Details

analyze0.0ms (0%)

Algorithm

1×

Search

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

Compiler

Compiled 13 to 11 computations (15.4% saved)

sample1.8s (19.1%)

Results

818.0ms	2288×	body	1024	valid
715.0ms	4953×	body	256	valid
259.0ms	1015×	body	512	valid

preprocess23.0ms (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)

simplify12.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

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

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	9	17
1	14	17
2	20	17
3	28	17
4	38	17
5	56	17
6	93	17
7	127	17
8	171	17
9	207	17
10	233	17
11	235	17

Stop Event

1×

saturated

Counts

1 → 2

Calls

Call 1

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

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

eval1.0ms (0%)

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

prune1.0ms (0%)

Pruning

2 alts after pruning (2 fresh and 0 done)

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

Error

20.4b

Counts

3 → 1

Alt Table

Click to see full alt table

Status	Error	Program
▶	20.4b	(-.f64 (/.f64 1 (sqrt.f64 x)) (/.f64 1 (sqrt.f64 (+.f64 x 1))))

Compiler

Compiled 12 to 10 computations (16.7% saved)

localize16.0ms (0.2%)

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))
✓	3.0b	(-.f64 (/.f64 1 (sqrt.f64 x)) (/.f64 1 (sqrt.f64 (+.f64 x 1))))

Compiler

Compiled 33 to 23 computations (30.3% saved)

series10.0ms (0.1%)

Counts

4 → 8

Calls

12 calls:

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

rewrite100.0ms (1.1%)

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))))))

simplify168.0ms (1.8%)

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)

eval107.0ms (1.1%)

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

prune74.0ms (0.8%)

Pruning

35 alts after pruning (34 fresh and 1 done)

	Pruned	Kept	Total
New	208	34	242
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	208	35	243

Error

19.7b

Counts

243 → 35

Alt Table

Click to see full alt table

Status	Error	Program
✓	20.4b	(-.f64 (/.f64 1 (sqrt.f64 x)) (/.f64 1 (sqrt.f64 (+.f64 x 1))))
	26.7b	(-.f64 (/.f64 1 (sqrt.f64 x)) (pow.f64 (cbrt.f64 (+.f64 1 x)) -3/2))
	38.9b	(-.f64 (cbrt.f64 (pow.f64 x -3/2)) (/.f64 1 (sqrt.f64 (+.f64 x 1))))
	26.6b	(-.f64 (pow.f64 (pow.f64 x -1/4) 2) (/.f64 1 (sqrt.f64 (+.f64 x 1))))
	22.5b	(-.f64 (pow.f64 x -1/2) (/.f64 1 (sqrt.f64 (+.f64 x 1))))
	31.4b	(fma.f64 (/.f64 1 (cbrt.f64 x)) (pow.f64 x -1/6) (/.f64 -1 (sqrt.f64 (+.f64 1 x))))
	29.9b	(-.f64 (/.f64 1 (sqrt.f64 x)) (cbrt.f64 (pow.f64 (+.f64 1 x) -3/2)))
	22.6b	(-.f64 (/.f64 1 (sqrt.f64 x)) (pow.f64 (+.f64 1 x) -1/2))
▶	31.8b	(-.f64 (/.f64 1 (sqrt.f64 x)) 1)
	27.5b	(+.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))))))
	30.5b	(-.f64 (/.f64 1 (sqrt.f64 x)) (/.f64 1 (+.f64 (*.f64 1/2 x) 1)))
	20.5b	(*.f64 (-.f64 (/.f64 1 x) (/.f64 1 (+.f64 1 x))) (/.f64 1 (+.f64 (pow.f64 x -1/2) (pow.f64 (+.f64 1 x) -1/2))))
	22.4b	(-.f64 (sqrt.f64 (/.f64 1 x)) (/.f64 1 (sqrt.f64 (+.f64 x 1))))
	29.8b	(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))
	30.1b	(fma.f64 (pow.f64 x -1/4) (pow.f64 x -1/4) (/.f64 -1 (sqrt.f64 (+.f64 1 x))))
	22.4b	(-.f64 (/.f64 1 (sqrt.f64 x)) (sqrt.f64 (/.f64 1 (+.f64 1 x))))
	26.3b	(/.f64 (-.f64 (/.f64 1 x) (pow.f64 (/.f64 -1 (sqrt.f64 (+.f64 1 x))) 2)) (-.f64 (pow.f64 x -1/2) (/.f64 -1 (sqrt.f64 (+.f64 1 x)))))
	26.6b	(-.f64 (/.f64 1 (sqrt.f64 x)) (/.f64 1 (pow.f64 (cbrt.f64 (+.f64 1 x)) 3/2)))
▶	20.5b	(/.f64 (-.f64 (/.f64 1 x) (/.f64 1 (+.f64 1 x))) (+.f64 (pow.f64 x -1/2) (pow.f64 (+.f64 1 x) -1/2)))
	29.1b	(.f64 (-.f64 (pow.f64 x -3/2) (pow.f64 (+.f64 1 x) -3/2)) (/.f64 1 (+.f64 (/.f64 1 x) (+.f64 (/.f64 1 (+.f64 1 x)) (pow.f64 (.f64 x (+.f64 1 x)) -1/2)))))
	29.9b	(fma.f64 (pow.f64 (+.f64 1 x) -1/4) (neg.f64 (pow.f64 (+.f64 1 x) -1/4)) (pow.f64 x -1/2))
	29.2b	(/.f64 (+.f64 (pow.f64 x -3/2) (pow.f64 (/.f64 -1 (sqrt.f64 (+.f64 1 x))) 3)) (+.f64 (/.f64 1 x) (-.f64 (pow.f64 (/.f64 -1 (sqrt.f64 (+.f64 1 x))) 2) (*.f64 (pow.f64 x -1/2) (/.f64 -1 (sqrt.f64 (+.f64 1 x)))))))
	43.1b	(-.f64 (pow.f64 (*.f64 x x) -1/4) (/.f64 1 (sqrt.f64 (+.f64 x 1))))
▶	29.1b	(/.f64 (-.f64 (pow.f64 x -3/2) (pow.f64 (+.f64 1 x) -3/2)) (+.f64 (/.f64 1 x) (+.f64 (/.f64 1 (+.f64 1 x)) (pow.f64 (*.f64 x (+.f64 1 x)) -1/2))))
▶	20.2b	(.f64 (-.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)) (pow.f64 (.f64 x (+.f64 1 x)) -1/2))
	29.7b	(-.f64 (/.f64 1 (sqrt.f64 x)) (/.f64 1 (cbrt.f64 (pow.f64 (+.f64 1 x) 3/2))))
	30.1b	(-.f64 (/.f64 1 (sqrt.f64 x)) (exp.f64 (*.f64 -1/2 (log1p.f64 x))))
▶	32.2b	(-.f64 (exp.f64 (*.f64 -1/2 (log.f64 x))) (/.f64 1 (sqrt.f64 (+.f64 x 1))))
	24.8b	(-.f64 (/.f64 1 (sqrt.f64 x)) (pow.f64 (pow.f64 (+.f64 1 x) 1/4) -2))
	20.4b	(/.f64 (-.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)) (sqrt.f64 (*.f64 x (+.f64 1 x))))
	26.5b	(-.f64 (/.f64 1 (sqrt.f64 x)) (pow.f64 (pow.f64 (+.f64 1 x) -1/4) 2))
	20.5b	(/.f64 1 (/.f64 (+.f64 (pow.f64 x -1/2) (pow.f64 (+.f64 1 x) -1/2)) (-.f64 (/.f64 1 x) (/.f64 1 (+.f64 1 x)))))
	24.8b	(-.f64 (pow.f64 (pow.f64 x 1/4) -2) (/.f64 1 (sqrt.f64 (+.f64 x 1))))
	31.2b	(-.f64 (/.f64 1 (sqrt.f64 x)) (+.f64 (*.f64 -1/2 x) 1))
	27.3b	(-.f64 (pow.f64 (cbrt.f64 x) -3/2) (/.f64 1 (sqrt.f64 (+.f64 x 1))))

