.f64 (log.f64 -1) (log.f64 (/.f64 -1 x))))) (*.f64 x x))
(/.f64 (/.f64 1/2 (.f64 (pow.f64 (/.f64 -1 x) 1/2) (pow.f64 -1 -1/2))) (.f64 x x))
(-.f64 (.f64 1/2 (/.f64 1 (.f64 (exp.f64 (.f64 -1/2 (+.f64 (.f64 -1 (log.f64 (/.f64 -1 x))) (log.f64 -1)))) (pow.f64 x 2)))) (.f64 3/8 (/.f64 1 (.f64 (exp.f64 (.f64 -1/2 (+.f64 (.f64 -1 (log.f64 (/.f64 -1 x))) (log.f64 -1)))) (pow.f64 x 3)))))
(-.f64 (/.f64 1/2 (.f64 (.f64 x x) (pow.f64 (exp.f64 -1/2) (fma.f64 -1 (log.f64 (/.f64 -1 x)) (log.f64 -1))))) (/.f64 3/8 (*.f64 (pow.f64 x 3) (pow.f64 (exp.f64 -1/2) (fma.f64 -1 (log.f64 (/.f64 -1 x)) (log.f64 -1))))))
(+.f64 (/.f64 (/.f64 1/2 (pow.f64 (exp.f64 -1/2) (-.f64 (log.f64 -1) (log.f64 (/.f64 -1 x))))) (.f64 x x)) (/.f64 -3/8 (.f64 (pow.f64 x 3) (pow.f64 (exp.f64 -1/2) (-.f64 (log.f64 -1) (log.f64 (/.f64 -1 x)))))))
(+.f64 (/.f64 (/.f64 1/2 (.f64 (pow.f64 (/.f64 -1 x) 1/2) (pow.f64 -1 -1/2))) (.f64 x x)) (/.f64 -3/8 (.f64 (pow.f64 (/.f64 -1 x) 1/2) (.f64 (pow.f64 -1 -1/2) (pow.f64 x 3)))))
(-.f64 (+.f64 (.f64 1/2 (/.f64 1 (.f64 (exp.f64 (.f64 -1/2 (+.f64 (.f64 -1 (log.f64 (/.f64 -1 x))) (log.f64 -1)))) (pow.f64 x 2)))) (.f64 5/16 (/.f64 1 (.f64 (exp.f64 (.f64 -1/2 (+.f64 (.f64 -1 (log.f64 (/.f64 -1 x))) (log.f64 -1)))) (pow.f64 x 4))))) (.f64 3/8 (/.f64 1 (.f64 (exp.f64 (.f64 -1/2 (+.f64 (.f64 -1 (log.f64 (/.f64 -1 x))) (log.f64 -1)))) (pow.f64 x 3)))))
(-.f64 (+.f64 (/.f64 1/2 (.f64 (.f64 x x) (pow.f64 (exp.f64 -1/2) (fma.f64 -1 (log.f64 (/.f64 -1 x)) (log.f64 -1))))) (/.f64 5/16 (.f64 (pow.f64 x 4) (pow.f64 (exp.f64 -1/2) (fma.f64 -1 (log.f64 (/.f64 -1 x)) (log.f64 -1)))))) (/.f64 3/8 (.f64 (pow.f64 x 3) (pow.f64 (exp.f64 -1/2) (fma.f64 -1 (log.f64 (/.f64 -1 x)) (log.f64 -1))))))
(+.f64 (/.f64 5/16 (.f64 (pow.f64 x 4) (pow.f64 (exp.f64 -1/2) (-.f64 (log.f64 -1) (log.f64 (/.f64 -1 x)))))) (+.f64 (/.f64 (/.f64 1/2 (pow.f64 (exp.f64 -1/2) (-.f64 (log.f64 -1) (log.f64 (/.f64 -1 x))))) (.f64 x x)) (/.f64 -3/8 (*.f64 (pow.f64 x 3) (pow.f64 (exp.f64 -1/2) (-.f64 (log.f64 -1) (log.f64 (/.f64 -1 x))))))))
(+.f64 (/.f64 5/16 (.f64 (pow.f64 x 4) (.f64 (pow.f64 (/.f64 -1 x) 1/2) (pow.f64 -1 -1/2)))) (+.f64 (/.f64 (/.f64 1/2 (.f64 (pow.f64 (/.f64 -1 x) 1/2) (pow.f64 -1 -1/2))) (.f64 x x)) (/.f64 -3/8 (.f64 (pow.f64 (/.f64 -1 x) 1/2) (.f64 (pow.f64 -1 -1/2) (pow.f64 x 3))))))
(-.f64 (+.f64 (.f64 1/2 (/.f64 1 (.f64 (exp.f64 (.f64 -1/2 (+.f64 (.f64 -1 (log.f64 (/.f64 -1 x))) (log.f64 -1)))) (pow.f64 x 2)))) (.f64 5/16 (/.f64 1 (.f64 (exp.f64 (.f64 -1/2 (+.f64 (.f64 -1 (log.f64 (/.f64 -1 x))) (log.f64 -1)))) (pow.f64 x 4))))) (+.f64 (.f64 3/8 (/.f64 1 (.f64 (exp.f64 (.f64 -1/2 (+.f64 (.f64 -1 (log.f64 (/.f64 -1 x))) (log.f64 -1)))) (pow.f64 x 3)))) (.f64 35/128 (/.f64 1 (.f64 (exp.f64 (.f64 -1/2 (+.f64 (.f64 -1 (log.f64 (/.f64 -1 x))) (log.f64 -1)))) (pow.f64 x 5))))))
(-.f64 (+.f64 (/.f64 1/2 (.f64 (.f64 x x) (pow.f64 (exp.f64 -1/2) (fma.f64 -1 (log.f64 (/.f64 -1 x)) (log.f64 -1))))) (/.f64 5/16 (.f64 (pow.f64 x 4) (pow.f64 (exp.f64 -1/2) (fma.f64 -1 (log.f64 (/.f64 -1 x)) (log.f64 -1)))))) (+.f64 (/.f64 3/8 (.f64 (pow.f64 x 3) (pow.f64 (exp.f64 -1/2) (fma.f64 -1 (log.f64 (/.f64 -1 x)) (log.f64 -1))))) (/.f64 35/128 (*.f64 (pow.f64 x 5) (pow.f64 (exp.f64 -1/2) (fma.f64 -1 (log.f64 (/.f64 -1 x)) (log.f64 -1)))))))
(+.f64 (/.f64 (/.f64 1/2 (pow.f64 (exp.f64 -1/2) (-.f64 (log.f64 -1) (log.f64 (/.f64 -1 x))))) (.f64 x x)) (-.f64 (-.f64 (/.f64 5/16 (.f64 (pow.f64 x 4) (pow.f64 (exp.f64 -1/2) (-.f64 (log.f64 -1) (log.f64 (/.f64 -1 x)))))) (/.f64 35/128 (.f64 (pow.f64 x 5) (pow.f64 (exp.f64 -1/2) (-.f64 (log.f64 -1) (log.f64 (/.f64 -1 x))))))) (/.f64 3/8 (.f64 (pow.f64 x 3) (pow.f64 (exp.f64 -1/2) (-.f64 (log.f64 -1) (log.f64 (/.f64 -1 x))))))))
(+.f64 (/.f64 (/.f64 1/2 (.f64 (pow.f64 (/.f64 -1 x) 1/2) (pow.f64 -1 -1/2))) (.f64 x x)) (+.f64 (/.f64 5/16 (.f64 (pow.f64 x 4) (.f64 (pow.f64 (/.f64 -1 x) 1/2) (pow.f64 -1 -1/2)))) (-.f64 (/.f64 -3/8 (.f64 (pow.f64 (/.f64 -1 x) 1/2) (.f64 (pow.f64 -1 -1/2) (pow.f64 x 3)))) (/.f64 (/.f64 (/.f64 35/128 (pow.f64 x 5)) (pow.f64 (/.f64 -1 x) 1/2)) (pow.f64 -1 -1/2)))))

localize54.0ms (0.5%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.3b	(/.f64 1 (sqrt.f64 (cbrt.f64 x)))
✓	0.6b	(cbrt.f64 x)
	0.9b	(cbrt.f64 (/.f64 1 x))
✓	29.6b	(fma.f64 (/.f64 1 (sqrt.f64 (cbrt.f64 x))) (cbrt.f64 (/.f64 1 x)) (/.f64 -1 (sqrt.f64 (+.f64 1 x))))

Compiler

Compiled 50 to 33 computations (34% saved)

series99.0ms (0.9%)

Counts

3 → 13

Calls

9 calls:

Time	Variable		Point	Expression
84.0ms	x	@	0	(/.f64 1 (sqrt.f64 (cbrt.f64 x)))
8.0ms	x	@	inf	(/.f64 1 (sqrt.f64 (cbrt.f64 x)))
2.0ms	x	@	-inf	(/.f64 1 (sqrt.f64 (cbrt.f64 x)))
1.0ms	x	@	-inf	(fma.f64 (/.f64 1 (sqrt.f64 (cbrt.f64 x))) (cbrt.f64 (/.f64 1 x)) (/.f64 -1 (sqrt.f64 (+.f64 1 x))))
1.0ms	x	@	0	(fma.f64 (/.f64 1 (sqrt.f64 (cbrt.f64 x))) (cbrt.f64 (/.f64 1 x)) (/.f64 -1 (sqrt.f64 (+.f64 1 x))))

rewrite73.0ms (0.6%)

Algorithm

1×	batch-egg-rewrite

Rules

517×	`log-prod_binary64`
352×	`prod-diff_binary64`
341×	`pow-prod-down_binary64`
296×	`pow2_binary64`
200×	`pow1/3_binary64`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	13	36
1	268	24
2	3248	21

Stop Event

1×	node limit

Counts

3 → 99

Calls

Call 1

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

Outputs

((#(struct:change #<rule egg-rr> (2) ((x +.f64 (sqrt.f64 (/.f64 1 (+.f64 1 x))) (pow.f64 x -1/2))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 0 (fma.f64 -1 (pow.f64 (+.f64 1 x) -1/2) (pow.f64 x -1/2)))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (pow.f64 x -1/2) (sqrt.f64 (/.f64 1 (+.f64 1 x))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (*.f64 (pow.f64 x -1/2) 1) (sqrt.f64 (/.f64 1 (+.f64 1 x))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (log.f64 (pow.f64 (cbrt.f64 (exp.f64 (fma.f64 -1 (pow.f64 (+.f64 1 x) -1/2) (pow.f64 x -1/2)))) 2)) (log.f64 (cbrt.f64 (exp.f64 (fma.f64 -1 (pow.f64 (+.f64 1 x) -1/2) (pow.f64 x -1/2))))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (log.f64 (sqrt.f64 (exp.f64 (fma.f64 -1 (pow.f64 (+.f64 1 x) -1/2) (pow.f64 x -1/2))))) (log.f64 (sqrt.f64 (exp.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 (fma.f64 -1 (pow.f64 (+.f64 1 x) -1/2) (pow.f64 x -1/2)))) 1)))) (#(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))) (pow.f64 (cbrt.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 (pow.f64 (cbrt.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 (+.f64 (pow.f64 x -3/2) (pow.f64 (neg.f64 (sqrt.f64 (+.f64 1 x))) -3)) (+.f64 (/.f64 1 x) (-.f64 (/.f64 1 (+.f64 1 x)) (*.f64 (pow.f64 x -1/2) (sqrt.f64 (/.f64 1 (+.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) (sqrt.f64 (/.f64 1 (+.f64 1 x)))))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (fma.f64 -1 (pow.f64 (+.f64 1 x) -1/2) (pow.f64 x -1/2)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (fma.f64 -1 (pow.f64 (+.f64 1 x) -1/2) (pow.f64 x -1/2)) 2) 1/2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (fma.f64 -1 (pow.f64 (+.f64 1 x) -1/2) (pow.f64 x -1/2)) 3) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (cbrt.f64 (fma.f64 -1 (pow.f64 (+.f64 1 x) -1/2) (pow.f64 x -1/2))) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (sqrt.f64 (fma.f64 -1 (pow.f64 (+.f64 1 x) -1/2) (pow.f64 x -1/2))) 2)))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.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 log.f64 (exp.f64 (fma.f64 -1 (pow.f64 (+.f64 1 x) -1/2) (pow.f64 x -1/2))))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (+.f64 1 (expm1.f64 (fma.f64 -1 (pow.f64 (+.f64 1 x) -1/2) (pow.f64 x -1/2)))))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (*.f64 (exp.f64 (sqrt.f64 (/.f64 1 (+.f64 1 x)))) (exp.f64 (pow.f64 x -1/2))))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (*.f64 (+.f64 1 (expm1.f64 (sqrt.f64 (/.f64 1 (+.f64 1 x))))) (exp.f64 (pow.f64 x -1/2))))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (*.f64 (exp.f64 (pow.f64 x -1/2)) (+.f64 1 (expm1.f64 (sqrt.f64 (/.f64 1 (+.f64 1 x)))))))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (pow.f64 (fma.f64 -1 (pow.f64 (+.f64 1 x) -1/2) (pow.f64 x -1/2)) 3))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (fma.f64 -1 (pow.f64 (+.f64 1 x) -1/2) (pow.f64 x -1/2))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (log.f64 (fma.f64 -1 (pow.f64 (+.f64 1 x) -1/2) (pow.f64 x -1/2))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (log.f64 (fma.f64 -1 (pow.f64 (+.f64 1 x) -1/2) (pow.f64 x -1/2))) 1))))) (#(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 0 (cbrt.f64 x))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (log.f64 (pow.f64 (cbrt.f64 (exp.f64 (cbrt.f64 x))) 2)) (log.f64 (cbrt.f64 (exp.f64 (cbrt.f64 x)))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (log.f64 (sqrt.f64 (exp.f64 (cbrt.f64 x)))) (log.f64 (sqrt.f64 (exp.f64 (cbrt.f64 x)))))))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (exp.f64 (log1p.f64 (cbrt.f64 x))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 1 (cbrt.f64 x))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 x) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 x 1/6) (pow.f64 x 1/6))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 (cbrt.f64 x)) (pow.f64 (pow.f64 x 1/18) 4))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (pow.f64 x 1/18) 4) (cbrt.f64 (cbrt.f64 x)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 x 1/12) (sqrt.f64 (sqrt.f64 x)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (sqrt.f64 (sqrt.f64 x)) (pow.f64 x 1/12))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 1 1/3) (cbrt.f64 x))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (*.f64 (pow.f64 x 1/6) (cbrt.f64 (cbrt.f64 x))) (pow.f64 x 1/18))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 x 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (cbrt.f64 x) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 x 1/6) 2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (*.f64 x x) 1/6)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (cbrt.f64 x) 2) 1/2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 x 1/18) 6)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (cbrt.f64 (cbrt.f64 x)) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 x 1/12) 4)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (sqrt.f64 x) 2/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 x 3) 1/9)))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f64 (pow.f64 (cbrt.f64 x) 2))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (exp.f64 (cbrt.f64 x)))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (+.f64 1 (expm1.f64 (cbrt.f64 x))))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (cbrt.f64 x)))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (log.f64 (cbrt.f64 x)))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (log.f64 x) 1/3))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (log.f64 (cbrt.f64 x)) 1))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (cbrt.f64 x)))))))

