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)

sample1.8s (21.2%)

Results

867.0ms	2343×	body	1024	valid
715.0ms	4861×	body	256	valid
238.0ms	1052×	body	512	valid

Bogosity

preprocess21.0ms (0.2%)

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)

simplify21.0ms (0.2%)

Algorithm

1×	egg-herbie

Rules

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

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	9	17
1	14	17
2	20	17
3	28	17
4	38	17
5	56	17
6	93	17
7	127	17
8	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

18.3b

Counts

3 → 1

Alt Table

Click to see full alt table

Status	Error	Program
▶	18.3b	(-.f64 (/.f64 1 (sqrt.f64 x)) (/.f64 1 (sqrt.f64 (+.f64 x 1))))

Compiler

Compiled 12 to 10 computations (16.7% saved)

localize15.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(sqrt.f64 (+.f64 x 1))
✓	0.1b	(/.f64 1 (sqrt.f64 (+.f64 x 1)))
✓	0.3b	(/.f64 1 (sqrt.f64 x))
✓	2.2b	(-.f64 (/.f64 1 (sqrt.f64 x)) (/.f64 1 (sqrt.f64 (+.f64 x 1))))

Compiler

Compiled 33 to 23 computations (30.3% saved)

series11.0ms (0.1%)

Counts

4 → 8

Calls

12 calls:

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

rewrite89.0ms (1%)

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 log1p.f64 (expm1.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 +.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 log1p.f64 (expm1.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 +.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 log1p.f64 (expm1.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))))))

simplify162.0ms (1.9%)

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)

eval130.0ms (1.5%)

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

prune88.0ms (1%)

Pruning

27 alts after pruning (26 fresh and 1 done)

	Pruned	Kept	Total
New	216	26	242
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	216	27	243

Error

17.8b

Counts

243 → 27

Alt Table

Click to see full alt table

Status	Error	Program
▶	18.4b	(/.f64 (-.f64 (/.f64 1 x) (/.f64 1 (+.f64 1 x))) (+.f64 (pow.f64 x -1/2) (pow.f64 (+.f64 1 x) -1/2)))
	20.8b	(-.f64 (/.f64 1 (sqrt.f64 x)) (pow.f64 (+.f64 1 x) -1/2))
	20.7b	(-.f64 (pow.f64 x -1/2) (/.f64 1 (sqrt.f64 (+.f64 x 1))))
▶	18.3b	(/.f64 (-.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)) (sqrt.f64 (*.f64 x (+.f64 1 x))))
	21.1b	(-.f64 (/.f64 1 (sqrt.f64 x)) (sqrt.f64 (/.f64 1 (+.f64 1 x))))
	30.4b	(fma.f64 (/.f64 1 (cbrt.f64 x)) (pow.f64 x -1/6) (/.f64 -1 (sqrt.f64 (+.f64 1 x))))
	30.0b	(-.f64 (/.f64 1 (sqrt.f64 x)) (+.f64 (*.f64 -1/2 x) 1))
	28.8b	(/.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))))
▶	30.3b	(-.f64 (/.f64 1 (sqrt.f64 x)) 1)
	26.7b	(+.f64 (fma.f64 (pow.f64 x -1/6) (cbrt.f64 (/.f64 1 x)) (neg.f64 (.f64 (pow.f64 (+.f64 1 x) -1/6) (/.f64 1 (cbrt.f64 (+.f64 1 x)))))) (fma.f64 (neg.f64 (pow.f64 (+.f64 1 x) -1/6)) (/.f64 1 (cbrt.f64 (+.f64 1 x))) (.f64 (pow.f64 (+.f64 1 x) -1/6) (/.f64 1 (cbrt.f64 (+.f64 1 x))))))
	24.5b	(-.f64 (/.f64 1 (sqrt.f64 x)) (pow.f64 (pow.f64 (+.f64 1 x) 1/4) -2))
	28.5b	(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))
▶	22.2b	(-.f64 (/.f64 1 (sqrt.f64 x)) (pow.f64 (pow.f64 (+.f64 1 x) -1/4) 2))
▶	29.0b	(fma.f64 (pow.f64 x -1/4) (pow.f64 x -1/4) (/.f64 -1 (sqrt.f64 (+.f64 1 x))))
	25.5b	(-.f64 (/.f64 1 (sqrt.f64 x)) (pow.f64 (cbrt.f64 (+.f64 1 x)) -3/2))
	24.6b	(-.f64 (pow.f64 (pow.f64 x 1/4) -2) (/.f64 1 (sqrt.f64 (+.f64 x 1))))
	28.5b	(fma.f64 (pow.f64 (+.f64 1 x) -1/4) (neg.f64 (pow.f64 (+.f64 1 x) -1/4)) (pow.f64 x -1/2))
	24.7b	(/.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)))))
	22.4b	(-.f64 (pow.f64 (pow.f64 x -1/4) 2) (/.f64 1 (sqrt.f64 (+.f64 x 1))))
✓	18.3b	(-.f64 (/.f64 1 (sqrt.f64 x)) (/.f64 1 (sqrt.f64 (+.f64 x 1))))
	29.0b	(/.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)))))))
	28.6b	(-.f64 (/.f64 1 (sqrt.f64 x)) (/.f64 1 (cbrt.f64 (pow.f64 (+.f64 1 x) 3/2))))
	28.6b	(-.f64 (/.f64 1 (sqrt.f64 x)) (cbrt.f64 (pow.f64 (+.f64 1 x) -3/2)))
	39.3b	(-.f64 (cbrt.f64 (pow.f64 x -3/2)) (/.f64 1 (sqrt.f64 (+.f64 x 1))))
	25.9b	(-.f64 (pow.f64 (cbrt.f64 x) -3/2) (/.f64 1 (sqrt.f64 (+.f64 x 1))))
	28.6b	(-.f64 (/.f64 1 (sqrt.f64 x)) (exp.f64 (*.f64 -1/2 (log1p.f64 x))))
	29.3b	(-.f64 (/.f64 1 (sqrt.f64 x)) (/.f64 1 (+.f64 (*.f64 1/2 x) 1)))

Compiler

Compiled 872 to 720 computations (17.4% saved)

localize21.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(*.f64 x (+.f64 1 x))
✓	0.2b	(/.f64 (-.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)) (sqrt.f64 (*.f64 x (+.f64 1 x))))
✓	2.2b	(-.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x))
✓	17.8b	(sqrt.f64 (*.f64 x (+.f64 1 x)))

Compiler

Compiled 44 to 28 computations (36.4% saved)

series15.0ms (0.2%)

Counts

4 → 21

Calls

12 calls:

Time	Variable		Point	Expression
3.0ms	x	@	inf	(*.f64 x (+.f64 1 x))
3.0ms	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))))

rewrite144.0ms (1.7%)

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	49
1	224	43
2	3303	40

Stop Event

1×	node limit

Counts

4 → 248

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

simplify63.0ms (0.7%)

Algorithm

1×	egg-herbie

Rules

792×	`fma-neg_binary64`
654×	`times-frac_binary64`
502×	`cancel-sign-sub-inv_binary64`
247×	`associate-*r/_binary64`
246×	`associate-*l/_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	35	141
1	98	123
2	290	123
3	668	123
4	2430	123

Stop Event

1×	node limit

Counts

269 → 263

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
x
(+.f64 (pow.f64 x 2) x)
(+.f64 (pow.f64 x 2) x)
(+.f64 (pow.f64 x 2) x)
(pow.f64 x 2)
(+.f64 (pow.f64 x 2) x)
(+.f64 (pow.f64 x 2) x)
(+.f64 (pow.f64 x 2) x)
(pow.f64 x 2)
(+.f64 (pow.f64 x 2) x)
(+.f64 (pow.f64 x 2) x)
(+.f64 (pow.f64 x 2) x)

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

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)

rewrite161.0ms (1.9%)

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 log1p.f64 (expm1.f64 (+.f64 (pow.f64 x -1/2) -1)))))) (#(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 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

localize83.0ms (1%)

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))
✓	0.3b	(/.f64 (-.f64 (/.f64 1 x) (/.f64 1 (+.f64 1 x))) (+.f64 (pow.f64 x -1/2) (pow.f64 (+.f64 1 x) -1/2)))
✓	2.1b	(-.f64 (/.f64 1 x) (/.f64 1 (+.f64 1 x)))

Compiler

Compiled 60 to 46 computations (23.3% saved)

series11.0ms (0.1%)

Counts

4 → 48

Calls

12 calls:

Time	Variable		Point	Expression
3.0ms	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)))
2.0ms	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)))
2.0ms	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))

rewrite293.0ms (3.4%)

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	61
1	296	46
2	4663	46

Stop Event

1×	node limit

Counts

4 → 363

Calls

Call 1

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

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

simplify106.0ms (1.2%)

Algorithm

1×	egg-herbie

Rules

637×	`fma-def_binary64`
625×	`fma-neg_binary64`
449×	`associate-+l+_binary64`
322×	`associate-+r+_binary64`
300×	`+-commutative_binary64`

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	189	1796
1	598	1716
2	1783	1560
3	6816	1493

Stop Event

1×	node limit

Counts

411 → 436

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

localize23.0ms (0.3%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(pow.f64 (+.f64 1 x) -1/4)
✓	0.2b	(pow.f64 (pow.f64 (+.f64 1 x) -1/4) 2)
	0.3b	(/.f64 1 (sqrt.f64 x))
✓	16.7b	(-.f64 (/.f64 1 (sqrt.f64 x)) (pow.f64 (pow.f64 (+.f64 1 x) -1/4) 2))

Compiler

Compiled 38 to 28 computations (26.3% saved)

series47.0ms (0.5%)

Counts

3 → 26

Calls

9 calls:

Time	Variable		Point	Expression
41.0ms	x	@	-inf	(-.f64 (/.f64 1 (sqrt.f64 x)) (pow.f64 (pow.f64 (+.f64 1 x) -1/4) 2))
1.0ms	x	@	inf	(-.f64 (/.f64 1 (sqrt.f64 x)) (pow.f64 (pow.f64 (+.f64 1 x) -1/4) 2))
1.0ms	x	@	inf	(pow.f64 (+.f64 1 x) -1/4)
1.0ms	x	@	0	(-.f64 (/.f64 1 (sqrt.f64 x)) (pow.f64 (pow.f64 (+.f64 1 x) -1/4) 2))
1.0ms	x	@	-inf	(pow.f64 (pow.f64 (+.f64 1 x) -1/4) 2)

rewrite218.0ms (2.5%)