Compiler

Compiled 1152 to 946 computations (17.9% saved)

localize27.0ms (0.3%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(.f64 (-.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)) (pow.f64 (.f64 x (+.f64 1 x)) -1/2))
✓	0.0b	(*.f64 x (+.f64 1 x))
✓	3.0b	(-.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x))
✓	14.0b	(pow.f64 (*.f64 x (+.f64 1 x)) -1/2)

Compiler

Compiled 47 to 31 computations (34% saved)

series12.0ms (0.1%)

Counts

4 → 25

Calls

12 calls:

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

rewrite86.0ms (0.9%)

Algorithm

1×	batch-egg-rewrite

Rules

542×	`log-prod_binary64`
516×	`fma-def_binary64`
427×	`pow-prod-down_binary64`
298×	`pow2_binary64`
232×	`fma-neg_binary64`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	11	51
1	245	51
2	3260	45

Stop Event

1×	node limit

Counts

4 → 192

Calls

Call 1

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

Outputs
((#(struct:change #<rule egg-rr> (2) ((x +.f64 0 (pow.f64 (fma.f64 x x x) -1/2))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (log.f64 (pow.f64 (cbrt.f64 (exp.f64 (pow.f64 (fma.f64 x x x) -1/2))) 2)) (log.f64 (cbrt.f64 (exp.f64 (pow.f64 (fma.f64 x x x) -1/2)))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (log.f64 (sqrt.f64 (exp.f64 (pow.f64 (fma.f64 x x x) -1/2)))) (log.f64 (sqrt.f64 (exp.f64 (pow.f64 (fma.f64 x x x) -1/2)))))))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (exp.f64 (log1p.f64 (pow.f64 (fma.f64 x x x) -1/2))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x .f64 1 (pow.f64 (fma.f64 x x x) -1/2))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (pow.f64 (fma.f64 x x x) -1/2) 1)))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (pow.f64 (fma.f64 x x x) -1/6) (cbrt.f64 (pow.f64 (fma.f64 x x x) -1)))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (cbrt.f64 (pow.f64 (fma.f64 x x x) -1)) (pow.f64 (fma.f64 x x x) -1/6))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (pow.f64 x -1/2) (pow.f64 (+.f64 x 1) -1/2))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (pow.f64 (+.f64 x 1) -1/2) (pow.f64 x -1/2))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (pow.f64 (fma.f64 x x x) -1/4) (pow.f64 (fma.f64 x x x) -1/4))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (pow.f64 1 -1/2) (pow.f64 (fma.f64 x x x) -1/2))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (pow.f64 (cbrt.f64 (fma.f64 x x x)) -1) (pow.f64 (fma.f64 x x x) -1/6))))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f64 (pow.f64 (fma.f64 x x x) -1))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (exp.f64 (pow.f64 (fma.f64 x x x) -1/2)))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (+.f64 1 (expm1.f64 (pow.f64 (fma.f64 x x x) -1/2))))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (pow.f64 (fma.f64 x x x) -3/2))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (pow.f64 (fma.f64 x x x) -1/2)))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (pow.f64 (fma.f64 x x x) -1/2)))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (.f64 -1/2 (log.f64 (fma.f64 x x x))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (.f64 (.f64 -1/2 (log.f64 (fma.f64 x x 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))) (pow.f64 (cbrt.f64 (-.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x))) 2))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (pow.f64 (cbrt.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> (2) ((x fma.f64 1 (-.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x)) (+.f64 (neg.f64 (sqrt.f64 x)) (sqrt.f64 x)))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 1 (neg.f64 (sqrt.f64 x)) (sqrt.f64 (+.f64 x 1)))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (sqrt.f64 (+.f64 x 1)) 1 (neg.f64 (sqrt.f64 x)))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (sqrt.f64 (+.f64 x 1)) 1 (.f64 (neg.f64 (sqrt.f64 x)) 1))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (-.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x)) 1 (fma.f64 (neg.f64 (sqrt.f64 x)) 1 (sqrt.f64 x)))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (-.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x)) 1 (fma.f64 (neg.f64 (pow.f64 x 1/6)) (cbrt.f64 x) (sqrt.f64 x)))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (-.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x)) 1 (+.f64 (neg.f64 (sqrt.f64 x)) (sqrt.f64 x)))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (pow.f64 (+.f64 x 1) 1/6) (cbrt.f64 (+.f64 x 1)) (neg.f64 (sqrt.f64 x)))))) 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simplify50.0ms (0.5%)