((#(struct:change #<rule egg-rr> (2) ((x +.f64 0 (pow.f64 x -1/6))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (log.f64 (pow.f64 (cbrt.f64 (exp.f64 (pow.f64 x -1/6))) 2)) (log.f64 (cbrt.f64 (exp.f64 (pow.f64 x -1/6)))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (log.f64 (sqrt.f64 (exp.f64 (pow.f64 x -1/6)))) (log.f64 (sqrt.f64 (exp.f64 (pow.f64 x -1/6)))))))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (exp.f64 (log1p.f64 (pow.f64 x -1/6))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 1 (pow.f64 x -1/6))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 x -1/6) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 -1 (/.f64 1 (neg.f64 (pow.f64 x 1/6))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (pow.f64 x 1/18) -2) (pow.f64 (cbrt.f64 x) -1/6))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (cbrt.f64 x) -1/6) (pow.f64 (pow.f64 x 1/18) -2))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 x -1/12) (pow.f64 x -1/12))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (sqrt.f64 (cbrt.f64 (pow.f64 (cbrt.f64 x) -2))) (sqrt.f64 (pow.f64 (pow.f64 x 1/18) -2)))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 x -1/6)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (cbrt.f64 x) -1/2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 x 1/6) -1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 x -1/6) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (/.f64 1 x) 1/6)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (/.f64 1 (cbrt.f64 x)) 1/2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 x -3) 1/18)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (cbrt.f64 x) 2) -1/4)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (pow.f64 x 1/18) -2) 3/2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 x 1/18) -3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (cbrt.f64 x) -1/6) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (cbrt.f64 (cbrt.f64 x)) -3/2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 x 1/12) -2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 x -1/12) 2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (sqrt.f64 x) -1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 x -1/2) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (neg.f64 (neg.f64 (pow.f64 x 1/6))) -1)))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f64 (/.f64 1 (cbrt.f64 x)))))) (#(struct:change #<rule egg-rr> (2) ((x fabs.f64 (pow.f64 x -1/6))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (exp.f64 (pow.f64 x -1/6)))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (+.f64 1 (expm1.f64 (pow.f64 x -1/6))))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (pow.f64 x -1/2))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (pow.f64 x -1/6)))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (log.f64 (pow.f64 x -1/6)))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (log.f64 (pow.f64 x 1/6)) -1))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (log.f64 (pow.f64 x -1/6)) 1))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (pow.f64 x -1/6)))))))

simplify151.0ms (1.3%)

Algorithm

1×	egg-herbie

Rules

1002×	`sqr-pow_binary64`
724×	`unswap-sqr_binary64`
595×	`associate-l_binary64`
504×	`cube-prod_binary64`
428×	`pow-sqr_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	13	125
1	23	125
2	34	125
3	60	125
4	137	125
5	443	125
6	1669	125
7	3003	125
8	3163	125
9	3442	125
10	3758	125
11	4209	125
12	4822	125
13	5632	125
14	6120	125
15	6593	125
16	6862	125
17	7113	125
18	7251	125

Stop Event

1×	node limit

Counts

112 → 102

Calls

Call 1

Inputs
-1
(pow.f64 (/.f64 1 x) 1/6)
(pow.f64 (/.f64 1 x) 1/6)
(pow.f64 (/.f64 1 x) 1/6)
(pow.f64 (/.f64 1 x) 1/6)
(pow.f64 (/.f64 1 x) 1/6)
(pow.f64 (/.f64 1 x) 1/6)
(pow.f64 (/.f64 1 x) 1/6)
(pow.f64 (/.f64 1 x) 1/6)
(*.f64 (pow.f64 (/.f64 -1 x) 1/6) (sqrt.f64 (/.f64 1 (cbrt.f64 -1))))
(*.f64 (pow.f64 (/.f64 -1 x) 1/6) (sqrt.f64 (/.f64 1 (cbrt.f64 -1))))
(*.f64 (pow.f64 (/.f64 -1 x) 1/6) (sqrt.f64 (/.f64 1 (cbrt.f64 -1))))
(*.f64 (pow.f64 (/.f64 -1 x) 1/6) (sqrt.f64 (/.f64 1 (cbrt.f64 -1))))

Outputs
-1
(pow.f64 (/.f64 1 x) 1/6)
(pow.f64 (/.f64 1 x) 1/6)
(pow.f64 (/.f64 1 x) 1/6)
(pow.f64 (/.f64 1 x) 1/6)
(pow.f64 (/.f64 1 x) 1/6)
(pow.f64 (/.f64 1 x) 1/6)
(pow.f64 (/.f64 1 x) 1/6)
(pow.f64 (/.f64 1 x) 1/6)
(*.f64 (pow.f64 (/.f64 -1 x) 1/6) (sqrt.f64 (/.f64 1 (cbrt.f64 -1))))
(*.f64 (sqrt.f64 (/.f64 1 (cbrt.f64 -1))) (pow.f64 (/.f64 -1 x) 1/6))
(*.f64 (pow.f64 (/.f64 -1 x) 1/6) (sqrt.f64 (/.f64 1 (cbrt.f64 -1))))
(*.f64 (sqrt.f64 (/.f64 1 (cbrt.f64 -1))) (pow.f64 (/.f64 -1 x) 1/6))
(*.f64 (pow.f64 (/.f64 -1 x) 1/6) (sqrt.f64 (/.f64 1 (cbrt.f64 -1))))
(*.f64 (sqrt.f64 (/.f64 1 (cbrt.f64 -1))) (pow.f64 (/.f64 -1 x) 1/6))
(*.f64 (pow.f64 (/.f64 -1 x) 1/6) (sqrt.f64 (/.f64 1 (cbrt.f64 -1))))
(*.f64 (sqrt.f64 (/.f64 1 (cbrt.f64 -1))) (pow.f64 (/.f64 -1 x) 1/6))

eval942.0ms (8.3%)

Compiler: Compiled 30084 to 22665 computations (24.7% saved)

prune826.0ms (7.3%)

Pruning

22 alts after pruning (18 fresh and 4 done)

	Pruned	Kept	Total
New	1149	11	1160
Fresh	13	7	20
Picked	1	0	1
Done	2	4	6
Total	1165	22	1187

Error

0.4b

Counts

1187 → 22

Alt Table

Click to see full alt table

Status	Error	Program
▶	31.5b	(pow.f64 x -1/2)
	51.9b	(/.f64 (/.f64 (+.f64 x (-.f64 1 x)) (+.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x))) (+.f64 (+.f64 x 1/2) (/.f64 -1/8 x)))
	50.5b	(/.f64 (/.f64 (+.f64 x (-.f64 1 x)) (+.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x))) (+.f64 x 1/2))
	51.1b	(/.f64 (/.f64 (+.f64 x (-.f64 1 x)) (+.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x))) x)
▶	5.0b	(/.f64 (/.f64 1 (+.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x))) (sqrt.f64 (*.f64 x (+.f64 1 x))))
▶	21.4b	(/.f64 (-.f64 (/.f64 1 x) (/.f64 1 (+.f64 1 x))) (+.f64 (pow.f64 x -1/2) (pow.f64 (+.f64 1 x) -1/2)))
	52.3b	(/.f64 (-.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)) (+.f64 (+.f64 x 1/2) (/.f64 -1/8 x)))
▶	50.8b	(/.f64 (-.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)) (+.f64 x 1/2))
	26.3b	(/.f64 1 (fma.f64 x (.f64 (sqrt.f64 (/.f64 1 x)) 3/2) (.f64 2 (pow.f64 x 3/2))))
	5.2b	(/.f64 1 (/.f64 (+.f64 (pow.f64 x -1/2) (pow.f64 (+.f64 1 x) -1/2)) (/.f64 (/.f64 (+.f64 1 (-.f64 x x)) x) (+.f64 1 x))))
✓	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)))))
	30.4b	(/.f64 1 (+.f64 x (sqrt.f64 x)))
	31.9b	(/.f64 1 (*.f64 2 (pow.f64 x 3/2)))
	21.0b	(-.f64 (pow.f64 x -1/2) (pow.f64 (+.f64 1 x) -1/2))
	22.7b	(-.f64 (pow.f64 x -1/2) (sqrt.f64 (/.f64 1 (+.f64 1 x))))
✓	31.8b	(-.f64 (pow.f64 x -1/2) 1)
✓	23.6b	(-.f64 (/.f64 1 (sqrt.f64 x)) (pow.f64 (+.f64 1 x) -1/2))
▶	30.7b	(-.f64 (/.f64 1 (sqrt.f64 x)) (/.f64 1 (+.f64 (*.f64 1/2 x) 1)))
	31.4b	(-.f64 (/.f64 1 (sqrt.f64 x)) (+.f64 (*.f64 -1/2 x) 1))
✓	31.9b	(-.f64 (/.f64 1 (sqrt.f64 x)) 1)
	42.4b	(*.f64 1/2 (sqrt.f64 (/.f64 1 (pow.f64 x 3))))
	62.8b	-1

Compiler

Compiled 516 to 402 computations (22.1% saved)

localize72.0ms (0.6%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(+.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x))
✓	0.2b	(/.f64 1 (+.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x)))
✓	0.2b	(/.f64 (/.f64 1 (+.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x))) (sqrt.f64 (*.f64 x (+.f64 1 x))))
	13.0b	(sqrt.f64 (*.f64 x (+.f64 1 x)))

Compiler

Compiled 58 to 38 computations (34.5% saved)

series13.0ms (0.1%)

Counts

3 → 2

Calls

9 calls:

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

rewrite246.0ms (2.2%)

Algorithm

1×	batch-egg-rewrite

Rules

597×	`log-prod_binary64`
581×	`fma-def_binary64`
303×	`pow2_binary64`
289×	`fma-neg_binary64`
226×	`pow-unpow_binary64`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	12	50
1	278	47
2	3821	46

Stop Event

1×	node limit

Counts

3 → 129

Calls

Call 1

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

Outputs

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

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

simplify16.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

1×	`1-exp_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	1	2
1	4	2

Stop Event

1×

saturated

Counts

131 → 130

Calls

Call 1

Inputs
1
1

Outputs
1
1

localize10.0ms (0.1%)

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

localize66.0ms (0.6%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.0b	(-.f64 (/.f64 1 (sqrt.f64 x)) (/.f64 1 (+.f64 (*.f64 1/2 x) 1)))
✓	0.0b	(/.f64 1 (+.f64 (*.f64 1/2 x) 1))
	0.3b	(/.f64 1 (sqrt.f64 x))

Compiler

Compiled 37 to 27 computations (27% saved)

series39.0ms (0.3%)

Counts

2 → 12

Calls

6 calls:

Time	Variable		Point	Expression
34.0ms	x	@	0	(-.f64 (/.f64 1 (sqrt.f64 x)) (/.f64 1 (+.f64 (*.f64 1/2 x) 1)))
1.0ms	x	@	inf	(-.f64 (/.f64 1 (sqrt.f64 x)) (/.f64 1 (+.f64 (*.f64 1/2 x) 1)))
1.0ms	x	@	-inf	(-.f64 (/.f64 1 (sqrt.f64 x)) (/.f64 1 (+.f64 (*.f64 1/2 x) 1)))
1.0ms	x	@	0	(/.f64 1 (+.f64 (*.f64 1/2 x) 1))
1.0ms	x	@	inf	(/.f64 1 (+.f64 (*.f64 1/2 x) 1))

rewrite259.0ms (2.3%)

Algorithm

1×	batch-egg-rewrite

Rules

982×	`prod-diff_binary64`
496×	`log-prod_binary64`
404×	`fma-def_binary64`
235×	`fma-neg_binary64`
191×	`pow1/3_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	10	24
1	229	22
2	3243	22

Stop Event

1×	node limit

Counts

2 → 165

Calls

Call 1

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

Outputs

((#(struct:change #<rule egg-rr> (2) ((x +.f64 0 (/.f64 1 (fma.f64 1/2 x 1)))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (log.f64 (*.f64 (cbrt.f64 (exp.f64 (/.f64 1 (fma.f64 1/2 x 1)))) (cbrt.f64 (exp.f64 (/.f64 1 (fma.f64 1/2 x 1)))))) (log.f64 (cbrt.f64 (exp.f64 (/.f64 1 (fma.f64 1/2 x 1))))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (log.f64 (sqrt.f64 (exp.f64 (/.f64 1 (fma.f64 1/2 x 1))))) (log.f64 (sqrt.f64 (exp.f64 (/.f64 1 (fma.f64 1/2 x 1))))))))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (exp.f64 (log1p.f64 (/.f64 1 (fma.f64 1/2 x 1)))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 1 (/.f64 1 (fma.f64 1/2 x 1)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 1 (fma.f64 1/2 x 1)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 1 (cbrt.f64 (fma.f64 1/2 x 1))) (cbrt.f64 (pow.f64 (fma.f64 1/2 x 1) -2)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 (pow.f64 (fma.f64 1/2 x 1) -2)) (/.f64 1 (cbrt.f64 (fma.f64 1/2 x 1))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (fma.f64 1/2 x 1) -1/2) (pow.f64 (fma.f64 1/2 x 1) -1/2))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 -1 (/.f64 -1 (fma.f64 1/2 x 1)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 1 (pow.f64 (cbrt.f64 (fma.f64 1/2 x 1)) 2)) (/.f64 1 (cbrt.f64 (fma.f64 1/2 x 1))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 1 (fma.f64 1/8 (pow.f64 x 3) 1)) (-.f64 (fma.f64 1/4 (*.f64 x x) 1) (*.f64 1/2 x)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 1 (fma.f64 1/4 (*.f64 x x) -1)) (fma.f64 1/2 x -1))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (fma.f64 1/2 x 1) -1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (/.f64 1 (fma.f64 1/2 x 1)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (/.f64 1 (cbrt.f64 (fma.f64 1/2 x 1))) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (fma.f64 1/2 x 1) -1/2) 2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (fma.f64 1/2 x 1) -3) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (neg.f64 (neg.f64 (fma.f64 1/2 x 1))) -1)))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f64 (pow.f64 (fma.f64 1/2 x 1) -2))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (exp.f64 (/.f64 1 (fma.f64 1/2 x 1))))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (+.f64 1 (expm1.f64 (/.f64 1 (fma.f64 1/2 x 1)))))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (pow.f64 (fma.f64 1/2 x 1) -3))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (/.f64 1 (fma.f64 1/2 x 1))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (neg.f64 (log1p.f64 (*.f64 1/2 x))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (log1p.f64 (*.f64 1/2 x)) -1))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (neg.f64 (log1p.f64 (*.f64 1/2 x))) 1))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (/.f64 1 (fma.f64 1/2 x 1))))))))