Algorithm

1×	batch-egg-rewrite

Rules

620×	`prod-diff_binary64`
465×	`log-prod_binary64`
317×	`fma-def_binary64`
285×	`pow2_binary64`
195×	`expm1-udef_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	11	29
1	252	27
2	3127	27

Stop Event

1×	node limit

Counts

3 → 182

Calls

Call 1

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

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)) (+.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 (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)) (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 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-1/2)))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (-.f64 (pow.f64 x -3/2) (pow.f64 (+.f64 1 x) -3/2)) (/.f64 1 (+.f64 (/.f64 1 x) (fma.f64 (pow.f64 x -1/2) (pow.f64 (+.f64 1 x) -1/2) (pow.f64 (+.f64 1 x) -1)))) (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 fma.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))) (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 x) (pow.f64 (+.f64 1 x) -1)) (/.f64 1 (+.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 fma.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))) (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 fma.f64 (pow.f64 (cbrt.f64 (neg.f64 (pow.f64 (+.f64 1 x) -1/2))) 2) (cbrt.f64 (neg.f64 (pow.f64 (+.f64 1 x) -1/2))) (pow.f64 x -1/2))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (sqrt.f64 (neg.f64 (pow.f64 (+.f64 1 x) -1/2))) (sqrt.f64 (neg.f64 (pow.f64 (+.f64 1 x) -1/2))) (pow.f64 x -1/2))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (neg.f64 (pow.f64 (+.f64 1 x) -1/4)) (pow.f64 (+.f64 1 x) -1/4) (pow.f64 x -1/2))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (/.f64 1 (cbrt.f64 x)) (pow.f64 x -1/6) (neg.f64 (pow.f64 (+.f64 1 x) -1/2)))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (/.f64 1 (cbrt.f64 x)) (pow.f64 x -1/6) (*.f64 (neg.f64 (pow.f64 (+.f64 1 x) -1/2)) 1))))) (#(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)) (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 (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 (neg.f64 (pow.f64 (+.f64 1 x) -1/2)) (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)) (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 fma.f64 (neg.f64 (cbrt.f64 (pow.f64 (+.f64 1 x) -1))) (pow.f64 (+.f64 1 x) -1/6) (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) -1/4) (pow.f64 (+.f64 1 x) -1/4))))) (#(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 (pow.f64 (+.f64 1 x) -1/6) (*.f64 (pow.f64 (+.f64 1 x) -1/12) (pow.f64 (+.f64 1 x) -1/4)))))) (#(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) -1/8) (*.f64 (pow.f64 (+.f64 1 x) -1/8) (pow.f64 (+.f64 1 x) -1/4)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (pow.f64 (+.f64 1 x) -1/8) 3) (pow.f64 (+.f64 1 x) -1/8))))) (#(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 (pow.f64 (cbrt.f64 (+.f64 1 x)) -1) (pow.f64 (+.f64 1 x) -1/6))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (*.f64 (pow.f64 (+.f64 1 x) -1/4) (pow.f64 (+.f64 1 x) -1/6)) (pow.f64 (+.f64 1 x) -1/12))))) (#(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 log1p.f64 (expm1.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 (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 +.f64 0 (pow.f64 (+.f64 1 x) -1/4))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (log.f64 (pow.f64 (cbrt.f64 (exp.f64 (pow.f64 (+.f64 1 x) -1/4))) 2)) (log.f64 (cbrt.f64 (exp.f64 (pow.f64 (+.f64 1 x) -1/4)))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (log.f64 (sqrt.f64 (exp.f64 (pow.f64 (+.f64 1 x) -1/4)))) (log.f64 (sqrt.f64 (exp.f64 (pow.f64 (+.f64 1 x) -1/4)))))))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (exp.f64 (log1p.f64 (pow.f64 (+.f64 1 x) -1/4))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 1 (pow.f64 (+.f64 1 x) -1/4))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (+.f64 1 x) -1/4) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (+.f64 1 x) -1/12) (pow.f64 (+.f64 1 x) -1/6))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (+.f64 1 x) -1/6) (pow.f64 (+.f64 1 x) -1/12))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (+.f64 1 x) -1/8) (pow.f64 (+.f64 1 x) -1/8))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (sqrt.f64 (cbrt.f64 (pow.f64 (+.f64 1 x) -1))) (sqrt.f64 (pow.f64 (+.f64 1 x) -1/6)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 1 -1/4) (pow.f64 (+.f64 1 x) -1/4))))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f64 (pow.f64 (+.f64 1 x) -1/2))))) (#(struct:change #<rule egg-rr> (2) ((x fabs.f64 (pow.f64 (+.f64 1 x) -1/4))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (exp.f64 (pow.f64 (+.f64 1 x) -1/4)))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (+.f64 1 (expm1.f64 (pow.f64 (+.f64 1 x) -1/4))))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (pow.f64 (+.f64 1 x) -3/4))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (pow.f64 (+.f64 1 x) -1/4)))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (pow.f64 (+.f64 1 x) -1/4)))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 -1/4 (log1p.f64 x)))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (*.f64 -1/4 (log1p.f64 x)) 1))))))

simplify56.0ms (0.6%)

Algorithm

1×	egg-herbie

Rules

649×	`associate-/r*_binary64`
525×	`associate-*l/_binary64`
420×	`fma-def_binary64`
365×	`*-commutative_binary64`
326×	`associate-*r/_binary64`

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	118	883
1	315	801
2	863	681
3	3028	495

Stop Event

1×	node limit

Counts

208 → 229

Calls

Call 1

Inputs
(*.f64 -1 (sqrt.f64 (/.f64 1 x)))
(.f64 -1 (pow.f64 (exp.f64 (.f64 -1/4 (+.f64 (*.f64 -1 (log.f64 (/.f64 -1 x))) (log.f64 -1)))) 2))
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 1/16 (sqrt.f64 (/.f64 1 (pow.f64 x 5)))) (+.f64 (sqrt.f64 (/.f64 1 x)) (+.f64 (.f64 5/16 (sqrt.f64 (/.f64 1 (pow.f64 x 5)))) (*.f64 -1/2 (sqrt.f64 (/.f64 1 (pow.f64 x 3)))))))
(+.f64 (.f64 -5/64 (sqrt.f64 (/.f64 1 (pow.f64 x 7)))) (+.f64 (.f64 1/16 (sqrt.f64 (/.f64 1 (pow.f64 x 5)))) (+.f64 (.f64 -15/64 (sqrt.f64 (/.f64 1 (pow.f64 x 7)))) (+.f64 (sqrt.f64 (/.f64 1 x)) (+.f64 (.f64 5/16 (sqrt.f64 (/.f64 1 (pow.f64 x 5)))) (*.f64 -1/2 (sqrt.f64 (/.f64 1 (pow.f64 x 3)))))))))
(pow.f64 (exp.f64 (.f64 -1/4 (+.f64 (.f64 -1 (log.f64 (/.f64 -1 x))) (log.f64 -1)))) 2)
(+.f64 (.f64 -1/2 (/.f64 (pow.f64 (exp.f64 (.f64 -1/4 (+.f64 (.f64 -1 (log.f64 (/.f64 -1 x))) (log.f64 -1)))) 2) x)) (pow.f64 (exp.f64 (.f64 -1/4 (+.f64 (*.f64 -1 (log.f64 (/.f64 -1 x))) (log.f64 -1)))) 2))
(+.f64 (.f64 -1/2 (/.f64 (pow.f64 (exp.f64 (.f64 -1/4 (+.f64 (.f64 -1 (log.f64 (/.f64 -1 x))) (log.f64 -1)))) 2) x)) (+.f64 (.f64 1/16 (/.f64 (pow.f64 (exp.f64 (.f64 -1/4 (+.f64 (.f64 -1 (log.f64 (/.f64 -1 x))) (log.f64 -1)))) 2) (pow.f64 x 2))) (+.f64 (.f64 5/16 (/.f64 (pow.f64 (exp.f64 (.f64 -1/4 (+.f64 (.f64 -1 (log.f64 (/.f64 -1 x))) (log.f64 -1)))) 2) (pow.f64 x 2))) (pow.f64 (exp.f64 (.f64 -1/4 (+.f64 (*.f64 -1 (log.f64 (/.f64 -1 x))) (log.f64 -1)))) 2))))
(+.f64 (.f64 -1/2 (/.f64 (pow.f64 (exp.f64 (.f64 -1/4 (+.f64 (.f64 -1 (log.f64 (/.f64 -1 x))) (log.f64 -1)))) 2) x)) (+.f64 (.f64 1/16 (/.f64 (pow.f64 (exp.f64 (.f64 -1/4 (+.f64 (.f64 -1 (log.f64 (/.f64 -1 x))) (log.f64 -1)))) 2) (pow.f64 x 2))) (+.f64 (.f64 -1 (/.f64 (+.f64 (.f64 5/64 (pow.f64 (exp.f64 (.f64 -1/4 (+.f64 (.f64 -1 (log.f64 (/.f64 -1 x))) (log.f64 -1)))) 2)) (.f64 15/64 (pow.f64 (exp.f64 (.f64 -1/4 (+.f64 (.f64 -1 (log.f64 (/.f64 -1 x))) (log.f64 -1)))) 2))) (pow.f64 x 3))) (+.f64 (.f64 5/16 (/.f64 (pow.f64 (exp.f64 (.f64 -1/4 (+.f64 (.f64 -1 (log.f64 (/.f64 -1 x))) (log.f64 -1)))) 2) (pow.f64 x 2))) (pow.f64 (exp.f64 (.f64 -1/4 (+.f64 (.f64 -1 (log.f64 (/.f64 -1 x))) (log.f64 -1)))) 2)))))
1
(+.f64 1 (*.f64 -1/4 x))
(+.f64 1 (+.f64 (.f64 -1/4 x) (.f64 5/32 (pow.f64 x 2))))
(+.f64 1 (+.f64 (.f64 -1/4 x) (+.f64 (.f64 -15/128 (pow.f64 x 3)) (*.f64 5/32 (pow.f64 x 2)))))
(pow.f64 (/.f64 1 x) 1/4)
(+.f64 (*.f64 -1/4 (pow.f64 (/.f64 1 (pow.f64 x 5)) 1/4)) (pow.f64 (/.f64 1 x) 1/4))
(+.f64 (.f64 5/32 (pow.f64 (/.f64 1 (pow.f64 x 9)) 1/4)) (+.f64 (.f64 -1/4 (pow.f64 (/.f64 1 (pow.f64 x 5)) 1/4)) (pow.f64 (/.f64 1 x) 1/4)))
(+.f64 (.f64 -15/128 (pow.f64 (/.f64 1 (pow.f64 x 13)) 1/4)) (+.f64 (.f64 5/32 (pow.f64 (/.f64 1 (pow.f64 x 9)) 1/4)) (+.f64 (*.f64 -1/4 (pow.f64 (/.f64 1 (pow.f64 x 5)) 1/4)) (pow.f64 (/.f64 1 x) 1/4))))
(exp.f64 (.f64 -1/4 (+.f64 (.f64 -1 (log.f64 (/.f64 -1 x))) (log.f64 -1))))
(+.f64 (.f64 -1/4 (/.f64 (exp.f64 (.f64 -1/4 (+.f64 (.f64 -1 (log.f64 (/.f64 -1 x))) (log.f64 -1)))) x)) (exp.f64 (.f64 -1/4 (+.f64 (*.f64 -1 (log.f64 (/.f64 -1 x))) (log.f64 -1)))))
(+.f64 (.f64 -1/4 (/.f64 (exp.f64 (.f64 -1/4 (+.f64 (.f64 -1 (log.f64 (/.f64 -1 x))) (log.f64 -1)))) x)) (+.f64 (exp.f64 (.f64 -1/4 (+.f64 (.f64 -1 (log.f64 (/.f64 -1 x))) (log.f64 -1)))) (.f64 5/32 (/.f64 (exp.f64 (.f64 -1/4 (+.f64 (.f64 -1 (log.f64 (/.f64 -1 x))) (log.f64 -1)))) (pow.f64 x 2)))))
(+.f64 (.f64 -1/4 (/.f64 (exp.f64 (.f64 -1/4 (+.f64 (.f64 -1 (log.f64 (/.f64 -1 x))) (log.f64 -1)))) x)) (+.f64 (exp.f64 (.f64 -1/4 (+.f64 (.f64 -1 (log.f64 (/.f64 -1 x))) (log.f64 -1)))) (+.f64 (.f64 5/32 (/.f64 (exp.f64 (.f64 -1/4 (+.f64 (.f64 -1 (log.f64 (/.f64 -1 x))) (log.f64 -1)))) (pow.f64 x 2))) (.f64 -15/128 (/.f64 (exp.f64 (.f64 -1/4 (+.f64 (*.f64 -1 (log.f64 (/.f64 -1 x))) (log.f64 -1)))) (pow.f64 x 3))))))