Algorithm

1×	egg-herbie

Rules

712×	`times-frac_binary64`
554×	`fma-def_binary64`
473×	`associate-l_binary64`
378×	`associate-r_binary64`
373×	`associate-*r/_binary64`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	45	282
1	119	264
2	285	258
3	713	258
4	2119	258

Stop Event

1×	node limit

Counts

217 → 218

Calls

Call 1

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

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

rewrite46.0ms (0.5%)

Algorithm

1×	batch-egg-rewrite

Rules

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

Iterations

Useful iterations: 1 (0.0ms)

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

Stop Event

1×	node limit

Counts

1 → 31

Calls

Call 1

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

Outputs

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

localize48.0ms (0.5%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(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)))
✓	3.0b	(-.f64 (/.f64 1 x) (/.f64 1 (+.f64 1 x)))

Compiler

Compiled 60 to 46 computations (23.3% saved)

series10.0ms (0.1%)

Counts

4 → 48

Calls

12 calls:

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

rewrite127.0ms (1.3%)

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	55
1	296	40
2	4663	40

Stop Event

1×	node limit

Counts

4 → 334

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

simplify91.0ms (1%)

Algorithm

1×	egg-herbie

Rules

726×	`sub-neg_binary64`
625×	`fma-neg_binary64`
588×	`fma-def_binary64`
384×	`associate-+l+_binary64`
291×	`associate-+r+_binary64`

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	187	1760
1	587	1672
2	1732	1512
3	6598	1449

Stop Event

1×	node limit

Counts

382 → 406

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

localize43.0ms (0.5%)

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)))
✓	4.7b	(exp.f64 (*.f64 -1/2 (log.f64 x)))
✓	29.8b	(-.f64 (exp.f64 (*.f64 -1/2 (log.f64 x))) (/.f64 1 (sqrt.f64 (+.f64 x 1))))

Compiler

Compiled 40 to 28 computations (30% saved)

series92.0ms (1%)

Counts

2 → 18

Calls

6 calls:

Time	Variable		Point	Expression
48.0ms	x	@	inf	(exp.f64 (*.f64 -1/2 (log.f64 x)))
22.0ms	x	@	0	(exp.f64 (*.f64 -1/2 (log.f64 x)))
21.0ms	x	@	-inf	(exp.f64 (*.f64 -1/2 (log.f64 x)))
1.0ms	x	@	inf	(-.f64 (exp.f64 (*.f64 -1/2 (log.f64 x))) (/.f64 1 (sqrt.f64 (+.f64 x 1))))
0.0ms	x	@	-inf	(-.f64 (exp.f64 (*.f64 -1/2 (log.f64 x))) (/.f64 1 (sqrt.f64 (+.f64 x 1))))

rewrite85.0ms (0.9%)

Algorithm

1×	batch-egg-rewrite

Rules

494×	`log-prod_binary64`
444×	`prod-diff_binary64`
314×	`pow-prod-down_binary64`
295×	`fma-def_binary64`
282×	`pow2_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	11	27
1	235	17
2	3038	17

Stop Event

1×	node limit

Counts

2 → 178

Calls

Call 1

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

Outputs

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

simplify57.0ms (0.6%)

Algorithm

1×	egg-herbie

Rules

594×	`associate-l_binary64`
518×	`times-frac_binary64`
430×	`fma-def_binary64`
387×	`associate-r_binary64`
231×	`fma-neg_binary64`

Iterations

Useful iterations: 5 (0.0ms)

Iter	Nodes	Cost
0	35	149
1	94	147
2	234	145
3	639	139
4	1875	138
5	5170	110

Stop Event

1×	node limit

Counts

196 → 188

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

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

localize94.0ms (1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.2b	(+.f64 (/.f64 1 x) (+.f64 (/.f64 1 (+.f64 1 x)) (pow.f64 (*.f64 x (+.f64 1 x)) -1/2)))
✓	2.9b	(-.f64 (pow.f64 x -3/2) (pow.f64 (+.f64 1 x) -3/2))
✓	8.5b	(/.f64 (-.f64 (pow.f64 x -3/2) (pow.f64 (+.f64 1 x) -3/2)) (+.f64 (/.f64 1 x) (+.f64 (/.f64 1 (+.f64 1 x)) (pow.f64 (*.f64 x (+.f64 1 x)) -1/2))))
	14.0b	(pow.f64 (*.f64 x (+.f64 1 x)) -1/2)

Compiler

Compiled 102 to 77 computations (24.5% saved)

series12.0ms (0.1%)

Counts

3 → 36

Calls

9 calls:

Time	Variable		Point	Expression
3.0ms	x	@	-inf	(/.f64 (-.f64 (pow.f64 x -3/2) (pow.f64 (+.f64 1 x) -3/2)) (+.f64 (/.f64 1 x) (+.f64 (/.f64 1 (+.f64 1 x)) (pow.f64 (*.f64 x (+.f64 1 x)) -1/2))))
3.0ms	x	@	inf	(/.f64 (-.f64 (pow.f64 x -3/2) (pow.f64 (+.f64 1 x) -3/2)) (+.f64 (/.f64 1 x) (+.f64 (/.f64 1 (+.f64 1 x)) (pow.f64 (*.f64 x (+.f64 1 x)) -1/2))))
2.0ms	x	@	0	(/.f64 (-.f64 (pow.f64 x -3/2) (pow.f64 (+.f64 1 x) -3/2)) (+.f64 (/.f64 1 x) (+.f64 (/.f64 1 (+.f64 1 x)) (pow.f64 (*.f64 x (+.f64 1 x)) -1/2))))
1.0ms	x	@	-inf	(-.f64 (pow.f64 x -3/2) (pow.f64 (+.f64 1 x) -3/2))
1.0ms	x	@	inf	(-.f64 (pow.f64 x -3/2) (pow.f64 (+.f64 1 x) -3/2))

rewrite187.0ms (2%)