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

simplify70.0ms (0.6%)

Algorithm

1×	egg-herbie

Rules

775×	`distribute-neg-frac_binary64`
729×	`fma-def_binary64`
721×	`associate-l_binary64`
494×	`associate-r_binary64`
417×	`times-frac_binary64`

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	35	181
1	93	177
2	231	177
3	626	171
4	1927	170
5	7347	170

Stop Event

1×	node limit

Counts

177 → 179

Calls

Call 1

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

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

localize57.0ms (0.5%)

Local error

Found 3 expressions with local error:

New	Error	Program
	0.0b	(sqrt.f64 (+.f64 1 x))
✓	0.0b	(/.f64 (-.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)) (+.f64 x 1/2))
	2.4b	(-.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x))

Compiler

Compiled 34 to 22 computations (35.3% saved)

series7.0ms (0.1%)

Counts

1 → 1

Calls

3 calls:

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

rewrite95.0ms (0.8%)

Algorithm

1×	batch-egg-rewrite

Rules

529×	`log-prod_binary64`
519×	`fma-def_binary64`
357×	`pow-prod-down_binary64`
297×	`pow2_binary64`
267×	`fma-neg_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	10	17
1	230	17
2	3360	17

Stop Event

1×	node limit

Counts

1 → 57

Calls

Call 1

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

Outputs

((#(struct:change #<rule egg-rr> (2) ((x +.f64 0 (/.f64 (-.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)) (+.f64 x 1/2)))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (/.f64 (sqrt.f64 (+.f64 1 x)) (+.f64 x 1/2)) (neg.f64 (/.f64 (sqrt.f64 x) (+.f64 x 1/2))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (log.f64 (pow.f64 (cbrt.f64 (exp.f64 (/.f64 (-.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)) (+.f64 x 1/2)))) 2)) (log.f64 (cbrt.f64 (exp.f64 (/.f64 (-.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)) (+.f64 x 1/2))))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (log.f64 (sqrt.f64 (exp.f64 (/.f64 (-.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)) (+.f64 x 1/2))))) (log.f64 (sqrt.f64 (exp.f64 (/.f64 (-.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)) (+.f64 x 1/2))))))))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (/.f64 (sqrt.f64 (+.f64 1 x)) (+.f64 x 1/2)) (/.f64 (sqrt.f64 x) (+.f64 x 1/2)))))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (exp.f64 (log1p.f64 (/.f64 (-.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)) (+.f64 x 1/2)))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 1 (/.f64 (-.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)) (+.f64 x 1/2)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (-.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)) (/.f64 1 (+.f64 x 1/2)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (-.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)) (+.f64 x 1/2)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 (/.f64 (-.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)) (+.f64 x 1/2))) (cbrt.f64 (pow.f64 (/.f64 (+.f64 x 1/2) (-.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x))) -2)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 (pow.f64 (/.f64 (+.f64 x 1/2) (-.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x))) -2)) (cbrt.f64 (/.f64 (-.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)) (+.f64 x 1/2))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (cbrt.f64 (-.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x))) 2) (*.f64 (cbrt.f64 (-.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x))) (/.f64 1 (+.f64 x 1/2))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (sqrt.f64 (/.f64 (-.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)) (+.f64 x 1/2))) (sqrt.f64 (/.f64 (-.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)) (+.f64 x 1/2))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (sqrt.f64 (-.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x))) (*.f64 (sqrt.f64 (-.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x))) (/.f64 1 (+.f64 x 1/2))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (neg.f64 (-.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x))) (/.f64 1 (+.f64 (neg.f64 x) -1/2)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 1 (+.f64 x 1/2)) (-.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (cbrt.f64 (+.f64 x 1/2)) -2) (/.f64 (-.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)) (cbrt.f64 (+.f64 x 1/2))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (+.f64 x 1/2) -1/2) (/.f64 (-.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)) (sqrt.f64 (+.f64 x 1/2))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (pow.f64 (cbrt.f64 (-.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x))) 2) 1) (/.f64 (cbrt.f64 (-.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x))) (+.f64 x 1/2)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (sqrt.f64 (-.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x))) 1) (/.f64 (sqrt.f64 (-.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x))) (+.f64 x 1/2)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (pow.f64 (cbrt.f64 (-.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x))) 2) (pow.f64 (cbrt.f64 (+.f64 x 1/2)) 2)) (cbrt.f64 (/.f64 (-.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)) (+.f64 x 1/2))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (sqrt.f64 (-.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x))) (pow.f64 (cbrt.f64 (+.f64 x 1/2)) 2)) (/.f64 (sqrt.f64 (-.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x))) (cbrt.f64 (+.f64 x 1/2))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (pow.f64 (cbrt.f64 (-.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x))) 2) (sqrt.f64 (+.f64 x 1/2))) (/.f64 (cbrt.f64 (-.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x))) (sqrt.f64 (+.f64 x 1/2))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (-.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)) (+.f64 1/8 (pow.f64 x 3))) (-.f64 (fma.f64 x x 1/4) (*.f64 x 1/2)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (-.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)) (fma.f64 x x -1/4)) (+.f64 x -1/2))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (/.f64 (-.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)) (+.f64 x 1/2)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (/.f64 (+.f64 x 1/2) (-.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x))) -2) 1/2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (/.f64 (-.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)) (+.f64 x 1/2)) 3) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (cbrt.f64 (/.f64 (-.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)) (+.f64 x 1/2))) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (sqrt.f64 (/.f64 (-.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)) (+.f64 x 1/2))) 2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (/.f64 (+.f64 x 1/2) (-.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x))) -1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (/.f64 (pow.f64 (-.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)) 3) (pow.f64 (+.f64 x 1/2) 3)) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (/.f64 (/.f64 (+.f64 x 1/2) (-.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x))) 1) -1)))) (#(struct:change #<rule egg-rr> (2) ((x neg.f64 (/.f64 (-.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)) (+.f64 (neg.f64 x) -1/2)))))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f64 (pow.f64 (/.f64 (+.f64 x 1/2) (-.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x))) -2))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (exp.f64 (/.f64 (-.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)) (+.f64 x 1/2))))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (+.f64 1 (expm1.f64 (/.f64 (-.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)) (+.f64 x 1/2)))))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (pow.f64 (/.f64 (-.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)) (+.f64 x 1/2)) 3))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (/.f64 (pow.f64 (-.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)) 3) (pow.f64 (+.f64 x 1/2) 3)))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (/.f64 (-.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)) (+.f64 x 1/2))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (log.f64 (/.f64 (-.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)) (+.f64 x 1/2))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (log.f64 (/.f64 (-.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)) (+.f64 x 1/2))) 1))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (/.f64 (-.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)) (+.f64 x 1/2))))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 1 (/.f64 (sqrt.f64 (+.f64 1 x)) (+.f64 x 1/2)) (neg.f64 (/.f64 (sqrt.f64 x) (+.f64 x 1/2))))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (sqrt.f64 (+.f64 1 x)) (/.f64 1 (+.f64 x 1/2)) (neg.f64 (/.f64 (sqrt.f64 x) (+.f64 x 1/2))))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (pow.f64 (cbrt.f64 (/.f64 (sqrt.f64 (+.f64 1 x)) (+.f64 x 1/2))) 2) (cbrt.f64 (/.f64 (sqrt.f64 (+.f64 1 x)) (+.f64 x 1/2))) (neg.f64 (/.f64 (sqrt.f64 x) (+.f64 x 1/2))))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (sqrt.f64 (/.f64 (sqrt.f64 (+.f64 1 x)) (+.f64 x 1/2))) (sqrt.f64 (/.f64 (sqrt.f64 (+.f64 1 x)) (+.f64 x 1/2))) (neg.f64 (/.f64 (sqrt.f64 x) (+.f64 x 1/2))))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (pow.f64 (cbrt.f64 (+.f64 x 1/2)) -2) (/.f64 (sqrt.f64 (+.f64 1 x)) (cbrt.f64 (+.f64 x 1/2))) (neg.f64 (/.f64 (sqrt.f64 x) (+.f64 x 1/2))))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (pow.f64 (+.f64 x 1/2) -1/2) (/.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 (+.f64 x 1/2))) (neg.f64 (/.f64 (sqrt.f64 x) (+.f64 x 1/2))))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (/.f64 (cbrt.f64 (+.f64 1 x)) 1) (/.f64 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(+.f64 1 x) 1/4) (sqrt.f64 (+.f64 x 1/2))) (/.f64 (pow.f64 (+.f64 1 x) 1/4) (sqrt.f64 (+.f64 x 1/2))) (neg.f64 (/.f64 (sqrt.f64 x) (+.f64 x 1/2))))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (/.f64 (sqrt.f64 (+.f64 1 x)) (+.f64 1/8 (pow.f64 x 3))) (-.f64 (fma.f64 x x 1/4) (*.f64 x 1/2)) (neg.f64 (/.f64 (sqrt.f64 x) (+.f64 x 1/2))))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (/.f64 (sqrt.f64 (+.f64 1 x)) (fma.f64 x x -1/4)) (+.f64 x -1/2) (neg.f64 (/.f64 (sqrt.f64 x) (+.f64 x 1/2))))))))

simplify13.0ms (0.1%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	1	1

Stop Event

1×

saturated

Counts

58 → 58

Calls

Call 1

Inputs
2

Outputs
2

localize71.0ms (0.6%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(+.f64 (pow.f64 x -1/2) (pow.f64 (+.f64 1 x) -1/2))
	0.0b	(/.f64 1 (+.f64 1 x))
✓	0.5b	(/.f64 (-.f64 (/.f64 1 x) (/.f64 1 (+.f64 1 x))) (+.f64 (pow.f64 x -1/2) (pow.f64 (+.f64 1 x) -1/2)))
	2.3b	(-.f64 (/.f64 1 x) (/.f64 1 (+.f64 1 x)))

Compiler

Compiled 60 to 46 computations (23.3% saved)

series5.0ms (0%)

Counts

2 → 24

Calls

6 calls:

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

rewrite121.0ms (1.1%)

Algorithm

1×	batch-egg-rewrite

Rules

678×	`log-prod_binary64`
654×	`fma-def_binary64`
347×	`fma-neg_binary64`
268×	`log-div_binary64`
243×	`expm1-udef_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	12	41
1	296	26
2	4663	26

Stop Event

1×	node limit

Counts

2 → 216

Calls

Call 1

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

Outputs

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simplify78.0ms (0.7%)

Algorithm

1×	egg-herbie

Rules

597×	`sub-neg_binary64`
545×	`fma-def_binary64`
491×	`fma-neg_binary64`
406×	`associate-+l+_binary64`
284×	`associate-+r+_binary64`

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	166	1418
1	525	1344
2	1573	1194
3	6151	1081