Outputs
(*.f64 -1 (sqrt.f64 (/.f64 1 x)))
(neg.f64 (sqrt.f64 (/.f64 1 x)))
(.f64 -1 (pow.f64 (exp.f64 (.f64 -1/4 (+.f64 (*.f64 -1 (log.f64 (/.f64 -1 x))) (log.f64 -1)))) 2))
(neg.f64 (pow.f64 (pow.f64 (exp.f64 -1/4) (fma.f64 -1 (log.f64 (/.f64 -1 x)) (log.f64 -1))) 2))
(neg.f64 (pow.f64 (pow.f64 (exp.f64 -1/4) (-.f64 (log.f64 -1) (log.f64 (/.f64 -1 x)))) 2))
(neg.f64 (pow.f64 (*.f64 (pow.f64 (/.f64 -1 x) 1/4) (pow.f64 -1 -1/4)) 2))
(neg.f64 (pow.f64 (exp.f64 (log.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))
(+.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 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)))
(sqrt.f64 (/.f64 1 x))
(+.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)))
(+.f64 (.f64 1/16 (sqrt.f64 (/.f64 1 (pow.f64 x 5)))) (+.f64 (sqrt.f64 (/.f64 1 x)) (+.f64 (.f64 5/16 (sqrt.f64 (/.f64 1 (pow.f64 x 5)))) (*.f64 -1/2 (sqrt.f64 (/.f64 1 (pow.f64 x 3)))))))
(fma.f64 1/16 (sqrt.f64 (/.f64 1 (pow.f64 x 5))) (+.f64 (sqrt.f64 (/.f64 1 x)) (fma.f64 5/16 (sqrt.f64 (/.f64 1 (pow.f64 x 5))) (*.f64 -1/2 (sqrt.f64 (/.f64 1 (pow.f64 x 3)))))))
(+.f64 (fma.f64 -1/2 (sqrt.f64 (/.f64 1 (pow.f64 x 3))) (*.f64 (sqrt.f64 (/.f64 1 (pow.f64 x 5))) 5/16)) (fma.f64 1/16 (sqrt.f64 (/.f64 1 (pow.f64 x 5))) (sqrt.f64 (/.f64 1 x))))
(fma.f64 1/16 (sqrt.f64 (/.f64 1 (pow.f64 x 5))) (fma.f64 (sqrt.f64 (/.f64 1 (pow.f64 x 5))) 5/16 (fma.f64 -1/2 (sqrt.f64 (/.f64 1 (pow.f64 x 3))) (sqrt.f64 (/.f64 1 x)))))
(+.f64 (fma.f64 -1/2 (sqrt.f64 (/.f64 1 (pow.f64 x 3))) (sqrt.f64 (/.f64 1 x))) (*.f64 (sqrt.f64 (/.f64 1 (pow.f64 x 5))) 3/8))
(+.f64 (.f64 -5/64 (sqrt.f64 (/.f64 1 (pow.f64 x 7)))) (+.f64 (.f64 1/16 (sqrt.f64 (/.f64 1 (pow.f64 x 5)))) (+.f64 (.f64 -15/64 (sqrt.f64 (/.f64 1 (pow.f64 x 7)))) (+.f64 (sqrt.f64 (/.f64 1 x)) (+.f64 (.f64 5/16 (sqrt.f64 (/.f64 1 (pow.f64 x 5)))) (*.f64 -1/2 (sqrt.f64 (/.f64 1 (pow.f64 x 3)))))))))
(fma.f64 -5/64 (sqrt.f64 (/.f64 1 (pow.f64 x 7))) (fma.f64 1/16 (sqrt.f64 (/.f64 1 (pow.f64 x 5))) (fma.f64 -15/64 (sqrt.f64 (/.f64 1 (pow.f64 x 7))) (+.f64 (sqrt.f64 (/.f64 1 x)) (fma.f64 5/16 (sqrt.f64 (/.f64 1 (pow.f64 x 5))) (*.f64 -1/2 (sqrt.f64 (/.f64 1 (pow.f64 x 3)))))))))
(fma.f64 -5/64 (sqrt.f64 (/.f64 1 (pow.f64 x 7))) (fma.f64 1/16 (sqrt.f64 (/.f64 1 (pow.f64 x 5))) (+.f64 (fma.f64 -1/2 (sqrt.f64 (/.f64 1 (pow.f64 x 3))) (*.f64 (sqrt.f64 (/.f64 1 (pow.f64 x 5))) 5/16)) (fma.f64 (sqrt.f64 (/.f64 1 (pow.f64 x 7))) -15/64 (sqrt.f64 (/.f64 1 x))))))
(fma.f64 -5/64 (sqrt.f64 (/.f64 1 (pow.f64 x 7))) (fma.f64 1/16 (sqrt.f64 (/.f64 1 (pow.f64 x 5))) (fma.f64 (sqrt.f64 (/.f64 1 (pow.f64 x 7))) -15/64 (fma.f64 (sqrt.f64 (/.f64 1 (pow.f64 x 5))) 5/16 (fma.f64 -1/2 (sqrt.f64 (/.f64 1 (pow.f64 x 3))) (sqrt.f64 (/.f64 1 x)))))))
(+.f64 (+.f64 (fma.f64 -1/2 (sqrt.f64 (/.f64 1 (pow.f64 x 3))) (sqrt.f64 (/.f64 1 x))) (.f64 (sqrt.f64 (/.f64 1 (pow.f64 x 5))) 3/8)) (.f64 (sqrt.f64 (/.f64 1 (pow.f64 x 7))) -5/16))
(pow.f64 (exp.f64 (.f64 -1/4 (+.f64 (.f64 -1 (log.f64 (/.f64 -1 x))) (log.f64 -1)))) 2)
(pow.f64 (pow.f64 (exp.f64 -1/4) (fma.f64 -1 (log.f64 (/.f64 -1 x)) (log.f64 -1))) 2)
(pow.f64 (pow.f64 (exp.f64 -1/4) (-.f64 (log.f64 -1) (log.f64 (/.f64 -1 x)))) 2)
(pow.f64 (*.f64 (pow.f64 (/.f64 -1 x) 1/4) (pow.f64 -1 -1/4)) 2)
(pow.f64 (exp.f64 (log.f64 x)) -1/2)
(+.f64 (.f64 -1/2 (/.f64 (pow.f64 (exp.f64 (.f64 -1/4 (+.f64 (.f64 -1 (log.f64 (/.f64 -1 x))) (log.f64 -1)))) 2) x)) (pow.f64 (exp.f64 (.f64 -1/4 (+.f64 (*.f64 -1 (log.f64 (/.f64 -1 x))) (log.f64 -1)))) 2))
(fma.f64 -1/2 (/.f64 (pow.f64 (pow.f64 (exp.f64 -1/4) (fma.f64 -1 (log.f64 (/.f64 -1 x)) (log.f64 -1))) 2) x) (pow.f64 (pow.f64 (exp.f64 -1/4) (fma.f64 -1 (log.f64 (/.f64 -1 x)) (log.f64 -1))) 2))
(fma.f64 -1/2 (/.f64 (pow.f64 (pow.f64 (exp.f64 -1/4) (-.f64 (log.f64 -1) (log.f64 (/.f64 -1 x)))) 2) x) (pow.f64 (pow.f64 (exp.f64 -1/4) (-.f64 (log.f64 -1) (log.f64 (/.f64 -1 x)))) 2))
(fma.f64 -1/2 (/.f64 (pow.f64 (.f64 (pow.f64 (/.f64 -1 x) 1/4) (pow.f64 -1 -1/4)) 2) x) (pow.f64 (.f64 (pow.f64 (/.f64 -1 x) 1/4) (pow.f64 -1 -1/4)) 2))
(*.f64 (+.f64 (/.f64 -1/2 x) 1) (pow.f64 (exp.f64 (log.f64 x)) -1/2))
(+.f64 (.f64 -1/2 (/.f64 (pow.f64 (exp.f64 (.f64 -1/4 (+.f64 (.f64 -1 (log.f64 (/.f64 -1 x))) (log.f64 -1)))) 2) x)) (+.f64 (.f64 1/16 (/.f64 (pow.f64 (exp.f64 (.f64 -1/4 (+.f64 (.f64 -1 (log.f64 (/.f64 -1 x))) (log.f64 -1)))) 2) (pow.f64 x 2))) (+.f64 (.f64 5/16 (/.f64 (pow.f64 (exp.f64 (.f64 -1/4 (+.f64 (.f64 -1 (log.f64 (/.f64 -1 x))) (log.f64 -1)))) 2) (pow.f64 x 2))) (pow.f64 (exp.f64 (.f64 -1/4 (+.f64 (*.f64 -1 (log.f64 (/.f64 -1 x))) (log.f64 -1)))) 2))))
(fma.f64 -1/2 (/.f64 (pow.f64 (pow.f64 (exp.f64 -1/4) (fma.f64 -1 (log.f64 (/.f64 -1 x)) (log.f64 -1))) 2) x) (fma.f64 1/16 (/.f64 (pow.f64 (pow.f64 (exp.f64 -1/4) (fma.f64 -1 (log.f64 (/.f64 -1 x)) (log.f64 -1))) 2) (.f64 x x)) (fma.f64 5/16 (/.f64 (pow.f64 (pow.f64 (exp.f64 -1/4) (fma.f64 -1 (log.f64 (/.f64 -1 x)) (log.f64 -1))) 2) (.f64 x x)) (pow.f64 (pow.f64 (exp.f64 -1/4) (fma.f64 -1 (log.f64 (/.f64 -1 x)) (log.f64 -1))) 2))))
(fma.f64 -1/2 (/.f64 (pow.f64 (pow.f64 (exp.f64 -1/4) (-.f64 (log.f64 -1) (log.f64 (/.f64 -1 x)))) 2) x) (+.f64 (pow.f64 (pow.f64 (exp.f64 -1/4) (-.f64 (log.f64 -1) (log.f64 (/.f64 -1 x)))) 2) (.f64 (/.f64 (pow.f64 (pow.f64 (exp.f64 -1/4) (-.f64 (log.f64 -1) (log.f64 (/.f64 -1 x)))) 2) (.f64 x x)) 3/8)))
(fma.f64 -1/2 (/.f64 (pow.f64 (.f64 (pow.f64 (/.f64 -1 x) 1/4) (pow.f64 -1 -1/4)) 2) x) (fma.f64 (/.f64 (pow.f64 (.f64 (pow.f64 (/.f64 -1 x) 1/4) (pow.f64 -1 -1/4)) 2) (.f64 x x)) 3/8 (pow.f64 (.f64 (pow.f64 (/.f64 -1 x) 1/4) (pow.f64 -1 -1/4)) 2)))
(fma.f64 (/.f64 (pow.f64 (exp.f64 (log.f64 x)) -1/2) (.f64 x x)) 3/8 (.f64 (+.f64 (/.f64 -1/2 x) 1) (pow.f64 (exp.f64 (log.f64 x)) -1/2)))
(+.f64 (.f64 -1/2 (/.f64 (pow.f64 (exp.f64 (.f64 -1/4 (+.f64 (.f64 -1 (log.f64 (/.f64 -1 x))) (log.f64 -1)))) 2) x)) (+.f64 (.f64 1/16 (/.f64 (pow.f64 (exp.f64 (.f64 -1/4 (+.f64 (.f64 -1 (log.f64 (/.f64 -1 x))) (log.f64 -1)))) 2) (pow.f64 x 2))) (+.f64 (.f64 -1 (/.f64 (+.f64 (.f64 5/64 (pow.f64 (exp.f64 (.f64 -1/4 (+.f64 (.f64 -1 (log.f64 (/.f64 -1 x))) (log.f64 -1)))) 2)) (.f64 15/64 (pow.f64 (exp.f64 (.f64 -1/4 (+.f64 (.f64 -1 (log.f64 (/.f64 -1 x))) (log.f64 -1)))) 2))) (pow.f64 x 3))) (+.f64 (.f64 5/16 (/.f64 (pow.f64 (exp.f64 (.f64 -1/4 (+.f64 (.f64 -1 (log.f64 (/.f64 -1 x))) (log.f64 -1)))) 2) (pow.f64 x 2))) (pow.f64 (exp.f64 (.f64 -1/4 (+.f64 (.f64 -1 (log.f64 (/.f64 -1 x))) (log.f64 -1)))) 2)))))
(fma.f64 -1/2 (/.f64 (pow.f64 (pow.f64 (exp.f64 -1/4) (fma.f64 -1 (log.f64 (/.f64 -1 x)) (log.f64 -1))) 2) x) (fma.f64 1/16 (/.f64 (pow.f64 (pow.f64 (exp.f64 -1/4) (fma.f64 -1 (log.f64 (/.f64 -1 x)) (log.f64 -1))) 2) (.f64 x x)) (fma.f64 -1 (/.f64 (.f64 (pow.f64 (pow.f64 (exp.f64 -1/4) (fma.f64 -1 (log.f64 (/.f64 -1 x)) (log.f64 -1))) 2) 5/16) (pow.f64 x 3)) (fma.f64 5/16 (/.f64 (pow.f64 (pow.f64 (exp.f64 -1/4) (fma.f64 -1 (log.f64 (/.f64 -1 x)) (log.f64 -1))) 2) (*.f64 x x)) (pow.f64 (pow.f64 (exp.f64 -1/4) (fma.f64 -1 (log.f64 (/.f64 -1 x)) (log.f64 -1))) 2)))))