Algorithm

1×	batch-egg-rewrite

Rules

446×	`fma-neg_binary64`
325×	`expm1-udef_binary64`
325×	`log1p-udef_binary64`
205×	`add-sqr-sqrt_binary64`
198×	`pow1_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	16	78
1	396	78
2	6125	78

Stop Event

1×	node limit

Counts

3 → 141

Calls

Call 1

Inputs

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

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

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

Outputs

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simplify84.0ms (0.9%)

Algorithm

1×	egg-herbie

Rules

610×	`distribute-rgt-in_binary64`
579×	`distribute-lft-in_binary64`
348×	`cancel-sign-sub-inv_binary64`
270×	`fma-def_binary64`
246×	`associate-/r*_binary64`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	251	2323
1	814	2236
2	2920	1844

Stop Event

1×	node limit

Counts

177 → 207

Calls

Call 1

Inputs
(*.f64 (-.f64 (pow.f64 x -3/2) 1) x)
(+.f64 (.f64 (-.f64 3/2 (.f64 (-.f64 (pow.f64 x -3/2) 1) (+.f64 (pow.f64 x -1/2) 1))) (pow.f64 x 2)) (*.f64 (-.f64 (pow.f64 x -3/2) 1) x))
(+.f64 (.f64 (-.f64 3/2 (.f64 (-.f64 (pow.f64 x -3/2) 1) (+.f64 (pow.f64 x -1/2) 1))) (pow.f64 x 2)) (+.f64 (.f64 -1 (.f64 (+.f64 15/8 (+.f64 (.f64 (-.f64 (pow.f64 x -3/2) 1) (-.f64 (.f64 -1/2 (sqrt.f64 (/.f64 1 x))) 1)) (.f64 (+.f64 (pow.f64 x -1/2) 1) (-.f64 3/2 (.f64 (+.f64 1 (pow.f64 x -1/2)) (-.f64 (pow.f64 x -3/2) 1)))))) (pow.f64 x 3))) (*.f64 (-.f64 (pow.f64 x -3/2) 1) x)))
(+.f64 (.f64 (-.f64 3/2 (.f64 (-.f64 (pow.f64 x -3/2) 1) (+.f64 (pow.f64 x -1/2) 1))) (pow.f64 x 2)) (+.f64 (.f64 -1 (.f64 (+.f64 15/8 (+.f64 (.f64 (-.f64 (pow.f64 x -3/2) 1) (-.f64 (.f64 -1/2 (sqrt.f64 (/.f64 1 x))) 1)) (.f64 (+.f64 (pow.f64 x -1/2) 1) (-.f64 3/2 (.f64 (+.f64 1 (pow.f64 x -1/2)) (-.f64 (pow.f64 x -3/2) 1)))))) (pow.f64 x 3))) (+.f64 (.f64 (-.f64 35/16 (+.f64 (.f64 (-.f64 (.f64 -1/2 (sqrt.f64 (/.f64 1 x))) 1) (-.f64 3/2 (.f64 (+.f64 1 (pow.f64 x -1/2)) (-.f64 (pow.f64 x -3/2) 1)))) (+.f64 (.f64 -1 (.f64 (+.f64 15/8 (+.f64 (.f64 (-.f64 (.f64 -1/2 (sqrt.f64 (/.f64 1 x))) 1) (-.f64 (pow.f64 x -3/2) 1)) (.f64 (+.f64 1 (pow.f64 x -1/2)) (-.f64 3/2 (.f64 (-.f64 (pow.f64 x -3/2) 1) (+.f64 (pow.f64 x -1/2) 1)))))) (+.f64 (pow.f64 x -1/2) 1))) (.f64 (-.f64 (pow.f64 x -3/2) 1) (+.f64 (.f64 3/8 (sqrt.f64 (/.f64 1 x))) 1))))) (pow.f64 x 4)) (*.f64 (-.f64 (pow.f64 x -3/2) 1) x))))
(*.f64 3/2 (sqrt.f64 (/.f64 1 (pow.f64 x 3))))
(-.f64 (+.f64 (.f64 -15/8 (sqrt.f64 (/.f64 1 (pow.f64 x 5)))) (.f64 3/2 (sqrt.f64 (/.f64 1 (pow.f64 x 3))))) (.f64 3/2 (.f64 (-.f64 2 (*.f64 1/2 (/.f64 1 x))) (sqrt.f64 (/.f64 1 (pow.f64 x 3))))))
(-.f64 (+.f64 (.f64 -15/8 (sqrt.f64 (/.f64 1 (pow.f64 x 5)))) (+.f64 (.f64 35/16 (sqrt.f64 (/.f64 1 (pow.f64 x 7)))) (.f64 3/2 (sqrt.f64 (/.f64 1 (pow.f64 x 3)))))) (+.f64 (/.f64 (.f64 (-.f64 (.f64 -15/8 (sqrt.f64 (/.f64 1 x))) (.f64 3/2 (.f64 (-.f64 2 (.f64 1/2 (/.f64 1 x))) (sqrt.f64 x)))) (-.f64 2 (.f64 1/2 (/.f64 1 x)))) (pow.f64 x 2)) (+.f64 (.f64 3/2 (.f64 (-.f64 (.f64 3/8 (/.f64 1 x)) 1) (sqrt.f64 (/.f64 1 (pow.f64 x 5))))) (.f64 3/2 (.f64 (-.f64 2 (*.f64 1/2 (/.f64 1 x))) (sqrt.f64 (/.f64 1 (pow.f64 x 3))))))))