Stop Event

1×	node limit

Counts

240 → 262

Calls

Call 1

Inputs
(/.f64 1 (*.f64 (+.f64 (pow.f64 x -1/2) 1) x))
(-.f64 (+.f64 (/.f64 1 (.f64 (+.f64 (pow.f64 x -1/2) 1) x)) (.f64 1/2 (/.f64 1 (*.f64 (+.f64 1 (pow.f64 x -1/2)) (+.f64 (pow.f64 x -1/2) 1))))) (/.f64 1 (+.f64 (pow.f64 x -1/2) 1)))
(-.f64 (+.f64 (/.f64 1 (.f64 (+.f64 (pow.f64 x -1/2) 1) x)) (+.f64 (.f64 (-.f64 (/.f64 1 (+.f64 (pow.f64 x -1/2) 1)) (+.f64 (.f64 3/8 (/.f64 1 (.f64 (+.f64 1 (pow.f64 x -1/2)) (+.f64 (pow.f64 x -1/2) 1)))) (.f64 -1/2 (/.f64 (-.f64 (.f64 1/2 (/.f64 1 (.f64 (+.f64 1 (pow.f64 x -1/2)) (+.f64 (pow.f64 x -1/2) 1)))) (/.f64 1 (+.f64 1 (pow.f64 x -1/2)))) (+.f64 (pow.f64 x -1/2) 1))))) x) (.f64 1/2 (/.f64 1 (*.f64 (+.f64 1 (pow.f64 x -1/2)) (+.f64 (pow.f64 x -1/2) 1)))))) (/.f64 1 (+.f64 (pow.f64 x -1/2) 1)))
(-.f64 (+.f64 (/.f64 1 (.f64 (+.f64 (pow.f64 x -1/2) 1) x)) (+.f64 (.f64 (-.f64 (.f64 5/16 (/.f64 1 (.f64 (+.f64 1 (pow.f64 x -1/2)) (+.f64 (pow.f64 x -1/2) 1)))) (+.f64 (.f64 -1/2 (/.f64 (-.f64 (/.f64 1 (+.f64 1 (pow.f64 x -1/2))) (+.f64 (.f64 -1/2 (/.f64 (-.f64 (.f64 1/2 (/.f64 1 (.f64 (+.f64 1 (pow.f64 x -1/2)) (+.f64 (pow.f64 x -1/2) 1)))) (/.f64 1 (+.f64 (pow.f64 x -1/2) 1))) (+.f64 1 (pow.f64 x -1/2)))) (.f64 3/8 (/.f64 1 (.f64 (+.f64 1 (pow.f64 x -1/2)) (+.f64 (pow.f64 x -1/2) 1)))))) (+.f64 (pow.f64 x -1/2) 1))) (+.f64 (.f64 3/8 (/.f64 (-.f64 (.f64 1/2 (/.f64 1 (.f64 (+.f64 1 (pow.f64 x -1/2)) (+.f64 (pow.f64 x -1/2) 1)))) (/.f64 1 (+.f64 1 (pow.f64 x -1/2)))) (+.f64 (pow.f64 x -1/2) 1))) (/.f64 1 (+.f64 (pow.f64 x -1/2) 1))))) (pow.f64 x 2)) (+.f64 (.f64 (-.f64 (/.f64 1 (+.f64 (pow.f64 x -1/2) 1)) (+.f64 (.f64 3/8 (/.f64 1 (.f64 (+.f64 1 (pow.f64 x -1/2)) (+.f64 (pow.f64 x -1/2) 1)))) (.f64 -1/2 (/.f64 (-.f64 (.f64 1/2 (/.f64 1 (.f64 (+.f64 1 (pow.f64 x -1/2)) (+.f64 (pow.f64 x -1/2) 1)))) (/.f64 1 (+.f64 1 (pow.f64 x -1/2)))) (+.f64 (pow.f64 x -1/2) 1))))) x) (.f64 1/2 (/.f64 1 (*.f64 (+.f64 1 (pow.f64 x -1/2)) (+.f64 (pow.f64 x -1/2) 1))))))) (/.f64 1 (+.f64 (pow.f64 x -1/2) 1)))
(*.f64 1/2 (sqrt.f64 (/.f64 1 (pow.f64 x 3))))
(-.f64 (+.f64 (.f64 1/2 (sqrt.f64 (/.f64 1 (pow.f64 x 3)))) (.f64 -1/2 (sqrt.f64 (/.f64 1 (pow.f64 x 5))))) (*.f64 -1/8 (sqrt.f64 (/.f64 1 (pow.f64 x 5)))))
(-.f64 (+.f64 (.f64 1/2 (sqrt.f64 (/.f64 1 (pow.f64 x 7)))) (+.f64 (.f64 1/2 (sqrt.f64 (/.f64 1 (pow.f64 x 3)))) (.f64 -1/2 (sqrt.f64 (/.f64 1 (pow.f64 x 5)))))) (+.f64 (.f64 -1/8 (sqrt.f64 (/.f64 1 (pow.f64 x 5)))) (+.f64 (.f64 -1/4 (/.f64 (-.f64 (.f64 -1/2 (sqrt.f64 x)) (.f64 -1/8 (sqrt.f64 x))) (pow.f64 x 4))) (.f64 3/32 (sqrt.f64 (/.f64 1 (pow.f64 x 7)))))))
(-.f64 (+.f64 (.f64 -1/2 (sqrt.f64 (/.f64 1 (pow.f64 x 9)))) (+.f64 (.f64 1/2 (sqrt.f64 (/.f64 1 (pow.f64 x 7)))) (+.f64 (.f64 -1/2 (sqrt.f64 (/.f64 1 (pow.f64 x 5)))) (.f64 1/2 (sqrt.f64 (/.f64 1 (pow.f64 x 3))))))) (+.f64 (.f64 -1/8 (sqrt.f64 (/.f64 1 (pow.f64 x 5)))) (+.f64 (.f64 3/16 (/.f64 (-.f64 (.f64 -1/2 (sqrt.f64 x)) (.f64 -1/8 (sqrt.f64 x))) (pow.f64 x 5))) (+.f64 (.f64 -1/4 (/.f64 (-.f64 (.f64 1/2 (sqrt.f64 x)) (+.f64 (.f64 3/32 (sqrt.f64 x)) (.f64 -1/4 (-.f64 (.f64 -1/2 (sqrt.f64 x)) (.f64 -1/8 (sqrt.f64 x)))))) (pow.f64 x 5))) (+.f64 (.f64 -5/64 (sqrt.f64 (/.f64 1 (pow.f64 x 9)))) (+.f64 (.f64 -1/4 (/.f64 (-.f64 (.f64 -1/2 (sqrt.f64 x)) (.f64 -1/8 (sqrt.f64 x))) (pow.f64 x 4))) (*.f64 3/32 (sqrt.f64 (/.f64 1 (pow.f64 x 7))))))))))
(/.f64 1/2 (.f64 (exp.f64 (.f64 -1/2 (+.f64 (*.f64 -1 (log.f64 (/.f64 -1 x))) (log.f64 -1)))) (pow.f64 x 2)))
(-.f64 (.f64 1/2 (/.f64 1 (.f64 (exp.f64 (.f64 -1/2 (+.f64 (.f64 -1 (log.f64 (/.f64 -1 x))) (log.f64 -1)))) (pow.f64 x 2)))) (.f64 3/8 (/.f64 1 (.f64 (exp.f64 (.f64 -1/2 (+.f64 (.f64 -1 (log.f64 (/.f64 -1 x))) (log.f64 -1)))) (pow.f64 x 3)))))
(-.f64 (+.f64 (.f64 1/2 (/.f64 1 (.f64 (exp.f64 (.f64 -1/2 (+.f64 (.f64 -1 (log.f64 (/.f64 -1 x))) (log.f64 -1)))) (pow.f64 x 2)))) (.f64 5/16 (/.f64 1 (.f64 (exp.f64 (.f64 -1/2 (+.f64 (.f64 -1 (log.f64 (/.f64 -1 x))) (log.f64 -1)))) (pow.f64 x 4))))) (.f64 3/8 (/.f64 1 (.f64 (exp.f64 (.f64 -1/2 (+.f64 (.f64 -1 (log.f64 (/.f64 -1 x))) (log.f64 -1)))) (pow.f64 x 3)))))
(-.f64 (+.f64 (.f64 1/2 (/.f64 1 (.f64 (exp.f64 (.f64 -1/2 (+.f64 (.f64 -1 (log.f64 (/.f64 -1 x))) (log.f64 -1)))) (pow.f64 x 2)))) (.f64 5/16 (/.f64 1 (.f64 (exp.f64 (.f64 -1/2 (+.f64 (.f64 -1 (log.f64 (/.f64 -1 x))) (log.f64 -1)))) (pow.f64 x 4))))) (+.f64 (.f64 3/8 (/.f64 1 (.f64 (exp.f64 (.f64 -1/2 (+.f64 (.f64 -1 (log.f64 (/.f64 -1 x))) (log.f64 -1)))) (pow.f64 x 3)))) (.f64 35/128 (/.f64 1 (.f64 (exp.f64 (.f64 -1/2 (+.f64 (.f64 -1 (log.f64 (/.f64 -1 x))) (log.f64 -1)))) (pow.f64 x 5))))))
(+.f64 1 (pow.f64 x -1/2))
(+.f64 (*.f64 -1/2 x) (+.f64 (pow.f64 x -1/2) 1))
(+.f64 (.f64 -1/2 x) (+.f64 (pow.f64 x -1/2) (+.f64 1 (.f64 3/8 (pow.f64 x 2)))))
(+.f64 (.f64 -1/2 x) (+.f64 (pow.f64 x -1/2) (+.f64 1 (+.f64 (.f64 3/8 (pow.f64 x 2)) (*.f64 -5/16 (pow.f64 x 3))))))
(*.f64 2 (sqrt.f64 (/.f64 1 x)))
(+.f64 (.f64 -1/2 (sqrt.f64 (/.f64 1 (pow.f64 x 3)))) (.f64 2 (sqrt.f64 (/.f64 1 x))))
(+.f64 (.f64 3/8 (sqrt.f64 (/.f64 1 (pow.f64 x 5)))) (+.f64 (.f64 -1/2 (sqrt.f64 (/.f64 1 (pow.f64 x 3)))) (*.f64 2 (sqrt.f64 (/.f64 1 x)))))
(+.f64 (.f64 3/8 (sqrt.f64 (/.f64 1 (pow.f64 x 5)))) (+.f64 (.f64 -5/16 (sqrt.f64 (/.f64 1 (pow.f64 x 7)))) (+.f64 (.f64 -1/2 (sqrt.f64 (/.f64 1 (pow.f64 x 3)))) (.f64 2 (sqrt.f64 (/.f64 1 x))))))
(.f64 2 (exp.f64 (.f64 -1/2 (+.f64 (*.f64 -1 (log.f64 (/.f64 -1 x))) (log.f64 -1)))))
(+.f64 (.f64 2 (exp.f64 (.f64 -1/2 (+.f64 (.f64 -1 (log.f64 (/.f64 -1 x))) (log.f64 -1))))) (.f64 -1/2 (/.f64 (exp.f64 (.f64 -1/2 (+.f64 (.f64 -1 (log.f64 (/.f64 -1 x))) (log.f64 -1)))) x)))
(+.f64 (.f64 3/8 (/.f64 (exp.f64 (.f64 -1/2 (+.f64 (.f64 -1 (log.f64 (/.f64 -1 x))) (log.f64 -1)))) (pow.f64 x 2))) (+.f64 (.f64 2 (exp.f64 (.f64 -1/2 (+.f64 (.f64 -1 (log.f64 (/.f64 -1 x))) (log.f64 -1))))) (.f64 -1/2 (/.f64 (exp.f64 (.f64 -1/2 (+.f64 (*.f64 -1 (log.f64 (/.f64 -1 x))) (log.f64 -1)))) x))))
(+.f64 (.f64 3/8 (/.f64 (exp.f64 (.f64 -1/2 (+.f64 (.f64 -1 (log.f64 (/.f64 -1 x))) (log.f64 -1)))) (pow.f64 x 2))) (+.f64 (.f64 -5/16 (/.f64 (exp.f64 (.f64 -1/2 (+.f64 (.f64 -1 (log.f64 (/.f64 -1 x))) (log.f64 -1)))) (pow.f64 x 3))) (+.f64 (.f64 2 (exp.f64 (.f64 -1/2 (+.f64 (.f64 -1 (log.f64 (/.f64 -1 x))) (log.f64 -1))))) (.f64 -1/2 (/.f64 (exp.f64 (.f64 -1/2 (+.f64 (.f64 -1 (log.f64 (/.f64 -1 x))) (log.f64 -1)))) x)))))