(+.f64 (fma.f64 -1/2 (/.f64 (pow.f64 (pow.f64 (exp.f64 -1/4) (-.f64 (log.f64 -1) (log.f64 (/.f64 -1 x)))) 2) x) (+.f64 (pow.f64 (pow.f64 (exp.f64 -1/4) (-.f64 (log.f64 -1) (log.f64 (/.f64 -1 x)))) 2) (.f64 (/.f64 (pow.f64 (pow.f64 (exp.f64 -1/4) (-.f64 (log.f64 -1) (log.f64 (/.f64 -1 x)))) 2) (.f64 x x)) 3/8))) (/.f64 (*.f64 (neg.f64 (pow.f64 (pow.f64 (exp.f64 -1/4) (-.f64 (log.f64 -1) (log.f64 (/.f64 -1 x)))) 2)) 5/16) (pow.f64 x 3)))
(+.f64 (pow.f64 (.f64 (pow.f64 (/.f64 -1 x) 1/4) (pow.f64 -1 -1/4)) 2) (+.f64 (.f64 (/.f64 (pow.f64 (.f64 (pow.f64 (/.f64 -1 x) 1/4) (pow.f64 -1 -1/4)) 2) x) (+.f64 -1/2 (/.f64 1/16 x))) (.f64 (+.f64 (/.f64 -1 x) 1) (.f64 (/.f64 5/16 (.f64 x x)) (pow.f64 (*.f64 (pow.f64 (/.f64 -1 x) 1/4) (pow.f64 -1 -1/4)) 2)))))
(+.f64 (.f64 (+.f64 (/.f64 -1/2 x) 1) (pow.f64 (exp.f64 (log.f64 x)) -1/2)) (.f64 (/.f64 (pow.f64 (exp.f64 (log.f64 x)) -1/2) (*.f64 x x)) (+.f64 (/.f64 -5/16 x) 3/8)))
1
(+.f64 1 (*.f64 -1/4 x))
(+.f64 1 (*.f64 x -1/4))
(fma.f64 x -1/4 1)
(+.f64 1 (+.f64 (.f64 -1/4 x) (.f64 5/32 (pow.f64 x 2))))
(+.f64 1 (fma.f64 -1/4 x (.f64 (.f64 x x) 5/32)))
(+.f64 1 (fma.f64 x -1/4 (.f64 (.f64 x x) 5/32)))
(fma.f64 x -1/4 (fma.f64 (*.f64 x x) 5/32 1))
(fma.f64 x (*.f64 x 5/32) (fma.f64 x -1/4 1))
(+.f64 1 (+.f64 (.f64 -1/4 x) (+.f64 (.f64 -15/128 (pow.f64 x 3)) (*.f64 5/32 (pow.f64 x 2)))))
(+.f64 1 (fma.f64 -1/4 x (fma.f64 -15/128 (pow.f64 x 3) (.f64 (.f64 x x) 5/32))))
(+.f64 1 (fma.f64 x -1/4 (fma.f64 (.f64 x x) 5/32 (.f64 (pow.f64 x 3) -15/128))))
(+.f64 1 (fma.f64 x -1/4 (.f64 (.f64 x x) (+.f64 5/32 (*.f64 x -15/128)))))
(+.f64 1 (.f64 x (+.f64 -1/4 (.f64 x (+.f64 (*.f64 x -15/128) 5/32)))))
(pow.f64 (/.f64 1 x) 1/4)
(+.f64 (*.f64 -1/4 (pow.f64 (/.f64 1 (pow.f64 x 5)) 1/4)) (pow.f64 (/.f64 1 x) 1/4))
(fma.f64 -1/4 (pow.f64 (/.f64 1 (pow.f64 x 5)) 1/4) (pow.f64 (/.f64 1 x) 1/4))
(+.f64 (.f64 5/32 (pow.f64 (/.f64 1 (pow.f64 x 9)) 1/4)) (+.f64 (.f64 -1/4 (pow.f64 (/.f64 1 (pow.f64 x 5)) 1/4)) (pow.f64 (/.f64 1 x) 1/4)))
(fma.f64 5/32 (pow.f64 (/.f64 1 (pow.f64 x 9)) 1/4) (fma.f64 -1/4 (pow.f64 (/.f64 1 (pow.f64 x 5)) 1/4) (pow.f64 (/.f64 1 x) 1/4)))
(fma.f64 -1/4 (pow.f64 (/.f64 1 (pow.f64 x 5)) 1/4) (fma.f64 5/32 (pow.f64 (/.f64 1 (pow.f64 x 9)) 1/4) (pow.f64 (/.f64 1 x) 1/4)))
(+.f64 (.f64 -15/128 (pow.f64 (/.f64 1 (pow.f64 x 13)) 1/4)) (+.f64 (.f64 5/32 (pow.f64 (/.f64 1 (pow.f64 x 9)) 1/4)) (+.f64 (*.f64 -1/4 (pow.f64 (/.f64 1 (pow.f64 x 5)) 1/4)) (pow.f64 (/.f64 1 x) 1/4))))
(fma.f64 -15/128 (pow.f64 (/.f64 1 (pow.f64 x 13)) 1/4) (fma.f64 5/32 (pow.f64 (/.f64 1 (pow.f64 x 9)) 1/4) (fma.f64 -1/4 (pow.f64 (/.f64 1 (pow.f64 x 5)) 1/4) (pow.f64 (/.f64 1 x) 1/4))))
(fma.f64 -15/128 (pow.f64 (/.f64 1 (pow.f64 x 13)) 1/4) (fma.f64 -1/4 (pow.f64 (/.f64 1 (pow.f64 x 5)) 1/4) (fma.f64 5/32 (pow.f64 (/.f64 1 (pow.f64 x 9)) 1/4) (pow.f64 (/.f64 1 x) 1/4))))
(fma.f64 5/32 (pow.f64 (/.f64 1 (pow.f64 x 9)) 1/4) (fma.f64 -15/128 (pow.f64 (/.f64 1 (pow.f64 x 13)) 1/4) (fma.f64 -1/4 (pow.f64 (/.f64 1 (pow.f64 x 5)) 1/4) (pow.f64 (/.f64 1 x) 1/4))))
(exp.f64 (.f64 -1/4 (+.f64 (.f64 -1 (log.f64 (/.f64 -1 x))) (log.f64 -1))))
(pow.f64 (exp.f64 -1/4) (fma.f64 -1 (log.f64 (/.f64 -1 x)) (log.f64 -1)))
(pow.f64 (exp.f64 -1/4) (-.f64 (log.f64 -1) (log.f64 (/.f64 -1 x))))
(*.f64 (pow.f64 (/.f64 -1 x) 1/4) (pow.f64 -1 -1/4))
(pow.f64 (exp.f64 -1/4) (log.f64 x))
(+.f64 (.f64 -1/4 (/.f64 (exp.f64 (.f64 -1/4 (+.f64 (.f64 -1 (log.f64 (/.f64 -1 x))) (log.f64 -1)))) x)) (exp.f64 (.f64 -1/4 (+.f64 (*.f64 -1 (log.f64 (/.f64 -1 x))) (log.f64 -1)))))
(fma.f64 -1/4 (/.f64 (pow.f64 (exp.f64 -1/4) (fma.f64 -1 (log.f64 (/.f64 -1 x)) (log.f64 -1))) x) (pow.f64 (exp.f64 -1/4) (fma.f64 -1 (log.f64 (/.f64 -1 x)) (log.f64 -1))))
(fma.f64 -1/4 (/.f64 (pow.f64 (exp.f64 -1/4) (-.f64 (log.f64 -1) (log.f64 (/.f64 -1 x)))) x) (pow.f64 (exp.f64 -1/4) (-.f64 (log.f64 -1) (log.f64 (/.f64 -1 x)))))
(fma.f64 (pow.f64 (/.f64 -1 x) 1/4) (pow.f64 -1 -1/4) (.f64 (/.f64 -1/4 x) (.f64 (pow.f64 (/.f64 -1 x) 1/4) (pow.f64 -1 -1/4))))
(*.f64 (+.f64 (/.f64 -1/4 x) 1) (pow.f64 (exp.f64 -1/4) (log.f64 x)))
(+.f64 (.f64 -1/4 (/.f64 (exp.f64 (.f64 -1/4 (+.f64 (.f64 -1 (log.f64 (/.f64 -1 x))) (log.f64 -1)))) x)) (+.f64 (exp.f64 (.f64 -1/4 (+.f64 (.f64 -1 (log.f64 (/.f64 -1 x))) (log.f64 -1)))) (.f64 5/32 (/.f64 (exp.f64 (.f64 -1/4 (+.f64 (.f64 -1 (log.f64 (/.f64 -1 x))) (log.f64 -1)))) (pow.f64 x 2)))))
(+.f64 (fma.f64 -1/4 (/.f64 (pow.f64 (exp.f64 -1/4) (fma.f64 -1 (log.f64 (/.f64 -1 x)) (log.f64 -1))) x) (pow.f64 (exp.f64 -1/4) (fma.f64 -1 (log.f64 (/.f64 -1 x)) (log.f64 -1)))) (.f64 5/32 (/.f64 (pow.f64 (exp.f64 -1/4) (fma.f64 -1 (log.f64 (/.f64 -1 x)) (log.f64 -1))) (.f64 x x))))
(fma.f64 -1/4 (/.f64 (pow.f64 (exp.f64 -1/4) (-.f64 (log.f64 -1) (log.f64 (/.f64 -1 x)))) x) (fma.f64 5/32 (/.f64 (pow.f64 (exp.f64 -1/4) (-.f64 (log.f64 -1) (log.f64 (/.f64 -1 x)))) (*.f64 x x)) (pow.f64 (exp.f64 -1/4) (-.f64 (log.f64 -1) (log.f64 (/.f64 -1 x))))))
(fma.f64 (pow.f64 (/.f64 -1 x) 1/4) (pow.f64 -1 -1/4) (.f64 (/.f64 (.f64 (pow.f64 (/.f64 -1 x) 1/4) (pow.f64 -1 -1/4)) x) (+.f64 -1/4 (/.f64 5/32 x))))
(+.f64 (pow.f64 (exp.f64 -1/4) (log.f64 x)) (/.f64 (*.f64 (pow.f64 (exp.f64 -1/4) (log.f64 x)) (+.f64 -1/4 (/.f64 5/32 x))) x))
(+.f64 (.f64 -1/4 (/.f64 (exp.f64 (.f64 -1/4 (+.f64 (.f64 -1 (log.f64 (/.f64 -1 x))) (log.f64 -1)))) x)) (+.f64 (exp.f64 (.f64 -1/4 (+.f64 (.f64 -1 (log.f64 (/.f64 -1 x))) (log.f64 -1)))) (+.f64 (.f64 5/32 (/.f64 (exp.f64 (.f64 -1/4 (+.f64 (.f64 -1 (log.f64 (/.f64 -1 x))) (log.f64 -1)))) (pow.f64 x 2))) (.f64 -15/128 (/.f64 (exp.f64 (.f64 -1/4 (+.f64 (*.f64 -1 (log.f64 (/.f64 -1 x))) (log.f64 -1)))) (pow.f64 x 3))))))
(+.f64 (fma.f64 -1/4 (/.f64 (pow.f64 (exp.f64 -1/4) (fma.f64 -1 (log.f64 (/.f64 -1 x)) (log.f64 -1))) x) (pow.f64 (exp.f64 -1/4) (fma.f64 -1 (log.f64 (/.f64 -1 x)) (log.f64 -1)))) (fma.f64 5/32 (/.f64 (pow.f64 (exp.f64 -1/4) (fma.f64 -1 (log.f64 (/.f64 -1 x)) (log.f64 -1))) (.f64 x x)) (.f64 -15/128 (/.f64 (pow.f64 (exp.f64 -1/4) (fma.f64 -1 (log.f64 (/.f64 -1 x)) (log.f64 -1))) (pow.f64 x 3)))))
(+.f64 (fma.f64 -1/4 (/.f64 (pow.f64 (exp.f64 -1/4) (-.f64 (log.f64 -1) (log.f64 (/.f64 -1 x)))) x) (pow.f64 (exp.f64 -1/4) (-.f64 (log.f64 -1) (log.f64 (/.f64 -1 x))))) (fma.f64 5/32 (/.f64 (pow.f64 (exp.f64 -1/4) (-.f64 (log.f64 -1) (log.f64 (/.f64 -1 x)))) (.f64 x x)) (.f64 -15/128 (/.f64 (pow.f64 (exp.f64 -1/4) (-.f64 (log.f64 -1) (log.f64 (/.f64 -1 x)))) (pow.f64 x 3)))))
(fma.f64 -1/4 (/.f64 (.f64 (pow.f64 (/.f64 -1 x) 1/4) (pow.f64 -1 -1/4)) x) (fma.f64 (pow.f64 (/.f64 -1 x) 1/4) (pow.f64 -1 -1/4) (.f64 (/.f64 (.f64 (pow.f64 (/.f64 -1 x) 1/4) (pow.f64 -1 -1/4)) (.f64 x x)) (+.f64 5/32 (/.f64 -15/128 x)))))
(+.f64 (pow.f64 (exp.f64 -1/4) (log.f64 x)) (.f64 (/.f64 (pow.f64 (exp.f64 -1/4) (log.f64 x)) x) (+.f64 -1/4 (+.f64 (/.f64 5/32 x) (/.f64 -15/128 (.f64 x x))))))