(-.f64 (+.f64 (.f64 3/2 (sqrt.f64 (/.f64 1 (pow.f64 x 3)))) (+.f64 (.f64 35/16 (sqrt.f64 (/.f64 1 (pow.f64 x 7)))) (+.f64 (.f64 -15/8 (sqrt.f64 (/.f64 1 (pow.f64 x 5)))) (.f64 -315/128 (sqrt.f64 (/.f64 1 (pow.f64 x 9))))))) (+.f64 (.f64 3/2 (.f64 (-.f64 (.f64 3/8 (/.f64 1 x)) 1) (sqrt.f64 (/.f64 1 (pow.f64 x 5))))) (+.f64 (.f64 3/2 (.f64 (sqrt.f64 (/.f64 1 (pow.f64 x 7))) (-.f64 1 (.f64 5/16 (/.f64 1 x))))) (+.f64 (/.f64 (.f64 (-.f64 2 (.f64 1/2 (/.f64 1 x))) (-.f64 (.f64 35/16 (sqrt.f64 (/.f64 1 x))) (+.f64 (.f64 (-.f64 (.f64 -15/8 (sqrt.f64 (/.f64 1 x))) (.f64 3/2 (.f64 (-.f64 2 (.f64 1/2 (/.f64 1 x))) (sqrt.f64 x)))) (.f64 (-.f64 2 (.f64 1/2 (/.f64 1 x))) x)) (.f64 3/2 (.f64 (-.f64 (.f64 3/8 (/.f64 1 x)) 1) (sqrt.f64 x)))))) (pow.f64 x 3)) (+.f64 (/.f64 (.f64 (-.f64 2 (.f64 1/2 (/.f64 1 x))) (-.f64 (.f64 -15/8 (sqrt.f64 (/.f64 1 x))) (.f64 3/2 (.f64 (-.f64 2 (.f64 1/2 (/.f64 1 x))) (sqrt.f64 x))))) (pow.f64 x 2)) (+.f64 (/.f64 (.f64 (-.f64 (.f64 -15/8 (sqrt.f64 (/.f64 1 x))) (.f64 3/2 (.f64 (-.f64 2 (.f64 1/2 (/.f64 1 x))) (sqrt.f64 x)))) (-.f64 (.f64 3/8 (/.f64 1 x)) 1)) (pow.f64 x 3)) (.f64 3/2 (.f64 (-.f64 2 (.f64 1/2 (/.f64 1 x))) (sqrt.f64 (/.f64 1 (pow.f64 x 3)))))))))))
(.f64 -3/2 (exp.f64 (.f64 -3/2 (+.f64 (*.f64 -1 (log.f64 (/.f64 -1 x))) (log.f64 -1)))))
(-.f64 (+.f64 (.f64 -3/2 (exp.f64 (.f64 -3/2 (+.f64 (.f64 -1 (log.f64 (/.f64 -1 x))) (log.f64 -1))))) (.f64 15/8 (/.f64 (exp.f64 (.f64 -3/2 (+.f64 (.f64 -1 (log.f64 (/.f64 -1 x))) (log.f64 -1)))) x))) (.f64 3/2 (.f64 (+.f64 2 (.f64 1/2 (/.f64 1 x))) (exp.f64 (.f64 -3/2 (+.f64 (*.f64 -1 (log.f64 (/.f64 -1 x))) (log.f64 -1)))))))
(-.f64 (+.f64 (.f64 -1 (/.f64 (-.f64 (.f64 35/16 (.f64 (exp.f64 (.f64 -3/2 (+.f64 (.f64 -1 (log.f64 (/.f64 -1 x))) (log.f64 -1)))) x)) (+.f64 (.f64 3/2 (.f64 (+.f64 1 (.f64 3/8 (/.f64 1 x))) (.f64 (exp.f64 (.f64 -3/2 (+.f64 (.f64 -1 (log.f64 (/.f64 -1 x))) (log.f64 -1)))) (pow.f64 x 2)))) (.f64 (+.f64 2 (.f64 1/2 (/.f64 1 x))) (.f64 (-.f64 (.f64 15/8 (.f64 (exp.f64 (.f64 -3/2 (+.f64 (.f64 -1 (log.f64 (/.f64 -1 x))) (log.f64 -1)))) x)) (.f64 3/2 (.f64 (+.f64 2 (.f64 1/2 (/.f64 1 x))) (.f64 (exp.f64 (.f64 -3/2 (+.f64 (.f64 -1 (log.f64 (/.f64 -1 x))) (log.f64 -1)))) (pow.f64 x 2))))) x)))) (pow.f64 x 3))) (+.f64 (.f64 -3/2 (exp.f64 (.f64 -3/2 (+.f64 (.f64 -1 (log.f64 (/.f64 -1 x))) (log.f64 -1))))) (.f64 15/8 (/.f64 (exp.f64 (.f64 -3/2 (+.f64 (.f64 -1 (log.f64 (/.f64 -1 x))) (log.f64 -1)))) x)))) (.f64 3/2 (.f64 (+.f64 2 (.f64 1/2 (/.f64 1 x))) (exp.f64 (.f64 -3/2 (+.f64 (*.f64 -1 (log.f64 (/.f64 -1 x))) (log.f64 -1)))))))
(-.f64 (+.f64 (.f64 -1 (/.f64 (-.f64 (.f64 35/16 (.f64 (exp.f64 (.f64 -3/2 (+.f64 (.f64 -1 (log.f64 (/.f64 -1 x))) (log.f64 -1)))) x)) (+.f64 (.f64 3/2 (.f64 (+.f64 1 (.f64 3/8 (/.f64 1 x))) (.f64 (exp.f64 (.f64 -3/2 (+.f64 (.f64 -1 (log.f64 (/.f64 -1 x))) (log.f64 -1)))) (pow.f64 x 2)))) (.f64 (+.f64 2 (.f64 1/2 (/.f64 1 x))) (.f64 (-.f64 (.f64 15/8 (.f64 (exp.f64 (.f64 -3/2 (+.f64 (.f64 -1 (log.f64 (/.f64 -1 x))) (log.f64 -1)))) x)) (.f64 3/2 (.f64 (+.f64 2 (.f64 1/2 (/.f64 1 x))) (.f64 (exp.f64 (.f64 -3/2 (+.f64 (.f64 -1 (log.f64 (/.f64 -1 x))) (log.f64 -1)))) (pow.f64 x 2))))) x)))) (pow.f64 x 3))) (+.f64 (.f64 -3/2 (exp.f64 (.f64 -3/2 (+.f64 (.f64 -1 (log.f64 (/.f64 -1 x))) (log.f64 -1))))) (+.f64 (.f64 15/8 (/.f64 (exp.f64 (.f64 -3/2 (+.f64 (.f64 -1 (log.f64 (/.f64 -1 x))) (log.f64 -1)))) x)) (.f64 315/128 (/.f64 (exp.f64 (.f64 -3/2 (+.f64 (.f64 -1 (log.f64 (/.f64 -1 x))) (log.f64 -1)))) (pow.f64 x 3)))))) (+.f64 (.f64 3/2 (.f64 (+.f64 2 (.f64 1/2 (/.f64 1 x))) (exp.f64 (.f64 -3/2 (+.f64 (.f64 -1 (log.f64 (/.f64 -1 x))) (log.f64 -1)))))) (+.f64 (.f64 3/2 (/.f64 (.f64 (+.f64 1 (.f64 5/16 (/.f64 1 x))) (exp.f64 (.f64 -3/2 (+.f64 (.f64 -1 (log.f64 (/.f64 -1 x))) (log.f64 -1))))) (pow.f64 x 2))) (+.f64 (/.f64 (.f64 (+.f64 1 (.f64 3/8 (/.f64 1 x))) (-.f64 (.f64 15/8 (.f64 (exp.f64 (.f64 -3/2 (+.f64 (.f64 -1 (log.f64 (/.f64 -1 x))) (log.f64 -1)))) x)) (.f64 3/2 (.f64 (+.f64 2 (.f64 1/2 (/.f64 1 x))) (.f64 (exp.f64 (.f64 -3/2 (+.f64 (.f64 -1 (log.f64 (/.f64 -1 x))) (log.f64 -1)))) (pow.f64 x 2)))))) (pow.f64 x 3)) (/.f64 (.f64 (+.f64 2 (.f64 1/2 (/.f64 1 x))) (-.f64 (.f64 35/16 (.f64 (exp.f64 (.f64 -3/2 (+.f64 (.f64 -1 (log.f64 (/.f64 -1 x))) (log.f64 -1)))) x)) (+.f64 (.f64 3/2 (.f64 (+.f64 1 (.f64 3/8 (/.f64 1 x))) (.f64 (exp.f64 (.f64 -3/2 (+.f64 (.f64 -1 (log.f64 (/.f64 -1 x))) (log.f64 -1)))) (pow.f64 x 2)))) (.f64 (+.f64 2 (.f64 1/2 (/.f64 1 x))) (.f64 (-.f64 (.f64 15/8 (.f64 (exp.f64 (.f64 -3/2 (+.f64 (.f64 -1 (log.f64 (/.f64 -1 x))) (log.f64 -1)))) x)) (.f64 3/2 (.f64 (+.f64 2 (.f64 1/2 (/.f64 1 x))) (.f64 (exp.f64 (.f64 -3/2 (+.f64 (.f64 -1 (log.f64 (/.f64 -1 x))) (log.f64 -1)))) (pow.f64 x 2))))) x))))) (pow.f64 x 3))))))
(-.f64 (pow.f64 x -3/2) 1)
(-.f64 (+.f64 (pow.f64 x -3/2) (*.f64 3/2 x)) 1)
(-.f64 (+.f64 (.f64 -15/8 (pow.f64 x 2)) (+.f64 (pow.f64 x -3/2) (.f64 3/2 x))) 1)
(-.f64 (+.f64 (.f64 -15/8 (pow.f64 x 2)) (+.f64 (pow.f64 x -3/2) (+.f64 (.f64 3/2 x) (*.f64 35/16 (pow.f64 x 3))))) 1)
(*.f64 3/2 (sqrt.f64 (/.f64 1 (pow.f64 x 5))))
(+.f64 (.f64 -15/8 (sqrt.f64 (/.f64 1 (pow.f64 x 7)))) (.f64 3/2 (sqrt.f64 (/.f64 1 (pow.f64 x 5)))))
(+.f64 (.f64 -15/8 (sqrt.f64 (/.f64 1 (pow.f64 x 7)))) (+.f64 (.f64 35/16 (sqrt.f64 (/.f64 1 (pow.f64 x 9)))) (*.f64 3/2 (sqrt.f64 (/.f64 1 (pow.f64 x 5))))))
(+.f64 (.f64 -315/128 (sqrt.f64 (/.f64 1 (pow.f64 x 11)))) (+.f64 (.f64 -15/8 (sqrt.f64 (/.f64 1 (pow.f64 x 7)))) (+.f64 (.f64 35/16 (sqrt.f64 (/.f64 1 (pow.f64 x 9)))) (.f64 3/2 (sqrt.f64 (/.f64 1 (pow.f64 x 5)))))))
(.f64 3/2 (/.f64 (exp.f64 (.f64 -3/2 (+.f64 (*.f64 -1 (log.f64 (/.f64 -1 x))) (log.f64 -1)))) x))
(+.f64 (.f64 3/2 (/.f64 (exp.f64 (.f64 -3/2 (+.f64 (.f64 -1 (log.f64 (/.f64 -1 x))) (log.f64 -1)))) x)) (.f64 -15/8 (/.f64 (exp.f64 (.f64 -3/2 (+.f64 (.f64 -1 (log.f64 (/.f64 -1 x))) (log.f64 -1)))) (pow.f64 x 2))))
(+.f64 (.f64 35/16 (/.f64 (exp.f64 (.f64 -3/2 (+.f64 (.f64 -1 (log.f64 (/.f64 -1 x))) (log.f64 -1)))) (pow.f64 x 3))) (+.f64 (.f64 3/2 (/.f64 (exp.f64 (.f64 -3/2 (+.f64 (.f64 -1 (log.f64 (/.f64 -1 x))) (log.f64 -1)))) x)) (.f64 -15/8 (/.f64 (exp.f64 (.f64 -3/2 (+.f64 (*.f64 -1 (log.f64 (/.f64 -1 x))) (log.f64 -1)))) (pow.f64 x 2)))))
(+.f64 (.f64 35/16 (/.f64 (exp.f64 (.f64 -3/2 (+.f64 (.f64 -1 (log.f64 (/.f64 -1 x))) (log.f64 -1)))) (pow.f64 x 3))) (+.f64 (.f64 3/2 (/.f64 (exp.f64 (.f64 -3/2 (+.f64 (.f64 -1 (log.f64 (/.f64 -1 x))) (log.f64 -1)))) x)) (+.f64 (.f64 -315/128 (/.f64 (exp.f64 (.f64 -3/2 (+.f64 (.f64 -1 (log.f64 (/.f64 -1 x))) (log.f64 -1)))) (pow.f64 x 4))) (.f64 -15/8 (/.f64 (exp.f64 (.f64 -3/2 (+.f64 (.f64 -1 (log.f64 (/.f64 -1 x))) (log.f64 -1)))) (pow.f64 x 2))))))
(/.f64 1 x)
(+.f64 (pow.f64 x -1/2) (+.f64 1 (/.f64 1 x)))
(+.f64 1 (+.f64 (pow.f64 x -1/2) (+.f64 (/.f64 1 x) (.f64 (-.f64 (.f64 -1/2 (sqrt.f64 (/.f64 1 x))) 1) x))))
(+.f64 1 (+.f64 (pow.f64 x -1/2) (+.f64 (.f64 (+.f64 (.f64 3/8 (sqrt.f64 (/.f64 1 x))) 1) (pow.f64 x 2)) (+.f64 (/.f64 1 x) (.f64 (-.f64 (.f64 -1/2 (sqrt.f64 (/.f64 1 x))) 1) x)))))
(/.f64 1 x)
(-.f64 (*.f64 3 (/.f64 1 x)) (/.f64 1/2 (pow.f64 x 2)))
(-.f64 (+.f64 (.f64 3/8 (/.f64 1 (pow.f64 x 3))) (+.f64 (.f64 2 (/.f64 1 x)) (/.f64 1 x))) (*.f64 3/2 (/.f64 1 (pow.f64 x 2))))
(-.f64 (+.f64 (.f64 11/8 (/.f64 1 (pow.f64 x 3))) (+.f64 (.f64 2 (/.f64 1 x)) (/.f64 1 x))) (+.f64 (.f64 5/16 (/.f64 1 (pow.f64 x 4))) (.f64 3/2 (/.f64 1 (pow.f64 x 2)))))
(/.f64 -1 x)
(+.f64 (/.f64 1/2 (pow.f64 x 2)) (/.f64 1 x))
(-.f64 (+.f64 (.f64 -1 (/.f64 (+.f64 1 (.f64 3/8 (/.f64 1 x))) (pow.f64 x 2))) (+.f64 (.f64 1/2 (/.f64 1 (pow.f64 x 2))) (.f64 2 (/.f64 1 x)))) (/.f64 1 x))
(-.f64 (+.f64 (.f64 -1 (/.f64 (+.f64 1 (.f64 3/8 (/.f64 1 x))) (pow.f64 x 2))) (+.f64 (.f64 5/16 (/.f64 1 (pow.f64 x 4))) (+.f64 (.f64 1/2 (/.f64 1 (pow.f64 x 2))) (+.f64 (*.f64 2 (/.f64 1 x)) (/.f64 1 (pow.f64 x 3)))))) (/.f64 1 x))