Outputs
(/.f64 1 (*.f64 (+.f64 (pow.f64 x -1/2) 1) x))
(/.f64 1 (*.f64 x (+.f64 1 (pow.f64 x -1/2))))
(/.f64 (/.f64 1 x) (+.f64 1 (pow.f64 x -1/2)))
(/.f64 1 (+.f64 x (sqrt.f64 x)))
(-.f64 (+.f64 (/.f64 1 (.f64 (+.f64 (pow.f64 x -1/2) 1) x)) (.f64 1/2 (/.f64 1 (*.f64 (+.f64 1 (pow.f64 x -1/2)) (+.f64 (pow.f64 x -1/2) 1))))) (/.f64 1 (+.f64 (pow.f64 x -1/2) 1)))
(+.f64 (/.f64 1 (.f64 x (+.f64 1 (pow.f64 x -1/2)))) (-.f64 (/.f64 1/2 (.f64 (+.f64 1 (pow.f64 x -1/2)) (+.f64 1 (pow.f64 x -1/2)))) (/.f64 1 (+.f64 1 (pow.f64 x -1/2)))))
(+.f64 (/.f64 (/.f64 1 x) (+.f64 1 (pow.f64 x -1/2))) (+.f64 (/.f64 1/2 (*.f64 (+.f64 1 (pow.f64 x -1/2)) (+.f64 1 (pow.f64 x -1/2)))) (/.f64 -1 (+.f64 1 (pow.f64 x -1/2)))))
(+.f64 (/.f64 1 (+.f64 x (sqrt.f64 x))) (+.f64 (/.f64 1/2 (*.f64 (+.f64 1 (pow.f64 x -1/2)) (+.f64 1 (pow.f64 x -1/2)))) (/.f64 -1 (+.f64 1 (pow.f64 x -1/2)))))
(-.f64 (+.f64 (/.f64 1 (.f64 (+.f64 (pow.f64 x -1/2) 1) x)) (+.f64 (.f64 (-.f64 (/.f64 1 (+.f64 (pow.f64 x -1/2) 1)) (+.f64 (.f64 3/8 (/.f64 1 (.f64 (+.f64 1 (pow.f64 x -1/2)) (+.f64 (pow.f64 x -1/2) 1)))) (.f64 -1/2 (/.f64 (-.f64 (.f64 1/2 (/.f64 1 (.f64 (+.f64 1 (pow.f64 x -1/2)) (+.f64 (pow.f64 x -1/2) 1)))) (/.f64 1 (+.f64 1 (pow.f64 x -1/2)))) (+.f64 (pow.f64 x -1/2) 1))))) x) (.f64 1/2 (/.f64 1 (*.f64 (+.f64 1 (pow.f64 x -1/2)) (+.f64 (pow.f64 x -1/2) 1)))))) (/.f64 1 (+.f64 (pow.f64 x -1/2) 1)))
(-.f64 (+.f64 (/.f64 1 (.f64 x (+.f64 1 (pow.f64 x -1/2)))) (fma.f64 (-.f64 (/.f64 1 (+.f64 1 (pow.f64 x -1/2))) (fma.f64 -1/2 (/.f64 (-.f64 (/.f64 1/2 (.f64 (+.f64 1 (pow.f64 x -1/2)) (+.f64 1 (pow.f64 x -1/2)))) (/.f64 1 (+.f64 1 (pow.f64 x -1/2)))) (+.f64 1 (pow.f64 x -1/2))) (/.f64 3/8 (.f64 (+.f64 1 (pow.f64 x -1/2)) (+.f64 1 (pow.f64 x -1/2)))))) x (/.f64 1/2 (.f64 (+.f64 1 (pow.f64 x -1/2)) (+.f64 1 (pow.f64 x -1/2)))))) (/.f64 1 (+.f64 1 (pow.f64 x -1/2))))
(+.f64 (fma.f64 x (-.f64 (/.f64 1 (+.f64 1 (pow.f64 x -1/2))) (fma.f64 -1/2 (/.f64 (+.f64 (/.f64 1/2 (.f64 (+.f64 1 (pow.f64 x -1/2)) (+.f64 1 (pow.f64 x -1/2)))) (/.f64 -1 (+.f64 1 (pow.f64 x -1/2)))) (+.f64 1 (pow.f64 x -1/2))) (/.f64 3/8 (.f64 (+.f64 1 (pow.f64 x -1/2)) (+.f64 1 (pow.f64 x -1/2)))))) (/.f64 1/2 (*.f64 (+.f64 1 (pow.f64 x -1/2)) (+.f64 1 (pow.f64 x -1/2))))) (-.f64 (/.f64 (/.f64 1 x) (+.f64 1 (pow.f64 x -1/2))) (/.f64 1 (+.f64 1 (pow.f64 x -1/2)))))
(+.f64 (/.f64 1 (+.f64 x (sqrt.f64 x))) (+.f64 (fma.f64 x (-.f64 (/.f64 1 (+.f64 1 (pow.f64 x -1/2))) (fma.f64 -1/2 (+.f64 (/.f64 1/2 (pow.f64 (+.f64 1 (pow.f64 x -1/2)) 3)) (/.f64 -1 (.f64 (+.f64 1 (pow.f64 x -1/2)) (+.f64 1 (pow.f64 x -1/2))))) (/.f64 3/8 (.f64 (+.f64 1 (pow.f64 x -1/2)) (+.f64 1 (pow.f64 x -1/2)))))) (/.f64 1/2 (*.f64 (+.f64 1 (pow.f64 x -1/2)) (+.f64 1 (pow.f64 x -1/2))))) (/.f64 -1 (+.f64 1 (pow.f64 x -1/2)))))
(+.f64 (/.f64 1 (+.f64 x (sqrt.f64 x))) (+.f64 (fma.f64 x (+.f64 (/.f64 1 (+.f64 1 (pow.f64 x -1/2))) (fma.f64 1/2 (+.f64 (/.f64 1/2 (pow.f64 (+.f64 1 (pow.f64 x -1/2)) 3)) (/.f64 -1 (.f64 (+.f64 1 (pow.f64 x -1/2)) (+.f64 1 (pow.f64 x -1/2))))) (/.f64 -3/8 (.f64 (+.f64 1 (pow.f64 x -1/2)) (+.f64 1 (pow.f64 x -1/2)))))) (/.f64 1/2 (*.f64 (+.f64 1 (pow.f64 x -1/2)) (+.f64 1 (pow.f64 x -1/2))))) (/.f64 -1 (+.f64 1 (pow.f64 x -1/2)))))
(-.f64 (+.f64 (/.f64 1 (.f64 (+.f64 (pow.f64 x -1/2) 1) x)) (+.f64 (.f64 (-.f64 (.f64 5/16 (/.f64 1 (.f64 (+.f64 1 (pow.f64 x -1/2)) (+.f64 (pow.f64 x -1/2) 1)))) (+.f64 (.f64 -1/2 (/.f64 (-.f64 (/.f64 1 (+.f64 1 (pow.f64 x -1/2))) (+.f64 (.f64 -1/2 (/.f64 (-.f64 (.f64 1/2 (/.f64 1 (.f64 (+.f64 1 (pow.f64 x -1/2)) (+.f64 (pow.f64 x -1/2) 1)))) (/.f64 1 (+.f64 (pow.f64 x -1/2) 1))) (+.f64 1 (pow.f64 x -1/2)))) (.f64 3/8 (/.f64 1 (.f64 (+.f64 1 (pow.f64 x -1/2)) (+.f64 (pow.f64 x -1/2) 1)))))) (+.f64 (pow.f64 x -1/2) 1))) (+.f64 (.f64 3/8 (/.f64 (-.f64 (.f64 1/2 (/.f64 1 (.f64 (+.f64 1 (pow.f64 x -1/2)) (+.f64 (pow.f64 x -1/2) 1)))) (/.f64 1 (+.f64 1 (pow.f64 x -1/2)))) (+.f64 (pow.f64 x -1/2) 1))) (/.f64 1 (+.f64 (pow.f64 x -1/2) 1))))) (pow.f64 x 2)) (+.f64 (.f64 (-.f64 (/.f64 1 (+.f64 (pow.f64 x -1/2) 1)) (+.f64 (.f64 3/8 (/.f64 1 (.f64 (+.f64 1 (pow.f64 x -1/2)) (+.f64 (pow.f64 x -1/2) 1)))) (.f64 -1/2 (/.f64 (-.f64 (.f64 1/2 (/.f64 1 (.f64 (+.f64 1 (pow.f64 x -1/2)) (+.f64 (pow.f64 x -1/2) 1)))) (/.f64 1 (+.f64 1 (pow.f64 x -1/2)))) (+.f64 (pow.f64 x -1/2) 1))))) x) (.f64 1/2 (/.f64 1 (*.f64 (+.f64 1 (pow.f64 x -1/2)) (+.f64 (pow.f64 x -1/2) 1))))))) (/.f64 1 (+.f64 (pow.f64 x -1/2) 1)))
(+.f64 (/.f64 1 (.f64 x (+.f64 1 (pow.f64 x -1/2)))) (-.f64 (fma.f64 (-.f64 (/.f64 5/16 (.f64 (+.f64 1 (pow.f64 x -1/2)) (+.f64 1 (pow.f64 x -1/2)))) (fma.f64 -1/2 (/.f64 (-.f64 (/.f64 1 (+.f64 1 (pow.f64 x -1/2))) (fma.f64 -1/2 (/.f64 (-.f64 (/.f64 1/2 (.f64 (+.f64 1 (pow.f64 x -1/2)) (+.f64 1 (pow.f64 x -1/2)))) (/.f64 1 (+.f64 1 (pow.f64 x -1/2)))) (+.f64 1 (pow.f64 x -1/2))) (/.f64 3/8 (.f64 (+.f64 1 (pow.f64 x -1/2)) (+.f64 1 (pow.f64 x -1/2)))))) (+.f64 1 (pow.f64 x -1/2))) (fma.f64 3/8 (/.f64 (-.f64 (/.f64 1/2 (.f64 (+.f64 1 (pow.f64 x -1/2)) (+.f64 1 (pow.f64 x -1/2)))) (/.f64 1 (+.f64 1 (pow.f64 x -1/2)))) (+.f64 1 (pow.f64 x -1/2))) (/.f64 1 (+.f64 1 (pow.f64 x -1/2)))))) (.f64 x x) (fma.f64 (-.f64 (/.f64 1 (+.f64 1 (pow.f64 x -1/2))) (fma.f64 -1/2 (/.f64 (-.f64 (/.f64 1/2 (.f64 (+.f64 1 (pow.f64 x -1/2)) (+.f64 1 (pow.f64 x -1/2)))) (/.f64 1 (+.f64 1 (pow.f64 x -1/2)))) (+.f64 1 (pow.f64 x -1/2))) (/.f64 3/8 (.f64 (+.f64 1 (pow.f64 x -1/2)) (+.f64 1 (pow.f64 x -1/2)))))) x (/.f64 1/2 (*.f64 (+.f64 1 (pow.f64 x -1/2)) (+.f64 1 (pow.f64 x -1/2)))))) (/.f64 1 (+.f64 1 (pow.f64 x -1/2)))))
(+.f64 (/.f64 (/.f64 1 x) (+.f64 1 (pow.f64 x -1/2))) (+.f64 (fma.f64 (-.f64 (/.f64 5/16 (.f64 (+.f64 1 (pow.f64 x -1/2)) (+.f64 1 (pow.f64 x -1/2)))) (fma.f64 -1/2 (/.f64 (-.f64 (/.f64 1 (+.f64 1 (pow.f64 x -1/2))) (fma.f64 -1/2 (/.f64 (+.f64 (/.f64 1/2 (.f64 (+.f64 1 (pow.f64 x -1/2)) (+.f64 1 (pow.f64 x -1/2)))) (/.f64 -1 (+.f64 1 (pow.f64 x -1/2)))) (+.f64 1 (pow.f64 x -1/2))) (/.f64 3/8 (.f64 (+.f64 1 (pow.f64 x -1/2)) (+.f64 1 (pow.f64 x -1/2)))))) (+.f64 1 (pow.f64 x -1/2))) (fma.f64 3/8 (/.f64 (+.f64 (/.f64 1/2 (.f64 (+.f64 1 (pow.f64 x -1/2)) (+.f64 1 (pow.f64 x -1/2)))) (/.f64 -1 (+.f64 1 (pow.f64 x -1/2)))) (+.f64 1 (pow.f64 x -1/2))) (/.f64 1 (+.f64 1 (pow.f64 x -1/2)))))) (.f64 x x) (fma.f64 x (-.f64 (/.f64 1 (+.f64 1 (pow.f64 x -1/2))) (fma.f64 -1/2 (/.f64 (+.f64 (/.f64 1/2 (.f64 (+.f64 1 (pow.f64 x -1/2)) (+.f64 1 (pow.f64 x -1/2)))) (/.f64 -1 (+.f64 1 (pow.f64 x -1/2)))) (+.f64 1 (pow.f64 x -1/2))) (/.f64 3/8 (.f64 (+.f64 1 (pow.f64 x -1/2)) (+.f64 1 (pow.f64 x -1/2)))))) (/.f64 1/2 (.f64 (+.f64 1 (pow.f64 x -1/2)) (+.f64 1 (pow.f64 x -1/2)))))) (/.f64 -1 (+.f64 1 (pow.f64 x -1/2)))))
(+.f64 (/.f64 1 (+.f64 x (sqrt.f64 x))) (+.f64 (fma.f64 x (-.f64 (/.f64 1 (+.f64 1 (pow.f64 x -1/2))) (fma.f64 -1/2 (+.f64 (/.f64 1/2 (pow.f64 (+.f64 1 (pow.f64 x -1/2)) 3)) (/.f64 -1 (.f64 (+.f64 1 (pow.f64 x -1/2)) (+.f64 1 (pow.f64 x -1/2))))) (/.f64 3/8 (.f64 (+.f64 1 (pow.f64 x -1/2)) (+.f64 1 (pow.f64 x -1/2)))))) (/.f64 1/2 (.f64 (+.f64 1 (pow.f64 x -1/2)) (+.f64 1 (pow.f64 x -1/2))))) (fma.f64 (-.f64 (/.f64 5/16 (.f64 (+.f64 1 (pow.f64 x -1/2)) (+.f64 1 (pow.f64 x -1/2)))) (fma.f64 -1/2 (-.f64 (/.f64 (-.f64 (/.f64 1 (+.f64 1 (pow.f64 x -1/2))) (.f64 -1/2 (+.f64 (/.f64 1/2 (pow.f64 (+.f64 1 (pow.f64 x -1/2)) 3)) (/.f64 -1 (.f64 (+.f64 1 (pow.f64 x -1/2)) (+.f64 1 (pow.f64 x -1/2))))))) (+.f64 1 (pow.f64 x -1/2))) (/.f64 3/8 (pow.f64 (+.f64 1 (pow.f64 x -1/2)) 3))) (fma.f64 3/8 (+.f64 (/.f64 1/2 (pow.f64 (+.f64 1 (pow.f64 x -1/2)) 3)) (/.f64 -1 (.f64 (+.f64 1 (pow.f64 x -1/2)) (+.f64 1 (pow.f64 x -1/2))))) (/.f64 1 (+.f64 1 (pow.f64 x -1/2)))))) (.f64 x x) (/.f64 -1 (+.f64 1 (pow.f64 x -1/2))))))
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(fma.f64 3/8 (sqrt.f64 (/.f64 1 (pow.f64 x 5))) (fma.f64 -5/16 (sqrt.f64 (/.f64 1 (pow.f64 x 7))) (fma.f64 -1/2 (sqrt.f64 (/.f64 1 (pow.f64 x 3))) (*.f64 2 (sqrt.f64 (/.f64 1 x))))))
(fma.f64 3/8 (sqrt.f64 (/.f64 1 (pow.f64 x 5))) (fma.f64 (sqrt.f64 (/.f64 1 (pow.f64 x 7))) -5/16 (fma.f64 -1/2 (sqrt.f64 (/.f64 1 (pow.f64 x 3))) (*.f64 2 (sqrt.f64 (/.f64 1 x))))))
(fma.f64 3/8 (sqrt.f64 (/.f64 1 (pow.f64 x 5))) (fma.f64 -1/2 (sqrt.f64 (/.f64 1 (pow.f64 x 3))) (fma.f64 2 (sqrt.f64 (/.f64 1 x)) (*.f64 (sqrt.f64 (/.f64 1 (pow.f64 x 7))) -5/16))))
(fma.f64 3/8 (sqrt.f64 (/.f64 1 (pow.f64 x 5))) (fma.f64 -1/2 (sqrt.f64 (/.f64 1 (pow.f64 x 3))) (fma.f64 2 (sqrt.f64 (pow.f64 x -1)) (*.f64 (sqrt.f64 (/.f64 1 (pow.f64 x 7))) -5/16))))
(.f64 2 (exp.f64 (.f64 -1/2 (+.f64 (*.f64 -1 (log.f64 (/.f64 -1 x))) (log.f64 -1)))))
(*.f64 2 (pow.f64 (exp.f64 -1/2) (fma.f64 -1 (log.f64 (/.f64 -1 x)) (log.f64 -1))))
(*.f64 2 (pow.f64 (exp.f64 -1/2) (-.f64 (log.f64 -1) (log.f64 (/.f64 -1 x)))))
(.f64 2 (.f64 (pow.f64 (/.f64 -1 x) 1/2) (pow.f64 -1 -1/2)))
(*.f64 2 (pow.f64 (exp.f64 -1/2) (log.f64 x)))
(+.f64 (.f64 2 (exp.f64 (.f64 -1/2 (+.f64 (.f64 -1 (log.f64 (/.f64 -1 x))) (log.f64 -1))))) (.f64 -1/2 (/.f64 (exp.f64 (.f64 -1/2 (+.f64 (.f64 -1 (log.f64 (/.f64 -1 x))) (log.f64 -1)))) x)))
(fma.f64 2 (pow.f64 (exp.f64 -1/2) (fma.f64 -1 (log.f64 (/.f64 -1 x)) (log.f64 -1))) (*.f64 -1/2 (/.f64 (pow.f64 (exp.f64 -1/2) (fma.f64 -1 (log.f64 (/.f64 -1 x)) (log.f64 -1))) x)))
(fma.f64 -1/2 (/.f64 (pow.f64 (exp.f64 -1/2) (-.f64 (log.f64 -1) (log.f64 (/.f64 -1 x)))) x) (*.f64 2 (pow.f64 (exp.f64 -1/2) (-.f64 (log.f64 -1) (log.f64 (/.f64 -1 x))))))
(fma.f64 2 (.f64 (pow.f64 (/.f64 -1 x) 1/2) (pow.f64 -1 -1/2)) (.f64 (/.f64 -1/2 x) (*.f64 (pow.f64 (/.f64 -1 x) 1/2) (pow.f64 -1 -1/2))))
(fma.f64 2 (pow.f64 (exp.f64 -1/2) (log.f64 x)) (*.f64 (/.f64 -1/2 x) (pow.f64 (exp.f64 -1/2) (log.f64 x))))
(+.f64 (.f64 3/8 (/.f64 (exp.f64 (.f64 -1/2 (+.f64 (.f64 -1 (log.f64 (/.f64 -1 x))) (log.f64 -1)))) (pow.f64 x 2))) (+.f64 (.f64 2 (exp.f64 (.f64 -1/2 (+.f64 (.f64 -1 (log.f64 (/.f64 -1 x))) (log.f64 -1))))) (.f64 -1/2 (/.f64 (exp.f64 (.f64 -1/2 (+.f64 (*.f64 -1 (log.f64 (/.f64 -1 x))) (log.f64 -1)))) x))))
(fma.f64 3/8 (/.f64 (pow.f64 (exp.f64 -1/2) (fma.f64 -1 (log.f64 (/.f64 -1 x)) (log.f64 -1))) (.f64 x x)) (fma.f64 2 (pow.f64 (exp.f64 -1/2) (fma.f64 -1 (log.f64 (/.f64 -1 x)) (log.f64 -1))) (.f64 -1/2 (/.f64 (pow.f64 (exp.f64 -1/2) (fma.f64 -1 (log.f64 (/.f64 -1 x)) (log.f64 -1))) x))))
(fma.f64 3/8 (/.f64 (pow.f64 (exp.f64 -1/2) (-.f64 (log.f64 -1) (log.f64 (/.f64 -1 x)))) (.f64 x x)) (fma.f64 -1/2 (/.f64 (pow.f64 (exp.f64 -1/2) (-.f64 (log.f64 -1) (log.f64 (/.f64 -1 x)))) x) (.f64 2 (pow.f64 (exp.f64 -1/2) (-.f64 (log.f64 -1) (log.f64 (/.f64 -1 x)))))))
(fma.f64 2 (.f64 (pow.f64 (/.f64 -1 x) 1/2) (pow.f64 -1 -1/2)) (.f64 (/.f64 (*.f64 (pow.f64 (/.f64 -1 x) 1/2) (pow.f64 -1 -1/2)) x) (+.f64 -1/2 (/.f64 3/8 x))))
(fma.f64 2 (pow.f64 (exp.f64 -1/2) (log.f64 x)) (*.f64 (/.f64 (pow.f64 (exp.f64 -1/2) (log.f64 x)) x) (+.f64 -1/2 (/.f64 3/8 x))))
(+.f64 (.f64 3/8 (/.f64 (exp.f64 (.f64 -1/2 (+.f64 (.f64 -1 (log.f64 (/.f64 -1 x))) (log.f64 -1)))) (pow.f64 x 2))) (+.f64 (.f64 -5/16 (/.f64 (exp.f64 (.f64 -1/2 (+.f64 (.f64 -1 (log.f64 (/.f64 -1 x))) (log.f64 -1)))) (pow.f64 x 3))) (+.f64 (.f64 2 (exp.f64 (.f64 -1/2 (+.f64 (.f64 -1 (log.f64 (/.f64 -1 x))) (log.f64 -1))))) (.f64 -1/2 (/.f64 (exp.f64 (.f64 -1/2 (+.f64 (.f64 -1 (log.f64 (/.f64 -1 x))) (log.f64 -1)))) x)))))
(fma.f64 3/8 (/.f64 (pow.f64 (exp.f64 -1/2) (fma.f64 -1 (log.f64 (/.f64 -1 x)) (log.f64 -1))) (.f64 x x)) (fma.f64 -5/16 (/.f64 (pow.f64 (exp.f64 -1/2) (fma.f64 -1 (log.f64 (/.f64 -1 x)) (log.f64 -1))) (pow.f64 x 3)) (fma.f64 2 (pow.f64 (exp.f64 -1/2) (fma.f64 -1 (log.f64 (/.f64 -1 x)) (log.f64 -1))) (.f64 -1/2 (/.f64 (pow.f64 (exp.f64 -1/2) (fma.f64 -1 (log.f64 (/.f64 -1 x)) (log.f64 -1))) x)))))
(fma.f64 3/8 (/.f64 (pow.f64 (exp.f64 -1/2) (-.f64 (log.f64 -1) (log.f64 (/.f64 -1 x)))) (.f64 x x)) (fma.f64 -5/16 (/.f64 (pow.f64 (exp.f64 -1/2) (-.f64 (log.f64 -1) (log.f64 (/.f64 -1 x)))) (pow.f64 x 3)) (fma.f64 -1/2 (/.f64 (pow.f64 (exp.f64 -1/2) (-.f64 (log.f64 -1) (log.f64 (/.f64 -1 x)))) x) (.f64 2 (pow.f64 (exp.f64 -1/2) (-.f64 (log.f64 -1) (log.f64 (/.f64 -1 x))))))))
(fma.f64 -5/16 (/.f64 (.f64 (pow.f64 (/.f64 -1 x) 1/2) (pow.f64 -1 -1/2)) (pow.f64 x 3)) (fma.f64 2 (.f64 (pow.f64 (/.f64 -1 x) 1/2) (pow.f64 -1 -1/2)) (.f64 (/.f64 (.f64 (pow.f64 (/.f64 -1 x) 1/2) (pow.f64 -1 -1/2)) x) (+.f64 -1/2 (/.f64 3/8 x)))))
(fma.f64 -5/16 (/.f64 (pow.f64 (exp.f64 -1/2) (log.f64 x)) (pow.f64 x 3)) (fma.f64 2 (pow.f64 (exp.f64 -1/2) (log.f64 x)) (*.f64 (/.f64 (pow.f64 (exp.f64 -1/2) (log.f64 x)) x) (+.f64 -1/2 (/.f64 3/8 x)))))