localize27.0ms (0.3%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(pow.f64 x -1/4)
✓	0.0b	(sqrt.f64 (+.f64 1 x))
✓	0.1b	(/.f64 -1 (sqrt.f64 (+.f64 1 x)))
✓	28.8b	(fma.f64 (pow.f64 x -1/4) (pow.f64 x -1/4) (/.f64 -1 (sqrt.f64 (+.f64 1 x))))

Compiler

Compiled 34 to 26 computations (23.5% saved)

series142.0ms (1.6%)

Counts

4 → 26

Calls

12 calls:

Time	Variable		Point	Expression
87.0ms	x	@	0	(pow.f64 x -1/4)
22.0ms	x	@	0	(fma.f64 (pow.f64 x -1/4) (pow.f64 x -1/4) (/.f64 -1 (sqrt.f64 (+.f64 1 x))))
20.0ms	x	@	-inf	(pow.f64 x -1/4)
8.0ms	x	@	inf	(pow.f64 x -1/4)
1.0ms	x	@	inf	(fma.f64 (pow.f64 x -1/4) (pow.f64 x -1/4) (/.f64 -1 (sqrt.f64 (+.f64 1 x))))

rewrite71.0ms (0.8%)

Algorithm

1×	batch-egg-rewrite

Rules

950×	`pow1_binary64`
889×	`add-log-exp_binary64`
887×	`log1p-expm1-u_binary64`
887×	`expm1-log1p-u_binary64`
101×	`add-sqr-sqrt_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	10	38
1	210	34
2	2455	34