Outputs
(*.f64 (-.f64 (pow.f64 x -3/2) 1) x)
(*.f64 x (+.f64 (pow.f64 x -3/2) -1))
(+.f64 (pow.f64 x -1/2) (neg.f64 x))
(+.f64 (.f64 (-.f64 3/2 (.f64 (-.f64 (pow.f64 x -3/2) 1) (+.f64 (pow.f64 x -1/2) 1))) (pow.f64 x 2)) (*.f64 (-.f64 (pow.f64 x -3/2) 1) x))
(fma.f64 (-.f64 3/2 (.f64 (+.f64 (pow.f64 x -3/2) -1) (+.f64 1 (pow.f64 x -1/2)))) (.f64 x x) (*.f64 x (+.f64 (pow.f64 x -3/2) -1)))
(fma.f64 (+.f64 3/2 (.f64 (+.f64 (pow.f64 x -3/2) -1) (-.f64 -1 (pow.f64 x -1/2)))) (.f64 x x) (+.f64 (pow.f64 x -1/2) (neg.f64 x)))
(+.f64 (.f64 (-.f64 3/2 (.f64 (-.f64 (pow.f64 x -3/2) 1) (+.f64 (pow.f64 x -1/2) 1))) (pow.f64 x 2)) (+.f64 (.f64 -1 (.f64 (+.f64 15/8 (+.f64 (.f64 (-.f64 (pow.f64 x -3/2) 1) (-.f64 (.f64 -1/2 (sqrt.f64 (/.f64 1 x))) 1)) (.f64 (+.f64 (pow.f64 x -1/2) 1) (-.f64 3/2 (.f64 (+.f64 1 (pow.f64 x -1/2)) (-.f64 (pow.f64 x -3/2) 1)))))) (pow.f64 x 3))) (*.f64 (-.f64 (pow.f64 x -3/2) 1) x)))
(fma.f64 (-.f64 3/2 (.f64 (+.f64 (pow.f64 x -3/2) -1) (+.f64 1 (pow.f64 x -1/2)))) (.f64 x x) (fma.f64 -1 (.f64 (pow.f64 x 3) (+.f64 15/8 (fma.f64 (+.f64 (pow.f64 x -3/2) -1) (fma.f64 -1/2 (sqrt.f64 (/.f64 1 x)) -1) (.f64 (+.f64 1 (pow.f64 x -1/2)) (-.f64 3/2 (.f64 (+.f64 (pow.f64 x -3/2) -1) (+.f64 1 (pow.f64 x -1/2)))))))) (.f64 x (+.f64 (pow.f64 x -3/2) -1))))
(fma.f64 (-.f64 3/2 (.f64 (+.f64 (pow.f64 x -3/2) -1) (+.f64 1 (pow.f64 x -1/2)))) (.f64 x x) (-.f64 (.f64 x (+.f64 (pow.f64 x -3/2) -1)) (.f64 (pow.f64 x 3) (+.f64 15/8 (fma.f64 (+.f64 1 (pow.f64 x -1/2)) (-.f64 3/2 (.f64 (+.f64 (pow.f64 x -3/2) -1) (+.f64 1 (pow.f64 x -1/2)))) (.f64 (+.f64 (pow.f64 x -3/2) -1) (fma.f64 -1/2 (sqrt.f64 (/.f64 1 x)) -1)))))))
(+.f64 (+.f64 (pow.f64 x -1/2) (neg.f64 x)) (.f64 (.f64 x x) (-.f64 (+.f64 3/2 (.f64 (+.f64 (pow.f64 x -3/2) -1) (-.f64 -1 (pow.f64 x -1/2)))) (.f64 (+.f64 15/8 (fma.f64 (+.f64 (pow.f64 x -3/2) -1) (fma.f64 -1/2 (sqrt.f64 (/.f64 1 x)) -1) (.f64 (+.f64 1 (pow.f64 x -1/2)) (+.f64 3/2 (.f64 (+.f64 (pow.f64 x -3/2) -1) (-.f64 -1 (pow.f64 x -1/2))))))) x))))