eval731.0ms (6.4%)

Compiler: Compiled 25837 to 19718 computations (23.7% saved)

prune424.0ms (3.7%)

Pruning

26 alts after pruning (20 fresh and 6 done)

	Pruned	Kept	Total
New	1014	10	1024
Fresh	3	10	13
Picked	0	1	1
Done	3	5	8
Total	1020	26	1046

Error

0.0b

Counts

1046 → 26

Alt Table

Click to see full alt table

Status	Error	Program
✓	31.5b	(pow.f64 x -1/2)
	5.2b	(/.f64 (/.f64 (/.f64 (+.f64 1 (-.f64 x x)) x) (+.f64 1 x)) (+.f64 (pow.f64 x -1/2) (pow.f64 (+.f64 1 x) -1/2)))
	31.5b	(/.f64 (/.f64 1 (+.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x))) (+.f64 (+.f64 x 1/2) (/.f64 -1/8 x)))
	30.1b	(/.f64 (/.f64 1 (+.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x))) (+.f64 x 1/2))
	30.7b	(/.f64 (/.f64 1 (+.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x))) x)
	36.5b	(/.f64 (/.f64 1 (*.f64 x x)) (+.f64 (pow.f64 x -1/2) (pow.f64 (+.f64 1 x) -1/2)))
✓	21.4b	(/.f64 (-.f64 (/.f64 1 x) (/.f64 1 (+.f64 1 x))) (+.f64 (pow.f64 x -1/2) (pow.f64 (+.f64 1 x) -1/2)))
	47.3b	(/.f64 (-.f64 (/.f64 1 x) (/.f64 1 (+.f64 1 x))) (*.f64 2 (sqrt.f64 (/.f64 1 x))))
	52.3b	(/.f64 (-.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)) (+.f64 (+.f64 x 1/2) (/.f64 -1/8 x)))
✓	50.8b	(/.f64 (-.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)) (+.f64 x 1/2))
	26.3b	(/.f64 1 (fma.f64 x (.f64 (sqrt.f64 (/.f64 1 x)) 3/2) (.f64 2 (pow.f64 x 3/2))))
	5.2b	(/.f64 1 (/.f64 (+.f64 (pow.f64 x -1/2) (pow.f64 (+.f64 1 x) -1/2)) (/.f64 (/.f64 (+.f64 1 (-.f64 x x)) x) (+.f64 1 x))))
	30.4b	(/.f64 1 (+.f64 x (sqrt.f64 x)))
	59.3b	(/.f64 1 (+.f64 x 1/2))
	31.9b	(/.f64 1 (*.f64 2 (pow.f64 x 3/2)))
	21.0b	(-.f64 (pow.f64 x -1/2) (pow.f64 (+.f64 1 x) -1/2))
	30.5b	(-.f64 (pow.f64 x -1/2) (/.f64 1 (+.f64 (*.f64 1/2 x) 1)))
	22.7b	(-.f64 (pow.f64 x -1/2) (sqrt.f64 (/.f64 1 (+.f64 1 x))))
✓	31.8b	(-.f64 (pow.f64 x -1/2) 1)
✓	23.6b	(-.f64 (/.f64 1 (sqrt.f64 x)) (pow.f64 (+.f64 1 x) -1/2))
	31.4b	(-.f64 (/.f64 1 (sqrt.f64 x)) (+.f64 (*.f64 -1/2 x) 1))
✓	31.9b	(-.f64 (/.f64 1 (sqrt.f64 x)) 1)
	0.3b	(*.f64 (/.f64 -1 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x))) (/.f64 1 (neg.f64 (hypot.f64 x (sqrt.f64 x)))))
	42.4b	(*.f64 1/2 (sqrt.f64 (/.f64 1 (pow.f64 x 3))))
	60.3b	2
	62.8b	-1

Compiler

Compiled 311 to 245 computations (21.2% saved)

regimes103.0ms (0.9%)

Counts

63 → 1

Calls

Call 1

Inputs
-1
2
(/.f64 1 (+.f64 x 1/2))
(pow.f64 x -1/2)
(-.f64 (pow.f64 x -1/2) 1)
(-.f64 (/.f64 1 (sqrt.f64 x)) 1)
(/.f64 1 (+.f64 x (sqrt.f64 x)))
(/.f64 1 (*.f64 2 (pow.f64 x 3/2)))
(/.f64 1 (sqrt.f64 (*.f64 x (+.f64 1 x))))
(-.f64 (/.f64 1 (sqrt.f64 x)) (+.f64 (*.f64 -1/2 x) 1))
(-.f64 (pow.f64 x -1/2) (/.f64 1 (+.f64 (*.f64 1/2 x) 1)))
(-.f64 (/.f64 1 (sqrt.f64 x)) (/.f64 1 (+.f64 (*.f64 1/2 x) 1)))
(/.f64 (-.f64 (/.f64 1 x) (/.f64 1 (+.f64 1 x))) (*.f64 2 (sqrt.f64 (/.f64 1 x))))
(*.f64 1/2 (sqrt.f64 (/.f64 1 (pow.f64 x 3))))
(-.f64 (/.f64 1 (sqrt.f64 x)) (sqrt.f64 (/.f64 1 x)))
(-.f64 (pow.f64 x -1/2) (pow.f64 (+.f64 1 x) -1/2))
(/.f64 (-.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)) x)
(-.f64 (/.f64 1 (sqrt.f64 x)) (pow.f64 (+.f64 1 x) -1/2))
(-.f64 (pow.f64 x -1/2) (sqrt.f64 (/.f64 1 (+.f64 1 x))))
(-.f64 (pow.f64 x -1/2) (/.f64 1 (sqrt.f64 (+.f64 x 1))))
(-.f64 (sqrt.f64 (/.f64 1 x)) (/.f64 1 (sqrt.f64 (+.f64 x 1))))
(-.f64 (/.f64 1 (sqrt.f64 x)) (sqrt.f64 (/.f64 1 (+.f64 1 x))))
(-.f64 (/.f64 1 (sqrt.f64 x)) (/.f64 1 (sqrt.f64 (+.f64 x 1))))
(/.f64 (-.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)) (+.f64 x 1/2))
(/.f64 (/.f64 1 (+.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x))) x)
(-.f64 (pow.f64 (*.f64 x x) -1/4) (/.f64 1 (sqrt.f64 (+.f64 x 1))))
(/.f64 (/.f64 1 (+.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x))) (+.f64 x 1/2))
(-.f64 (/.f64 1 (sqrt.f64 x)) (sqrt.f64 (+.f64 (/.f64 1 x) (/.f64 (/.f64 -1 x) x))))
(/.f64 (-.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)) (+.f64 (+.f64 x 1/2) (/.f64 -1/8 x)))
(/.f64 (/.f64 1 (*.f64 x x)) (+.f64 (pow.f64 x -1/2) (pow.f64 (+.f64 1 x) -1/2)))
(/.f64 (/.f64 (+.f64 x (-.f64 1 x)) (+.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x))) x)
(/.f64 (/.f64 1 (+.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x))) (+.f64 (+.f64 x 1/2) (/.f64 -1/8 x)))
(/.f64 (/.f64 (+.f64 x (-.f64 1 x)) (+.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x))) (+.f64 x 1/2))
(/.f64 (-.f64 (/.f64 1 x) (/.f64 1 (+.f64 1 x))) (+.f64 (pow.f64 x -1/2) (pow.f64 (+.f64 1 x) -1/2)))
(/.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)))))
(/.f64 (/.f64 (+.f64 x (-.f64 1 x)) (+.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x))) (+.f64 (+.f64 x 1/2) (/.f64 -1/8 x)))
(/.f64 (/.f64 (/.f64 (+.f64 1 (-.f64 x x)) x) (+.f64 1 x)) (+.f64 (pow.f64 x -1/2) (pow.f64 (+.f64 1 x) -1/2)))
(/.f64 1 (/.f64 (+.f64 (pow.f64 x -1/2) (pow.f64 (+.f64 1 x) -1/2)) (/.f64 (/.f64 (+.f64 1 (-.f64 x x)) x) (+.f64 1 x))))
(-.f64 (/.f64 1 (sqrt.f64 x)) (exp.f64 (*.f64 -1/2 (log1p.f64 x))))
(-.f64 (/.f64 1 (sqrt.f64 x)) (cbrt.f64 (pow.f64 (+.f64 1 x) -3/2)))
(-.f64 (/.f64 1 (sqrt.f64 x)) (pow.f64 (cbrt.f64 (+.f64 1 x)) -3/2))
(-.f64 (/.f64 1 (sqrt.f64 x)) (pow.f64 (pow.f64 (+.f64 1 x) -1/4) 2))
(-.f64 (pow.f64 (pow.f64 x 1/4) -2) (/.f64 1 (sqrt.f64 (+.f64 x 1))))
(/.f64 (-.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)) (sqrt.f64 (*.f64 x (+.f64 1 x))))
(/.f64 1 (fma.f64 x (.f64 (sqrt.f64 (/.f64 1 x)) 3/2) (.f64 2 (pow.f64 x 3/2))))
(/.f64 (/.f64 1 (+.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x))) (sqrt.f64 (*.f64 x (+.f64 1 x))))
(/.f64 (/.f64 (+.f64 x (-.f64 1 x)) (+.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x))) (sqrt.f64 (*.f64 x (+.f64 1 x))))
(/.f64 (-.f64 (pow.f64 x -3/2) (pow.f64 (+.f64 1 x) -3/2)) (+.f64 (/.f64 1 x) (+.f64 (/.f64 1 (+.f64 1 x)) (pow.f64 (*.f64 x (+.f64 1 x)) -1/2))))
(/.f64 (-.f64 (pow.f64 x -3/2) (pow.f64 (+.f64 1 x) -3/2)) (+.f64 (/.f64 1 x) (+.f64 (/.f64 1 (+.f64 1 x)) (pow.f64 (*.f64 (+.f64 1 x) x) -1/2))))
(/.f64 1 (/.f64 (+.f64 (/.f64 1 x) (+.f64 (/.f64 1 (+.f64 1 x)) (pow.f64 (*.f64 x (+.f64 1 x)) -1/2))) (-.f64 (pow.f64 x -3/2) (pow.f64 (+.f64 1 x) -3/2))))
(fma.f64 (pow.f64 x -1/4) (pow.f64 x -1/4) (/.f64 -1 (sqrt.f64 (+.f64 1 x))))
(fma.f64 (pow.f64 x -1/6) (cbrt.f64 (/.f64 1 x)) (/.f64 -1 (sqrt.f64 (+.f64 1 x))))
(fma.f64 (pow.f64 (+.f64 1 x) -1/4) (neg.f64 (pow.f64 (+.f64 1 x) -1/4)) (pow.f64 x -1/2))
(*.f64 (/.f64 -1 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x))) (/.f64 1 (neg.f64 (hypot.f64 x (sqrt.f64 x)))))
(/.f64 (-.f64 (/.f64 1 x) (pow.f64 (/.f64 -1 (sqrt.f64 (+.f64 1 x))) 2)) (-.f64 (pow.f64 x -1/2) (/.f64 -1 (sqrt.f64 (+.f64 1 x)))))
(fma.f64 (/.f64 1 (sqrt.f64 (cbrt.f64 x))) (cbrt.f64 (/.f64 1 x)) (/.f64 -1 (sqrt.f64 (+.f64 1 x))))
(/.f64 (fma.f64 (pow.f64 (+.f64 x 1) 1/4) (pow.f64 (+.f64 x 1) 1/4) (neg.f64 (sqrt.f64 x))) (sqrt.f64 (*.f64 x (+.f64 1 x))))
(fma.f64 (pow.f64 x -1/6) (cbrt.f64 (/.f64 1 x)) (*.f64 (/.f64 -1 (pow.f64 (+.f64 x 1) 1/6)) (cbrt.f64 (/.f64 1 (+.f64 x 1)))))
(fma.f64 (/.f64 (pow.f64 (+.f64 x 1) 1/4) 1) (/.f64 (pow.f64 (+.f64 x 1) 1/4) (hypot.f64 x (sqrt.f64 x))) (neg.f64 (/.f64 1 (sqrt.f64 (+.f64 x 1)))))
(fma.f64 (pow.f64 (cbrt.f64 (/.f64 -1 (sqrt.f64 (+.f64 1 x)))) 2) (cbrt.f64 (/.f64 -1 (sqrt.f64 (+.f64 1 x)))) (pow.f64 x -1/2))
(/.f64 (+.f64 (pow.f64 x -3/2) (pow.f64 (/.f64 -1 (sqrt.f64 (+.f64 1 x))) 3)) (+.f64 (/.f64 1 x) (-.f64 (pow.f64 (/.f64 -1 (sqrt.f64 (+.f64 1 x))) 2) (*.f64 (pow.f64 x -1/2) (/.f64 -1 (sqrt.f64 (+.f64 1 x)))))))
(fma.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))) (fma.f64 (neg.f64 (pow.f64 (+.f64 1 x) -1/6)) (cbrt.f64 (/.f64 1 (+.f64 1 x))) (pow.f64 (+.f64 1 x) -1/2)))
(fma.f64 (/.f64 (cbrt.f64 (+.f64 x 1)) (cbrt.f64 (fma.f64 x x x))) (/.f64 (pow.f64 (+.f64 x 1) 1/6) (pow.f64 (fma.f64 x x x) 1/6)) (neg.f64 (/.f64 1 (sqrt.f64 (+.f64 x 1)))))