Stop Event

1×	node limit

Counts

4 → 84

Calls

Call 1

Inputs
(fma.f64 (pow.f64 x -1/4) (pow.f64 x -1/4) (/.f64 -1 (sqrt.f64 (+.f64 1 x))))
(/.f64 -1 (sqrt.f64 (+.f64 1 x)))
(sqrt.f64 (+.f64 1 x))
(pow.f64 x -1/4)

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

simplify58.0ms (0.7%)

Algorithm

1×	egg-herbie

Rules

841×	`times-frac_binary64`
596×	`fma-def_binary64`
325×	`unswap-sqr_binary64`
320×	`fma-neg_binary64`
269×	`*-commutative_binary64`

Iterations

Useful iterations: 5 (0.0ms)

Iter	Nodes	Cost
0	51	249
1	143	241
2	346	239
3	992	221
4	2785	183
5	5924	171

Stop Event

1×	node limit

Counts

110 → 112

Calls

Call 1

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

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

eval1.5s (17.6%)

Compiler: Compiled 27915 to 21563 computations (22.8% saved)

prune326.0ms (3.8%)

Pruning

16 alts after pruning (16 fresh and 0 done)

	Pruned	Kept	Total
New	1145	14	1159
Fresh	19	2	21
Picked	1	0	1
Done	5	0	5
Total	1170	16	1186

Error

7.1b

Counts

1186 → 16

Alt Table

Click to see full alt table

Status	Error	Program
	62.8b	-1
	45.6b	(/.f64 (-.f64 (/.f64 1 x) (/.f64 1 (+.f64 1 x))) (*.f64 2 (sqrt.f64 (/.f64 1 x))))
	18.2b	(-.f64 (pow.f64 x -1/2) (pow.f64 (+.f64 1 x) -1/2))
▶	30.2b	(pow.f64 x -1/2)
	30.0b	(-.f64 (/.f64 1 (sqrt.f64 x)) (+.f64 (*.f64 -1/2 x) 1))
▶	29.1b	(/.f64 1 (+.f64 x (sqrt.f64 x)))
	30.2b	(-.f64 (pow.f64 x -1/2) 1)
▶	7.5b	(/.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)))
	40.4b	(/.f64 (/.f64 1 (*.f64 x x)) (+.f64 (pow.f64 x -1/2) (pow.f64 (+.f64 1 x) -1/2)))
▶	43.5b	(*.f64 1/2 (sqrt.f64 (/.f64 1 (pow.f64 x 3))))
	30.3b	(sqrt.f64 (/.f64 1 x))
	41.3b	(fma.f64 1/2 (/.f64 (pow.f64 (/.f64 -1 (/.f64 -1 x)) 1/2) (.f64 x x)) (/.f64 -3/8 (.f64 (pow.f64 x 3) (pow.f64 (/.f64 -1 (/.f64 -1 x)) -1/2))))
	40.3b	(/.f64 (pow.f64 (/.f64 -1 (/.f64 -1 x)) 1/2) (/.f64 (*.f64 x x) 1/2))
	18.1b	(/.f64 (/.f64 (+.f64 x (-.f64 1 x)) (+.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x))) (sqrt.f64 (*.f64 x (+.f64 1 x))))
	19.6b	(/.f64 1 (sqrt.f64 (*.f64 x (+.f64 1 x))))
▶	29.3b	(-.f64 (/.f64 1 (sqrt.f64 x)) (/.f64 1 (+.f64 (*.f64 1/2 x) 1)))

Compiler

Compiled 384 to 302 computations (21.4% saved)

localize38.0ms (0.4%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(pow.f64 (+.f64 1 x) -1/2)
	0.0b	(+.f64 (pow.f64 x -1/2) (pow.f64 (+.f64 1 x) -1/2))
✓	0.1b	(/.f64 (/.f64 (+.f64 1 (-.f64 x x)) x) (+.f64 1 x))
✓	7.5b	(/.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)))

Compiler

Compiled 71 to 44 computations (38% saved)

series13.0ms (0.1%)

Counts

3 → 36

Calls

9 calls:

Time	Variable		Point	Expression
6.0ms	x	@	-inf	(/.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)))
2.0ms	x	@	0	(/.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)))
2.0ms	x	@	inf	(/.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)))
0.0ms	x	@	inf	(pow.f64 (+.f64 1 x) -1/2)
0.0ms	x	@	-inf	(pow.f64 (+.f64 1 x) -1/2)

rewrite81.0ms (0.9%)

Algorithm

1×	batch-egg-rewrite

Rules

934×	`prod-diff_binary64`
458×	`fma-def_binary64`
246×	`log-div_binary64`
225×	`expm1-udef_binary64`
225×	`log1p-udef_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	13	42
1	331	42
2	4279	42

Stop Event

1×	node limit

Counts

3 → 94

Calls

Call 1

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

Outputs

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

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

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

simplify64.0ms (0.7%)

Algorithm

1×	egg-herbie

Rules

946×	`times-frac_binary64`
925×	`fma-def_binary64`
500×	`associate-/r*_binary64`
477×	`distribute-rgt-in_binary64`
468×	`distribute-lft-in_binary64`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	202	2175
1	649	1994
2	2343	1533

Stop Event

1×	node limit

Counts

130 → 154

Calls

Call 1

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

localize6.0ms (0.1%)

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

localize6.0ms (0.1%)

Local error

Found 2 expressions with local error:

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

Compiler

Compiled 15 to 6 computations (60% saved)

series5.0ms (0.1%)

Counts

2 → 4

Calls

6 calls:

Time	Variable		Point	Expression
2.0ms	x	@	inf	(/.f64 1 (+.f64 x (sqrt.f64 x)))
1.0ms	x	@	0	(/.f64 1 (+.f64 x (sqrt.f64 x)))
1.0ms	x	@	-inf	(/.f64 1 (+.f64 x (sqrt.f64 x)))
0.0ms	x	@	0	(+.f64 x (sqrt.f64 x))
0.0ms	x	@	-inf	(+.f64 x (sqrt.f64 x))

rewrite62.0ms (0.7%)

Algorithm

1×	batch-egg-rewrite

Rules

636×	`pow1_binary64`
595×	`add-log-exp_binary64`
595×	`log1p-expm1-u_binary64`
595×	`expm1-log1p-u_binary64`
581×	`add-exp-log_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	6	15
1	129	15
2	1710	15

Stop Event

1×	node limit

Counts

2 → 63

Calls

Call 1

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

Outputs

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

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

simplify9.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

1×	`1-exp_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	4	10
1	6	10

Stop Event

1×

saturated

Counts

67 → 65

Calls

Call 1

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

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

localize17.0ms (0.2%)

Local error

Found 3 expressions with local error:

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

Compiler

Compiled 37 to 27 computations (27% saved)

series3.0ms (0%)

Counts

2 → 12

Calls

6 calls:

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

rewrite87.0ms (1%)

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

Outputs

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

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

simplify56.0ms (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)))))

localize14.0ms (0.2%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.0b	(*.f64 1/2 (sqrt.f64 (/.f64 1 (pow.f64 x 3))))
✓	0.4b	(/.f64 1 (pow.f64 x 3))
✓	20.2b	(sqrt.f64 (/.f64 1 (pow.f64 x 3)))

Compiler

Compiled 27 to 22 computations (18.5% saved)

series7.0ms (0.1%)

Counts

3 → 0

Calls

9 calls:

Time	Variable		Point	Expression
3.0ms	x	@	0	(sqrt.f64 (/.f64 1 (pow.f64 x 3)))
1.0ms	x	@	0	(/.f64 1 (pow.f64 x 3))
1.0ms	x	@	-inf	(*.f64 1/2 (sqrt.f64 (/.f64 1 (pow.f64 x 3))))
1.0ms	x	@	-inf	(sqrt.f64 (/.f64 1 (pow.f64 x 3)))
1.0ms	x	@	inf	(*.f64 1/2 (sqrt.f64 (/.f64 1 (pow.f64 x 3))))

rewrite62.0ms (0.7%)

Algorithm

1×	batch-egg-rewrite

Rules

725×	`pow1_binary64`
682×	`add-log-exp_binary64`
680×	`log1p-expm1-u_binary64`
680×	`expm1-log1p-u_binary64`
665×	`add-exp-log_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	9	19
1	191	15
2	1997	15

Stop Event

1×	node limit

Counts

3 → 67

Calls

Call 1

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

Outputs

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

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

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

simplify7.0ms (0.1%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	0	0

Stop Event

1×

saturated

Counts

67 → 67

Calls

Call 1

Inputs

Outputs

eval532.0ms (6.1%)

Compiler: Compiled 14226 to 11048 computations (22.3% saved)

prune188.0ms (2.2%)

Pruning

14 alts after pruning (13 fresh and 1 done)

	Pruned	Kept	Total
New	566	8	574
Fresh	6	5	11
Picked	1	0	1
Done	3	1	4
Total	576	14	590

Error

Counts

590 → 14

Alt Table

Click to see full alt table

Status	Error	Program
	62.8b	-1
	45.6b	(/.f64 (-.f64 (/.f64 1 x) (/.f64 1 (+.f64 1 x))) (*.f64 2 (sqrt.f64 (/.f64 1 x))))
▶	32.6b	(.f64 1/2 (.f64 (/.f64 1 (sqrt.f64 x)) (/.f64 1 x)))
▶	29.2b	(-.f64 (pow.f64 x -1/2) (/.f64 1 (+.f64 (*.f64 1/2 x) 1)))
✓	30.2b	(pow.f64 x -1/2)
	34.8b	(/.f64 (/.f64 (/.f64 (+.f64 1 (-.f64 x x)) x) (+.f64 1 x)) (*.f64 2 (sqrt.f64 (/.f64 1 x))))
	18.2b	(-.f64 (pow.f64 x -1/2) (pow.f64 (+.f64 1 x) -1/2))
	30.0b	(-.f64 (/.f64 1 (sqrt.f64 x)) (+.f64 (*.f64 -1/2 x) 1))
	8.0b	(/.f64 (pow.f64 (*.f64 x (+.f64 1 x)) -1) (+.f64 (pow.f64 x -1/2) (pow.f64 (+.f64 1 x) -1/2)))
▶	7.5b	(/.f64 (*.f64 (/.f64 1 (+.f64 1 x)) (/.f64 1 x)) (+.f64 (pow.f64 x -1/2) (pow.f64 (+.f64 1 x) -1/2)))
	32.4b	(*.f64 1/2 (pow.f64 x -3/2))
▶	30.2b	(-.f64 (pow.f64 x -1/2) 1)
▶	59.4b	(/.f64 1 x)
	32.9b	(/.f64 1/2 (pow.f64 x 3/2))

Compiler

Compiled 286 to 229 computations (19.9% saved)

localize56.0ms (0.7%)

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))
✓	0.1b	(*.f64 (/.f64 1 (+.f64 1 x)) (/.f64 1 x))
✓	7.5b	(/.f64 (*.f64 (/.f64 1 (+.f64 1 x)) (/.f64 1 x)) (+.f64 (pow.f64 x -1/2) (pow.f64 (+.f64 1 x) -1/2)))

Compiler

Compiled 60 to 46 computations (23.3% saved)

series3.0ms (0%)

Counts

2 → 24

Calls

6 calls:

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

rewrite87.0ms (1%)

Algorithm

1×	batch-egg-rewrite

Rules

680×	`log-prod_binary64`
422×	`fma-def_binary64`
261×	`log-div_binary64`
243×	`fma-neg_binary64`
234×	`pow1/3_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	12	35
1	286	35
2	4248	35

Stop Event

1×	node limit

Counts

2 → 111

Calls

Call 1

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

Outputs

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

simplify67.0ms (0.8%)

Algorithm

1×	egg-herbie

Rules

902×	`times-frac_binary64`
741×	`fma-def_binary64`
477×	`distribute-rgt-in_binary64`
468×	`distribute-lft-in_binary64`
466×	`associate-/r*_binary64`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	169	1811
1	560	1650
2	2094	1241

Stop Event

1×	node limit

Counts

135 → 149

Calls

Call 1

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

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

localize3.0ms (0%)

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

localize115.0ms (1.3%)

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)

rewrite48.0ms (0.6%)

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 log1p.f64 (expm1.f64 (+.f64 (pow.f64 x -1/2) -1)))))) (#(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 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)))))

simplify48.0ms (0.6%)

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))

localize13.0ms (0.1%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.0b	(.f64 1/2 (.f64 (/.f64 1 (sqrt.f64 x)) (/.f64 1 x)))
✓	0.2b	(*.f64 (/.f64 1 (sqrt.f64 x)) (/.f64 1 x))
	0.3b	(/.f64 1 (sqrt.f64 x))

Compiler

Compiled 31 to 20 computations (35.5% saved)

series5.0ms (0.1%)

Counts

2 → 0

Calls

6 calls:

Time	Variable		Point	Expression
2.0ms	x	@	-inf	(.f64 1/2 (.f64 (/.f64 1 (sqrt.f64 x)) (/.f64 1 x)))
1.0ms	x	@	-inf	(*.f64 (/.f64 1 (sqrt.f64 x)) (/.f64 1 x))
0.0ms	x	@	0	(*.f64 (/.f64 1 (sqrt.f64 x)) (/.f64 1 x))
0.0ms	x	@	inf	(*.f64 (/.f64 1 (sqrt.f64 x)) (/.f64 1 x))
0.0ms	x	@	inf	(.f64 1/2 (.f64 (/.f64 1 (sqrt.f64 x)) (/.f64 1 x)))

rewrite57.0ms (0.7%)

Algorithm

1×	batch-egg-rewrite

Rules

767×	`pow1_binary64`
713×	`add-log-exp_binary64`
713×	`log1p-expm1-u_binary64`
713×	`expm1-log1p-u_binary64`
696×	`add-exp-log_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	9	21
1	190	11
2	2363	11

Stop Event

1×	node limit

Counts

2 → 58

Calls

Call 1

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

Outputs

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

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

simplify10.0ms (0.1%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	0	0

Stop Event

1×

saturated

Counts

58 → 58

Calls

Call 1

Inputs

Outputs

localize20.0ms (0.2%)

Local error

Found 2 expressions with local error:

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

Compiler

Compiled 34 to 27 computations (20.6% saved)

series3.0ms (0%)

Counts

1 → 12

Calls

3 calls:

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

rewrite76.0ms (0.9%)

Algorithm

1×	batch-egg-rewrite

Rules

665×	`prod-diff_binary64`
455×	`log-prod_binary64`
312×	`fma-def_binary64`
275×	`pow-prod-down_binary64`
272×	`pow2_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	10	14
1	228	14
2	2933	14

Stop Event

1×	node limit

Counts

1 → 124

Calls

Call 1

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

Outputs

((#(struct:change #<rule egg-rr> (2) ((x +.f64 (pow.f64 x -1/2) (/.f64 -1 (fma.f64 x 1/2 1)))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (pow.f64 x -1/2) (*.f64 (/.f64 -1 (fma.f64 x 1/2 1)) 1))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (+.f64 (pow.f64 x -1/2) (/.f64 -1 (fma.f64 x 1/2 1))) (fma.f64 (/.f64 -1 (fma.f64 x 1/2 1)) 1 (/.f64 1 (fma.f64 x 1/2 1))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (+.f64 (pow.f64 x -1/2) (/.f64 -1 (fma.f64 x 1/2 1))) (fma.f64 (neg.f64 (/.f64 1 (cbrt.f64 (fma.f64 x 1/2 1)))) (cbrt.f64 (pow.f64 (fma.f64 x 1/2 1) -2)) (/.f64 1 (fma.f64 x 1/2 1))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (+.f64 (pow.f64 x -1/2) (/.f64 -1 (fma.f64 x 1/2 1))) (+.f64 (/.f64 -1 (fma.f64 x 1/2 1)) (/.f64 1 (fma.f64 x 1/2 1))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (+.f64 (pow.f64 x -1/2) (/.f64 -1 (fma.f64 x 1/2 1))) (fma.f64 -1 (/.f64 1 (fma.f64 x 1/2 1)) (/.f64 1 (fma.f64 x 1/2 1))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (+.f64 (pow.f64 x -1/2) (/.f64 -1 (fma.f64 x 1/2 1))) (fma.f64 (neg.f64 (cbrt.f64 (pow.f64 (fma.f64 x 1/2 1) -2))) (/.f64 1 (cbrt.f64 (fma.f64 x 1/2 1))) (/.f64 1 (fma.f64 x 1/2 1))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 0 (+.f64 (pow.f64 x -1/2) (/.f64 -1 (fma.f64 x 1/2 1))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (/.f64 -1 (fma.f64 x 1/2 1)) (pow.f64 x -1/2))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (fma.f64 (pow.f64 x -1/2) 1 (neg.f64 (*.f64 (/.f64 -1 (fma.f64 x 1/2 1)) -1))) (fma.f64 (neg.f64 (/.f64 -1 (fma.f64 x 1/2 1))) -1 (*.f64 (/.f64 -1 (fma.f64 x 1/2 1)) -1)))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (fma.f64 1 (pow.f64 x -1/2) (neg.f64 (*.f64 (/.f64 -1 (fma.f64 x 1/2 1)) -1))) (fma.f64 (neg.f64 (/.f64 -1 (fma.f64 x 1/2 1))) -1 (*.f64 (/.f64 -1 (fma.f64 x 1/2 1)) -1)))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (fma.f64 (pow.f64 x -1/6) (cbrt.f64 (pow.f64 x -1)) (neg.f64 (*.f64 (/.f64 -1 (fma.f64 x 1/2 1)) -1))) (fma.f64 (neg.f64 (/.f64 -1 (fma.f64 x 1/2 1))) -1 (*.f64 (/.f64 -1 (fma.f64 x 1/2 1)) -1)))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (fma.f64 (cbrt.f64 (pow.f64 x -1)) (pow.f64 x -1/6) (neg.f64 (*.f64 (/.f64 -1 (fma.f64 x 1/2 1)) -1))) (fma.f64 (neg.f64 (/.f64 -1 (fma.f64 x 1/2 1))) -1 (*.f64 (/.f64 -1 (fma.f64 x 1/2 1)) -1)))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (fma.f64 (pow.f64 x -1/4) (pow.f64 x -1/4) (neg.f64 (*.f64 (/.f64 -1 (fma.f64 x 1/2 1)) -1))) (fma.f64 (neg.f64 (/.f64 -1 (fma.f64 x 1/2 1))) -1 (*.f64 (/.f64 -1 (fma.f64 x 1/2 1)) -1)))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (fma.f64 (pow.f64 1 -1/2) (pow.f64 x -1/2) (neg.f64 (*.f64 (/.f64 -1 (fma.f64 x 1/2 1)) -1))) (fma.f64 (neg.f64 (/.f64 -1 (fma.f64 x 1/2 1))) -1 (*.f64 (/.f64 -1 (fma.f64 x 1/2 1)) -1)))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (fma.f64 (pow.f64 (cbrt.f64 x) -1) (pow.f64 x -1/6) (neg.f64 (*.f64 (/.f64 -1 (fma.f64 x 1/2 1)) -1))) (fma.f64 (neg.f64 (/.f64 -1 (fma.f64 x 1/2 1))) -1 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simplify52.0ms (0.6%)

Algorithm

1×	egg-herbie

Rules

593×	`associate-l_binary64`
592×	`fma-def_binary64`
528×	`fma-neg_binary64`
461×	`associate-/r*_binary64`
348×	`cancel-sign-sub-inv_binary64`

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	51	247
1	148	241
2	384	221
3	1077	201
4	3107	184

Stop Event

1×	node limit

Counts

136 → 147

Calls

Call 1

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

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

eval333.0ms (3.8%)

Compiler: Compiled 14032 to 11350 computations (19.1% saved)

prune98.0ms (1.1%)

Pruning

16 alts after pruning (11 fresh and 5 done)

	Pruned	Kept	Total
New	576	8	584
Fresh	5	3	8
Picked	0	1	1
Done	1	4	5
Total	582	16	598