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

Calls

3 calls:

41.0ms	x
17.0ms	(-.f64 (/.f64 1 (sqrt.f64 x)) (/.f64 1 (sqrt.f64 (+.f64 x 1))))
15.0ms	(-.f64 (/.f64 1 (sqrt.f64 x)) (/.f64 1 (sqrt.f64 (+.f64 x 1))))

Results

Error	Segments	Branch
0.3b	1	`x`
0.3b	1	`(-.f64 (/.f64 1 (sqrt.f64 x)) (/.f64 1 (sqrt.f64 (+.f64 x 1))))`
0.3b	1	`(-.f64 (/.f64 1 (sqrt.f64 x)) (/.f64 1 (sqrt.f64 (+.f64 x 1))))`

Compiler

Compiled 957 to 714 computations (25.4% saved)

regimes116.0ms (1%)

Counts

53 → 2

Calls

Call 1

Inputs
-1
2
(/.f64 1 (+.f64 x 1/2))
(pow.f64 x -1/2)
(-.f64 (pow.f64 x -1/2) 1)
(-.f64 (/.f64 1 (sqrt.f64 x)) 1)
(/.f64 1 (+.f64 x (sqrt.f64 x)))
(/.f64 1 (*.f64 2 (pow.f64 x 3/2)))
(/.f64 1 (sqrt.f64 (*.f64 x (+.f64 1 x))))
(-.f64 (/.f64 1 (sqrt.f64 x)) (+.f64 (*.f64 -1/2 x) 1))
(-.f64 (pow.f64 x -1/2) (/.f64 1 (+.f64 (*.f64 1/2 x) 1)))
(-.f64 (/.f64 1 (sqrt.f64 x)) (/.f64 1 (+.f64 (*.f64 1/2 x) 1)))
(/.f64 (-.f64 (/.f64 1 x) (/.f64 1 (+.f64 1 x))) (*.f64 2 (sqrt.f64 (/.f64 1 x))))
(*.f64 1/2 (sqrt.f64 (/.f64 1 (pow.f64 x 3))))
(-.f64 (/.f64 1 (sqrt.f64 x)) (sqrt.f64 (/.f64 1 x)))
(-.f64 (pow.f64 x -1/2) (pow.f64 (+.f64 1 x) -1/2))
(/.f64 (-.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)) x)
(-.f64 (/.f64 1 (sqrt.f64 x)) (pow.f64 (+.f64 1 x) -1/2))
(-.f64 (pow.f64 x -1/2) (sqrt.f64 (/.f64 1 (+.f64 1 x))))
(-.f64 (pow.f64 x -1/2) (/.f64 1 (sqrt.f64 (+.f64 x 1))))
(-.f64 (sqrt.f64 (/.f64 1 x)) (/.f64 1 (sqrt.f64 (+.f64 x 1))))
(-.f64 (/.f64 1 (sqrt.f64 x)) (sqrt.f64 (/.f64 1 (+.f64 1 x))))
(-.f64 (/.f64 1 (sqrt.f64 x)) (/.f64 1 (sqrt.f64 (+.f64 x 1))))
(/.f64 (-.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)) (+.f64 x 1/2))
(/.f64 (/.f64 1 (+.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x))) x)
(-.f64 (pow.f64 (*.f64 x x) -1/4) (/.f64 1 (sqrt.f64 (+.f64 x 1))))
(/.f64 (/.f64 1 (+.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x))) (+.f64 x 1/2))
(-.f64 (/.f64 1 (sqrt.f64 x)) (sqrt.f64 (+.f64 (/.f64 1 x) (/.f64 (/.f64 -1 x) x))))
(/.f64 (-.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)) (+.f64 (+.f64 x 1/2) (/.f64 -1/8 x)))
(/.f64 (/.f64 1 (*.f64 x x)) (+.f64 (pow.f64 x -1/2) (pow.f64 (+.f64 1 x) -1/2)))
(/.f64 (/.f64 (+.f64 x (-.f64 1 x)) (+.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x))) x)
(/.f64 (/.f64 1 (+.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x))) (+.f64 (+.f64 x 1/2) (/.f64 -1/8 x)))
(/.f64 (/.f64 (+.f64 x (-.f64 1 x)) (+.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x))) (+.f64 x 1/2))
(/.f64 (-.f64 (/.f64 1 x) (/.f64 1 (+.f64 1 x))) (+.f64 (pow.f64 x -1/2) (pow.f64 (+.f64 1 x) -1/2)))
(/.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)))))
(/.f64 (/.f64 (+.f64 x (-.f64 1 x)) (+.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x))) (+.f64 (+.f64 x 1/2) (/.f64 -1/8 x)))
(/.f64 (/.f64 (/.f64 (+.f64 1 (-.f64 x x)) x) (+.f64 1 x)) (+.f64 (pow.f64 x -1/2) (pow.f64 (+.f64 1 x) -1/2)))
(/.f64 1 (/.f64 (+.f64 (pow.f64 x -1/2) (pow.f64 (+.f64 1 x) -1/2)) (/.f64 (/.f64 (+.f64 1 (-.f64 x x)) x) (+.f64 1 x))))
(-.f64 (/.f64 1 (sqrt.f64 x)) (exp.f64 (*.f64 -1/2 (log1p.f64 x))))
(-.f64 (/.f64 1 (sqrt.f64 x)) (cbrt.f64 (pow.f64 (+.f64 1 x) -3/2)))
(-.f64 (/.f64 1 (sqrt.f64 x)) (pow.f64 (cbrt.f64 (+.f64 1 x)) -3/2))
(-.f64 (/.f64 1 (sqrt.f64 x)) (pow.f64 (pow.f64 (+.f64 1 x) -1/4) 2))
(-.f64 (pow.f64 (pow.f64 x 1/4) -2) (/.f64 1 (sqrt.f64 (+.f64 x 1))))
(/.f64 (-.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)) (sqrt.f64 (*.f64 x (+.f64 1 x))))
(/.f64 1 (fma.f64 x (.f64 (sqrt.f64 (/.f64 1 x)) 3/2) (.f64 2 (pow.f64 x 3/2))))
(/.f64 (/.f64 1 (+.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x))) (sqrt.f64 (*.f64 x (+.f64 1 x))))
(/.f64 (/.f64 (+.f64 x (-.f64 1 x)) (+.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x))) (sqrt.f64 (*.f64 x (+.f64 1 x))))
(/.f64 (-.f64 (pow.f64 x -3/2) (pow.f64 (+.f64 1 x) -3/2)) (+.f64 (/.f64 1 x) (+.f64 (/.f64 1 (+.f64 1 x)) (pow.f64 (*.f64 x (+.f64 1 x)) -1/2))))
(/.f64 (-.f64 (pow.f64 x -3/2) (pow.f64 (+.f64 1 x) -3/2)) (+.f64 (/.f64 1 x) (+.f64 (/.f64 1 (+.f64 1 x)) (pow.f64 (*.f64 (+.f64 1 x) x) -1/2))))
(/.f64 1 (/.f64 (+.f64 (/.f64 1 x) (+.f64 (/.f64 1 (+.f64 1 x)) (pow.f64 (*.f64 x (+.f64 1 x)) -1/2))) (-.f64 (pow.f64 x -3/2) (pow.f64 (+.f64 1 x) -3/2))))
(fma.f64 (pow.f64 x -1/4) (pow.f64 x -1/4) (/.f64 -1 (sqrt.f64 (+.f64 1 x))))
(fma.f64 (pow.f64 x -1/6) (cbrt.f64 (/.f64 1 x)) (/.f64 -1 (sqrt.f64 (+.f64 1 x))))
(fma.f64 (pow.f64 (+.f64 1 x) -1/4) (neg.f64 (pow.f64 (+.f64 1 x) -1/4)) (pow.f64 x -1/2))

Outputs
(/.f64 (/.f64 1 (+.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x))) (+.f64 (+.f64 x 1/2) (/.f64 -1/8 x)))
(-.f64 (pow.f64 x -1/2) (pow.f64 (+.f64 1 x) -1/2))

Calls

3 calls:

50.0ms	x
21.0ms	(-.f64 (/.f64 1 (sqrt.f64 x)) (/.f64 1 (sqrt.f64 (+.f64 x 1))))
20.0ms	(-.f64 (/.f64 1 (sqrt.f64 x)) (/.f64 1 (sqrt.f64 (+.f64 x 1))))

Results

Error	Segments	Branch
0.2b	2	`x`
0.2b	2	`(-.f64 (/.f64 1 (sqrt.f64 x)) (/.f64 1 (sqrt.f64 (+.f64 x 1))))`
0.2b	2	`(-.f64 (/.f64 1 (sqrt.f64 x)) (/.f64 1 (sqrt.f64 (+.f64 x 1))))`

Compiler

Compiled 708 to 521 computations (26.4% saved)

bsearch1.0ms (0%)

Algorithm

1×	left-value

Steps

Time	Left	Right
0.0ms	3.513291095286891e-8	2.7816499947146134e-6

Compiler

Compiled 16 to 13 computations (18.8% saved)

regimes67.0ms (0.6%)

Counts

31 → 2

Calls

Call 1

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

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

Calls

3 calls:

29.0ms	x
17.0ms	(-.f64 (/.f64 1 (sqrt.f64 x)) (/.f64 1 (sqrt.f64 (+.f64 x 1))))
11.0ms	(-.f64 (/.f64 1 (sqrt.f64 x)) (/.f64 1 (sqrt.f64 (+.f64 x 1))))

Results

Error	Segments	Branch
0.3b	2	`x`
0.3b	2	`(-.f64 (/.f64 1 (sqrt.f64 x)) (/.f64 1 (sqrt.f64 (+.f64 x 1))))`
0.3b	2	`(-.f64 (/.f64 1 (sqrt.f64 x)) (/.f64 1 (sqrt.f64 (+.f64 x 1))))`

Compiler

Compiled 323 to 236 computations (26.9% saved)

bsearch0.0ms (0%)

Algorithm

1×	left-value

Steps

Time	Left	Right
0.0ms	3.858536481646246e-9	3.513291095286891e-8

Compiler

Compiled 16 to 13 computations (18.8% saved)

regimes60.0ms (0.5%)

Counts

26 → 2

Calls

Call 1

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

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

Calls

3 calls:

25.0ms	x
15.0ms	(-.f64 (/.f64 1 (sqrt.f64 x)) (/.f64 1 (sqrt.f64 (+.f64 x 1))))
11.0ms	(-.f64 (/.f64 1 (sqrt.f64 x)) (/.f64 1 (sqrt.f64 (+.f64 x 1))))

Results

Error	Segments	Branch
0.6b	2	`x`
0.6b	2	`(-.f64 (/.f64 1 (sqrt.f64 x)) (/.f64 1 (sqrt.f64 (+.f64 x 1))))`
0.6b	2	`(-.f64 (/.f64 1 (sqrt.f64 x)) (/.f64 1 (sqrt.f64 (+.f64 x 1))))`

Compiler

Compiled 250 to 188 computations (24.8% saved)

bsearch0.0ms (0%)

Algorithm

1×	left-value

Steps

Time	Left	Right
0.0ms	6.52993406417314e-13	3.913074183257981e-12

Compiler

Compiled 16 to 13 computations (18.8% saved)

regimes51.0ms (0.4%)

Counts

24 → 2

Calls

Call 1

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

Outputs
(/.f64 1 (*.f64 2 (pow.f64 x 3/2)))
(-.f64 (pow.f64 x -1/2) (sqrt.f64 (/.f64 1 (+.f64 1 x))))

Calls

3 calls:

22.0ms	x
12.0ms	(-.f64 (/.f64 1 (sqrt.f64 x)) (/.f64 1 (sqrt.f64 (+.f64 x 1))))
9.0ms	(-.f64 (/.f64 1 (sqrt.f64 x)) (/.f64 1 (sqrt.f64 (+.f64 x 1))))

Results

Error	Segments	Branch
1.0b	2	`x`
1.0b	2	`(-.f64 (/.f64 1 (sqrt.f64 x)) (/.f64 1 (sqrt.f64 (+.f64 x 1))))`
1.0b	2	`(-.f64 (/.f64 1 (sqrt.f64 x)) (/.f64 1 (sqrt.f64 (+.f64 x 1))))`

Compiler

Compiled 227 to 172 computations (24.2% saved)

bsearch0.0ms (0%)

Algorithm

1×	left-value

Steps

Time	Left	Right
0.0ms	6.52993406417314e-13	3.913074183257981e-12

Compiler

Compiled 16 to 13 computations (18.8% saved)

regimes25.0ms (0.2%)

Counts

18 → 2

Calls

Call 1

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

Outputs
(-.f64 (pow.f64 x -1/2) (pow.f64 (+.f64 1 x) -1/2))
(/.f64 1 (*.f64 2 (pow.f64 x 3/2)))

Calls

1 calls:

20.0ms

Results

Error	Segments	Branch
1.0b	2	`x`

Compiler

Compiled 139 to 104 computations (25.2% saved)

bsearch23.0ms (0.2%)

Algorithm

1×	binary-search

Steps

Time	Left	Right
22.0ms	25368878.874387436	83696533.72948863

Compiler

Compiled 16 to 13 computations (18.8% saved)

regimes22.0ms (0.2%)