Error

Counts

598 → 16

Alt Table

Click to see full alt table

Status	Error	Program
✓	29.2b	(-.f64 (pow.f64 x -1/2) (/.f64 1 (+.f64 (*.f64 1/2 x) 1)))
	32.5b	(/.f64 (/.f64 1/2 (sqrt.f64 x)) x)
✓	30.2b	(pow.f64 x -1/2)
	34.8b	(/.f64 (/.f64 (/.f64 (+.f64 1 (-.f64 x x)) x) (+.f64 1 x)) (*.f64 2 (sqrt.f64 (/.f64 1 x))))
	18.2b	(-.f64 (pow.f64 x -1/2) (pow.f64 (+.f64 1 x) -1/2))
	34.8b	(/.f64 (.f64 (/.f64 1 (+.f64 1 x)) (/.f64 1 x)) (.f64 2 (sqrt.f64 (/.f64 1 x))))
✓	7.5b	(/.f64 (*.f64 (/.f64 1 (+.f64 1 x)) (/.f64 1 x)) (+.f64 (pow.f64 x -1/2) (pow.f64 (+.f64 1 x) -1/2)))
	62.8b	-1
	32.4b	(*.f64 1/2 (pow.f64 x -3/2))
	32.9b	(/.f64 1/2 (pow.f64 x 3/2))
	29.9b	(-.f64 (pow.f64 x -1/2) (+.f64 (*.f64 -1/2 x) 1))
	32.9b	(*.f64 1/2 (/.f64 1 (/.f64 (sqrt.f64 x) (/.f64 1 x))))
	7.5b	(/.f64 (/.f64 (/.f64 1 (+.f64 1 x)) x) (+.f64 (pow.f64 x -1/2) (pow.f64 (+.f64 1 x) -1/2)))
✓	30.2b	(-.f64 (pow.f64 x -1/2) 1)
✓	59.4b	(/.f64 1 x)
	32.5b	(.f64 1/2 (.f64 (pow.f64 x -1/2) (/.f64 1 x)))

Compiler

Compiled 162 to 129 computations (20.4% saved)

regimes131.0ms (1.5%)

Counts

57 → 2

Calls

Call 1

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

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

Calls

3 calls:

62.0ms	x
23.0ms	(-.f64 (/.f64 1 (sqrt.f64 x)) (/.f64 1 (sqrt.f64 (+.f64 x 1))))
21.0ms	(-.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 762 to 585 computations (23.2% saved)

bsearch1.0ms (0%)

Algorithm

1×	left-value

Steps

Time	Left	Right
0.0ms	0.0	5.345564621376045e-14

Compiler

Compiled 16 to 13 computations (18.8% saved)

regimes99.0ms (1.1%)

Counts

47 → 2

Calls

Call 1

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

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

Calls

3 calls:

45.0ms	x
19.0ms	(-.f64 (/.f64 1 (sqrt.f64 x)) (/.f64 1 (sqrt.f64 (+.f64 x 1))))
18.0ms	(-.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 519 to 392 computations (24.5% saved)

bsearch1.0ms (0%)

Algorithm

1×	left-value

Steps

Time	Left	Right
0.0ms	7.069045598450535e-14	0.13753457278268333

Compiler

Compiled 16 to 13 computations (18.8% saved)

regimes32.0ms (0.4%)

Counts

25 → 2

Calls

Call 1

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

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

Calls

1 calls:

25.0ms

Results

Error	Segments	Branch
0.7b	2	`x`

Compiler

Compiled 207 to 156 computations (24.6% saved)

bsearch22.0ms (0.3%)

Algorithm

1×	binary-search

Steps

Time	Left	Right
21.0ms	0.00819371255162915	1.9080813715442384

Compiler

Compiled 16 to 13 computations (18.8% saved)

regimes25.0ms (0.3%)

Counts

18 → 2

Calls

Call 1

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

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

Calls

1 calls:

19.0ms

Results

Error	Segments	Branch
0.7b	2	`x`

Compiler

Compiled 113 to 82 computations (27.4% saved)

bsearch23.0ms (0.3%)

Algorithm

1×	binary-search

Steps

Time	Left	Right
23.0ms	0.00819371255162915	1.9080813715442384

Compiler

Compiled 16 to 13 computations (18.8% saved)

regimes20.0ms (0.2%)

Counts

13 → 2

Calls

Call 1

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

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

Calls

1 calls:

16.0ms

Results

Error	Segments	Branch
0.9b	2	`x`

Compiler

Compiled 65 to 47 computations (27.7% saved)

bsearch23.0ms (0.3%)

Algorithm

1×	binary-search

Steps

Time	Left	Right
22.0ms	0.00819371255162915	1.9080813715442384

Compiler

Compiled 16 to 13 computations (18.8% saved)

regimes14.0ms (0.2%)

Counts

8 → 2

Calls

Call 1

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

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

Calls

1 calls:

12.0ms

Results

Error	Segments	Branch
1.7b	2	`x`

Compiler

Compiled 34 to 26 computations (23.5% saved)

bsearch22.0ms (0.3%)

Algorithm

1×	binary-search

Steps

Time	Left	Right
21.0ms	0.00819371255162915	1.9080813715442384

Compiler

Compiled 16 to 13 computations (18.8% saved)

regimes8.0ms (0.1%)

Counts

4 → 1

Calls

Call 1

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

Outputs
(pow.f64 x -1/2)

Calls

1 calls:

6.0ms

Results

Error	Segments	Branch
30.2b	1	`x`

Compiler

Compiled 14 to 10 computations (28.6% saved)

regimes4.0ms (0%)

Accuracy

Total -3.4b remaining (-5.7%)

Threshold costs -3.4b (-5.7%)

Counts

2 → 1

Calls

Call 1

Inputs
-1
(/.f64 1 x)

Outputs
(/.f64 1 x)

Calls

1 calls:

3.0ms

Results

Error	Segments	Branch
59.4b	1	`x`

Compiler

Compiled 7 to 5 computations (28.6% saved)

simplify14.0ms (0.2%)

Algorithm

1×	egg-herbie

Rules

18×	`+-commutative_binary64`
12×	`sub-neg_binary64`
10×	`*-commutative_binary64`
6×	`neg-sub0_binary64`
6×	`neg-mul-1_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	48	203
1	70	203
2	91	203
3	109	203
4	117	203
5	118	203

Stop Event

1×	fuel
1×	saturated

Calls

Call 1

Inputs
(if (<=.f64 (-.f64 (/.f64 1 (sqrt.f64 x)) (/.f64 1 (sqrt.f64 (+.f64 x 1)))) 0) (.f64 1/2 (pow.f64 x -3/2)) (/.f64 (/.f64 (+.f64 x (-.f64 1 x)) (+.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x))) (sqrt.f64 (.f64 x (+.f64 1 x)))))
(if (<=.f64 (-.f64 (/.f64 1 (sqrt.f64 x)) (/.f64 1 (sqrt.f64 (+.f64 x 1)))) 3961408125713217/39614081257132168796771975168) (*.f64 1/2 (pow.f64 x -3/2)) (-.f64 (pow.f64 x -1/2) (pow.f64 (+.f64 1 x) -1/2)))
(if (<=.f64 x 4723353701670143/576460752303423488) (-.f64 (pow.f64 x -1/2) (/.f64 1 (+.f64 (.f64 1/2 x) 1))) (.f64 1/2 (pow.f64 x -3/2)))
(if (<=.f64 x 4723353701670143/576460752303423488) (-.f64 (pow.f64 x -1/2) (+.f64 (.f64 -1/2 x) 1)) (.f64 1/2 (pow.f64 x -3/2)))
(if (<=.f64 x 4723353701670143/576460752303423488) (-.f64 (pow.f64 x -1/2) 1) (*.f64 1/2 (pow.f64 x -3/2)))
(if (<=.f64 x 4723353701670143/576460752303423488) (pow.f64 x -1/2) (*.f64 1/2 (pow.f64 x -3/2)))
(pow.f64 x -1/2)
(/.f64 1 x)
-1

Outputs
(if (<=.f64 (-.f64 (/.f64 1 (sqrt.f64 x)) (/.f64 1 (sqrt.f64 (+.f64 x 1)))) 0) (.f64 1/2 (pow.f64 x -3/2)) (/.f64 (/.f64 (+.f64 x (-.f64 1 x)) (+.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x))) (sqrt.f64 (.f64 x (+.f64 1 x)))))
(if (<=.f64 (-.f64 (/.f64 1 (sqrt.f64 x)) (/.f64 1 (sqrt.f64 (+.f64 1 x)))) 0) (.f64 1/2 (pow.f64 x -3/2)) (/.f64 (/.f64 (+.f64 x (-.f64 1 x)) (+.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 1 x)))) (sqrt.f64 (.f64 x (+.f64 1 x)))))
(if (<=.f64 (-.f64 (/.f64 1 (sqrt.f64 x)) (/.f64 1 (sqrt.f64 (+.f64 x 1)))) 3961408125713217/39614081257132168796771975168) (*.f64 1/2 (pow.f64 x -3/2)) (-.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)))) 3961408125713217/39614081257132168796771975168) (*.f64 1/2 (pow.f64 x -3/2)) (-.f64 (pow.f64 x -1/2) (pow.f64 (+.f64 1 x) -1/2)))
(if (<=.f64 x 4723353701670143/576460752303423488) (-.f64 (pow.f64 x -1/2) (/.f64 1 (+.f64 (.f64 1/2 x) 1))) (.f64 1/2 (pow.f64 x -3/2)))
(if (<=.f64 x 4723353701670143/576460752303423488) (-.f64 (pow.f64 x -1/2) (/.f64 1 (+.f64 1 (.f64 x 1/2)))) (.f64 1/2 (pow.f64 x -3/2)))
(if (<=.f64 x 4723353701670143/576460752303423488) (-.f64 (pow.f64 x -1/2) (+.f64 (.f64 -1/2 x) 1)) (.f64 1/2 (pow.f64 x -3/2)))
(if (<=.f64 x 4723353701670143/576460752303423488) (-.f64 (pow.f64 x -1/2) (+.f64 1 (.f64 x -1/2))) (.f64 1/2 (pow.f64 x -3/2)))
(if (<=.f64 x 4723353701670143/576460752303423488) (-.f64 (pow.f64 x -1/2) 1) (*.f64 1/2 (pow.f64 x -3/2)))
(if (<=.f64 x 4723353701670143/576460752303423488) (+.f64 (pow.f64 x -1/2) -1) (*.f64 1/2 (pow.f64 x -3/2)))
(if (<=.f64 x 4723353701670143/576460752303423488) (pow.f64 x -1/2) (*.f64 1/2 (pow.f64 x -3/2)))
(pow.f64 x -1/2)
(/.f64 1 x)
-1

Compiler

Compiled 147 to 116 computations (21.1% saved)

soundness0.0ms (0%)

end93.0ms (1.1%)

Compiler: Compiled 139 to 107 computations (23% 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