Counts

15 → 2

Calls

Call 1

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

Outputs
(-.f64 (pow.f64 x -1/2) (/.f64 1 (+.f64 (*.f64 1/2 x) 1)))
(/.f64 1 (*.f64 2 (pow.f64 x 3/2)))

Calls

1 calls:

18.0ms

Results

Error	Segments	Branch
1.6b	2	`x`

Compiler

Compiled 111 to 85 computations (23.4% saved)

bsearch25.0ms (0.2%)

Algorithm

1×	binary-search

Steps

Time	Left	Right
24.0ms	0.001837971661049503	5.084189196427086

Compiler

Compiled 16 to 13 computations (18.8% saved)

regimes15.0ms (0.1%)

Counts

10 → 2

Calls

Call 1

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

Outputs
(-.f64 (/.f64 1 (sqrt.f64 x)) (+.f64 (*.f64 -1/2 x) 1))
(/.f64 1 (*.f64 2 (pow.f64 x 3/2)))

Calls

1 calls:

12.0ms

Results

Error	Segments	Branch
1.7b	2	`x`

Compiler

Compiled 55 to 41 computations (25.5% saved)

bsearch25.0ms (0.2%)

Algorithm

1×	binary-search

Steps

Time	Left	Right
24.0ms	0.001837971661049503	5.084189196427086

Compiler

Compiled 16 to 13 computations (18.8% saved)

regimes17.0ms (0.1%)

Counts

9 → 2

Calls

Call 1

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

Outputs
(-.f64 (pow.f64 x -1/2) 1)
(/.f64 1 (*.f64 2 (pow.f64 x 3/2)))

Calls

1 calls:

14.0ms

Results

Error	Segments	Branch
1.8b	2	`x`

Compiler

Compiled 45 to 34 computations (24.4% saved)

bsearch23.0ms (0.2%)

Algorithm

1×	binary-search

Steps

Time	Left	Right
23.0ms	0.001837971661049503	5.084189196427086

Compiler

Compiled 16 to 13 computations (18.8% saved)

regimes8.0ms (0.1%)

Counts

7 → 1

Calls

Call 1

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

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

Calls

1 calls:

6.0ms

Results

Error	Segments	Branch
30.4b	1	`x`

Compiler

Compiled 30 to 22 computations (26.7% saved)

regimes11.0ms (0.1%)

Counts

6 → 2

Calls

Call 1

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

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

Calls

1 calls:

9.0ms

Results

Error	Segments	Branch
30.0b	2	`x`

Compiler

Compiled 24 to 19 computations (20.8% saved)

bsearch23.0ms (0.2%)

Algorithm

1×	binary-search

Steps

Time	Left	Right
23.0ms	0.001837971661049503	5.084189196427086

Compiler

Compiled 16 to 13 computations (18.8% saved)

regimes6.0ms (0.1%)

Counts

4 → 1

Calls

Call 1

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

Outputs
(pow.f64 x -1/2)

Calls

1 calls:

4.0ms

Results

Error	Segments	Branch
31.5b	1	`x`

Compiler

Compiled 13 to 10 computations (23.1% saved)

regimes5.0ms (0%)

Counts

3 → 1

Calls

Call 1

Inputs
-1
2
(/.f64 1 (+.f64 x 1/2))

Outputs
(/.f64 1 (+.f64 x 1/2))

Calls

1 calls:

4.0ms

Results

Error	Segments	Branch
59.3b	1	`x`

Compiler

Compiled 10 to 8 computations (20% saved)

regimes4.0ms (0%)

Accuracy

Total -2.5b remaining (-4.1%)

Threshold costs -2.5b (-4.1%)

Counts

2 → 1

Calls

Call 1

Inputs
-1
2

Outputs
2

Calls

1 calls:

3.0ms

Results

Error	Segments	Branch
60.3b	1	`x`

Compiler

Compiled 5 to 4 computations (20% saved)

simplify26.0ms (0.2%)

Algorithm

1×	egg-herbie

Rules

23×	`+-commutative_binary64`
14×	`sub-neg_binary64`
12×	`*-commutative_binary64`
8×	`neg-sub0_binary64`
8×	`neg-mul-1_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	71	401
1	99	401
2	122	401
3	142	401
4	152	401
5	155	401
6	156	401

Stop Event

1×	fuel
1×	saturated

Calls

Call 1

Inputs
(*.f64 (/.f64 -1 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x))) (/.f64 1 (neg.f64 (hypot.f64 x (sqrt.f64 x)))))
(if (<=.f64 (-.f64 (/.f64 1 (sqrt.f64 x)) (/.f64 1 (sqrt.f64 (+.f64 x 1)))) 944473296573929/18889465931478580854784) (/.f64 (/.f64 1 (+.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x))) (+.f64 (+.f64 x 1/2) (/.f64 -1/8 x))) (-.f64 (pow.f64 x -1/2) (pow.f64 (+.f64 1 x) -1/2)))
(if (<=.f64 (-.f64 (/.f64 1 (sqrt.f64 x)) (/.f64 1 (sqrt.f64 (+.f64 x 1)))) 3022314549036573/604462909807314587353088) (/.f64 (/.f64 1 (+.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x))) (+.f64 x 1/2)) (-.f64 (pow.f64 x -1/2) (pow.f64 (+.f64 1 x) -1/2)))
(if (<=.f64 (-.f64 (/.f64 1 (sqrt.f64 x)) (/.f64 1 (sqrt.f64 (+.f64 x 1)))) 4951760157141521/4951760157141521099596496896) (/.f64 (/.f64 1 (+.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x))) x) (-.f64 (pow.f64 x -1/2) (sqrt.f64 (/.f64 1 (+.f64 1 x)))))
(if (<=.f64 (-.f64 (/.f64 1 (sqrt.f64 x)) (/.f64 1 (sqrt.f64 (+.f64 x 1)))) 4951760157141521/4951760157141521099596496896) (/.f64 1 (*.f64 2 (pow.f64 x 3/2))) (-.f64 (pow.f64 x -1/2) (sqrt.f64 (/.f64 1 (+.f64 1 x)))))
(if (<=.f64 x 3404953284427479/134217728) (-.f64 (pow.f64 x -1/2) (pow.f64 (+.f64 1 x) -1/2)) (/.f64 1 (*.f64 2 (pow.f64 x 3/2))))
(if (<=.f64 x 8476148211527755/4611686018427387904) (-.f64 (pow.f64 x -1/2) (/.f64 1 (+.f64 (.f64 1/2 x) 1))) (/.f64 1 (.f64 2 (pow.f64 x 3/2))))
(if (<=.f64 x 8476148211527755/4611686018427387904) (-.f64 (/.f64 1 (sqrt.f64 x)) (+.f64 (.f64 -1/2 x) 1)) (/.f64 1 (.f64 2 (pow.f64 x 3/2))))
(if (<=.f64 x 8476148211527755/4611686018427387904) (-.f64 (pow.f64 x -1/2) 1) (/.f64 1 (*.f64 2 (pow.f64 x 3/2))))
(/.f64 1 (+.f64 x (sqrt.f64 x)))
(if (<=.f64 x 8476148211527755/4611686018427387904) (-.f64 (pow.f64 x -1/2) 1) (/.f64 1 (+.f64 x 1/2)))
(pow.f64 x -1/2)
(/.f64 1 (+.f64 x 1/2))
2
-1

Outputs
(*.f64 (/.f64 -1 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x))) (/.f64 1 (neg.f64 (hypot.f64 x (sqrt.f64 x)))))
(*.f64 (/.f64 -1 (+.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 1 x)))) (/.f64 1 (neg.f64 (hypot.f64 x (sqrt.f64 x)))))
(if (<=.f64 (-.f64 (/.f64 1 (sqrt.f64 x)) (/.f64 1 (sqrt.f64 (+.f64 x 1)))) 944473296573929/18889465931478580854784) (/.f64 (/.f64 1 (+.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x))) (+.f64 (+.f64 x 1/2) (/.f64 -1/8 x))) (-.f64 (pow.f64 x -1/2) (pow.f64 (+.f64 1 x) -1/2)))
(if (<=.f64 (-.f64 (/.f64 1 (sqrt.f64 x)) (/.f64 1 (sqrt.f64 (+.f64 1 x)))) 944473296573929/18889465931478580854784) (/.f64 (/.f64 1 (+.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 1 x)))) (+.f64 (+.f64 x 1/2) (/.f64 -1/8 x))) (-.f64 (pow.f64 x -1/2) (pow.f64 (+.f64 1 x) -1/2)))
(if (<=.f64 (-.f64 (/.f64 1 (sqrt.f64 x)) (/.f64 1 (sqrt.f64 (+.f64 x 1)))) 3022314549036573/604462909807314587353088) (/.f64 (/.f64 1 (+.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x))) (+.f64 x 1/2)) (-.f64 (pow.f64 x -1/2) (pow.f64 (+.f64 1 x) -1/2)))
(if (<=.f64 (-.f64 (/.f64 1 (sqrt.f64 x)) (/.f64 1 (sqrt.f64 (+.f64 1 x)))) 3022314549036573/604462909807314587353088) (/.f64 (/.f64 1 (+.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 1 x)))) (+.f64 x 1/2)) (-.f64 (pow.f64 x -1/2) (pow.f64 (+.f64 1 x) -1/2)))
(if (<=.f64 (-.f64 (/.f64 1 (sqrt.f64 x)) (/.f64 1 (sqrt.f64 (+.f64 x 1)))) 4951760157141521/4951760157141521099596496896) (/.f64 (/.f64 1 (+.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x))) x) (-.f64 (pow.f64 x -1/2) (sqrt.f64 (/.f64 1 (+.f64 1 x)))))
(if (<=.f64 (-.f64 (/.f64 1 (sqrt.f64 x)) (/.f64 1 (sqrt.f64 (+.f64 1 x)))) 4951760157141521/4951760157141521099596496896) (/.f64 (/.f64 1 (+.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 1 x)))) x) (-.f64 (pow.f64 x -1/2) (sqrt.f64 (/.f64 1 (+.f64 1 x)))))
(if (<=.f64 (-.f64 (/.f64 1 (sqrt.f64 x)) (/.f64 1 (sqrt.f64 (+.f64 x 1)))) 4951760157141521/4951760157141521099596496896) (/.f64 1 (*.f64 2 (pow.f64 x 3/2))) (-.f64 (pow.f64 x -1/2) (sqrt.f64 (/.f64 1 (+.f64 1 x)))))
(if (<=.f64 (-.f64 (/.f64 1 (sqrt.f64 x)) (/.f64 1 (sqrt.f64 (+.f64 1 x)))) 4951760157141521/4951760157141521099596496896) (/.f64 1 (*.f64 2 (pow.f64 x 3/2))) (-.f64 (pow.f64 x -1/2) (sqrt.f64 (/.f64 1 (+.f64 1 x)))))
(if (<=.f64 x 3404953284427479/134217728) (-.f64 (pow.f64 x -1/2) (pow.f64 (+.f64 1 x) -1/2)) (/.f64 1 (*.f64 2 (pow.f64 x 3/2))))
(if (<=.f64 x 8476148211527755/4611686018427387904) (-.f64 (pow.f64 x -1/2) (/.f64 1 (+.f64 (.f64 1/2 x) 1))) (/.f64 1 (.f64 2 (pow.f64 x 3/2))))
(if (<=.f64 x 8476148211527755/4611686018427387904) (-.f64 (pow.f64 x -1/2) (/.f64 1 (+.f64 1 (.f64 x 1/2)))) (/.f64 1 (.f64 2 (pow.f64 x 3/2))))
(if (<=.f64 x 8476148211527755/4611686018427387904) (+.f64 (pow.f64 x -1/2) (/.f64 -1 (+.f64 1 (.f64 x 1/2)))) (/.f64 1 (.f64 2 (pow.f64 x 3/2))))
(if (<=.f64 x 8476148211527755/4611686018427387904) (+.f64 (pow.f64 x -1/2) (/.f64 -1 (-.f64 1 (.f64 x -1/2)))) (/.f64 1 (.f64 2 (pow.f64 x 3/2))))
(if (<=.f64 x 8476148211527755/4611686018427387904) (-.f64 (/.f64 1 (sqrt.f64 x)) (+.f64 (.f64 -1/2 x) 1)) (/.f64 1 (.f64 2 (pow.f64 x 3/2))))
(if (<=.f64 x 8476148211527755/4611686018427387904) (-.f64 (/.f64 1 (sqrt.f64 x)) (+.f64 1 (.f64 x -1/2))) (/.f64 1 (.f64 2 (pow.f64 x 3/2))))
(if (<=.f64 x 8476148211527755/4611686018427387904) (+.f64 (/.f64 1 (sqrt.f64 x)) (-.f64 -1 (.f64 x -1/2))) (/.f64 1 (.f64 2 (pow.f64 x 3/2))))
(if (<=.f64 x 8476148211527755/4611686018427387904) (-.f64 (pow.f64 x -1/2) 1) (/.f64 1 (*.f64 2 (pow.f64 x 3/2))))
(if (<=.f64 x 8476148211527755/4611686018427387904) (+.f64 (pow.f64 x -1/2) -1) (/.f64 1 (*.f64 2 (pow.f64 x 3/2))))
(if (<=.f64 x 8476148211527755/4611686018427387904) (+.f64 -1 (pow.f64 x -1/2)) (/.f64 1 (*.f64 2 (pow.f64 x 3/2))))
(/.f64 1 (+.f64 x (sqrt.f64 x)))
(if (<=.f64 x 8476148211527755/4611686018427387904) (-.f64 (pow.f64 x -1/2) 1) (/.f64 1 (+.f64 x 1/2)))
(if (<=.f64 x 8476148211527755/4611686018427387904) (+.f64 (pow.f64 x -1/2) -1) (/.f64 1 (+.f64 x 1/2)))
(if (<=.f64 x 8476148211527755/4611686018427387904) (+.f64 -1 (pow.f64 x -1/2)) (/.f64 1 (+.f64 x 1/2)))
(pow.f64 x -1/2)
(/.f64 1 (+.f64 x 1/2))
2
-1

Compiler

Compiled 283 to 226 computations (20.1% saved)

soundness98.0ms (0.9%)

Algorithm

1×	egg-herbie

Rules

671×	`fma-neg_binary64`
642×	`times-frac_binary64`
433×	`cancel-sign-sub-inv_binary64`
393×	`fma-def_binary64`
385×	`associate-l_binary64`

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	45	108
1	129	106
2	371	106
3	920	100
4	3432	100

Stop Event

1×	node limit

Compiler

Compiled 240 to 200 computations (16.7% saved)

end174.0ms (1.5%)

Compiler: Compiled 269 to 206 computations (23.4% 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	171	17
9	207	17
10	233	17
11	235	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	171	17
9	207	17
10	233	17
11	235	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	171	17
9	207	17
10	233	17
11	235	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	171	17
9	207	17
10	233	17
11	235	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	171	17
9	207	17
10	233	17
11	235	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	171	17
9	207	17
10	233	17
11	235	17