(+.f64 (.f64 (-.f64 3/2 (.f64 (-.f64 (pow.f64 x -3/2) 1) (+.f64 (pow.f64 x -1/2) 1))) (pow.f64 x 2)) (+.f64 (.f64 -1 (.f64 (+.f64 15/8 (+.f64 (.f64 (-.f64 (pow.f64 x -3/2) 1) (-.f64 (.f64 -1/2 (sqrt.f64 (/.f64 1 x))) 1)) (.f64 (+.f64 (pow.f64 x -1/2) 1) (-.f64 3/2 (.f64 (+.f64 1 (pow.f64 x -1/2)) (-.f64 (pow.f64 x -3/2) 1)))))) (pow.f64 x 3))) (+.f64 (.f64 (-.f64 35/16 (+.f64 (.f64 (-.f64 (.f64 -1/2 (sqrt.f64 (/.f64 1 x))) 1) (-.f64 3/2 (.f64 (+.f64 1 (pow.f64 x -1/2)) (-.f64 (pow.f64 x -3/2) 1)))) (+.f64 (.f64 -1 (.f64 (+.f64 15/8 (+.f64 (.f64 (-.f64 (.f64 -1/2 (sqrt.f64 (/.f64 1 x))) 1) (-.f64 (pow.f64 x -3/2) 1)) (.f64 (+.f64 1 (pow.f64 x -1/2)) (-.f64 3/2 (.f64 (-.f64 (pow.f64 x -3/2) 1) (+.f64 (pow.f64 x -1/2) 1)))))) (+.f64 (pow.f64 x -1/2) 1))) (.f64 (-.f64 (pow.f64 x -3/2) 1) (+.f64 (.f64 3/8 (sqrt.f64 (/.f64 1 x))) 1))))) (pow.f64 x 4)) (*.f64 (-.f64 (pow.f64 x -3/2) 1) x))))
(fma.f64 (-.f64 3/2 (.f64 (+.f64 (pow.f64 x -3/2) -1) (+.f64 1 (pow.f64 x -1/2)))) (.f64 x x) (fma.f64 -1 (.f64 (pow.f64 x 3) (+.f64 15/8 (fma.f64 (+.f64 (pow.f64 x -3/2) -1) (fma.f64 -1/2 (sqrt.f64 (/.f64 1 x)) -1) (.f64 (+.f64 1 (pow.f64 x -1/2)) (-.f64 3/2 (.f64 (+.f64 (pow.f64 x -3/2) -1) (+.f64 1 (pow.f64 x -1/2)))))))) (fma.f64 (-.f64 35/16 (fma.f64 (fma.f64 -1/2 (sqrt.f64 (/.f64 1 x)) -1) (-.f64 3/2 (.f64 (+.f64 (pow.f64 x -3/2) -1) (+.f64 1 (pow.f64 x -1/2)))) (fma.f64 -1 (.f64 (+.f64 1 (pow.f64 x -1/2)) (+.f64 15/8 (fma.f64 (+.f64 (pow.f64 x -3/2) -1) (fma.f64 -1/2 (sqrt.f64 (/.f64 1 x)) -1) (.f64 (+.f64 1 (pow.f64 x -1/2)) (-.f64 3/2 (.f64 (+.f64 (pow.f64 x -3/2) -1) (+.f64 1 (pow.f64 x -1/2)))))))) (.f64 (+.f64 (pow.f64 x -3/2) -1) (fma.f64 3/8 (sqrt.f64 (/.f64 1 x)) 1))))) (pow.f64 x 4) (*.f64 x (+.f64 (pow.f64 x -3/2) -1)))))
(fma.f64 (-.f64 3/2 (.f64 (+.f64 (pow.f64 x -3/2) -1) (+.f64 1 (pow.f64 x -1/2)))) (.f64 x x) (-.f64 (fma.f64 (-.f64 35/16 (fma.f64 (-.f64 3/2 (.f64 (+.f64 (pow.f64 x -3/2) -1) (+.f64 1 (pow.f64 x -1/2)))) (fma.f64 -1/2 (sqrt.f64 (/.f64 1 x)) -1) (-.f64 (.f64 (+.f64 (pow.f64 x -3/2) -1) (fma.f64 (sqrt.f64 (/.f64 1 x)) 3/8 1)) (.f64 (+.f64 1 (pow.f64 x -1/2)) (+.f64 15/8 (fma.f64 (+.f64 1 (pow.f64 x -1/2)) (-.f64 3/2 (.f64 (+.f64 (pow.f64 x -3/2) -1) (+.f64 1 (pow.f64 x -1/2)))) (.f64 (+.f64 (pow.f64 x -3/2) -1) (fma.f64 -1/2 (sqrt.f64 (/.f64 1 x)) -1)))))))) (pow.f64 x 4) (.f64 x (+.f64 (pow.f64 x -3/2) -1))) (.f64 (pow.f64 x 3) (+.f64 15/8 (fma.f64 (+.f64 1 (pow.f64 x -1/2)) (-.f64 3/2 (.f64 (+.f64 (pow.f64 x -3/2) -1) (+.f64 1 (pow.f64 x -1/2)))) (*.f64 (+.f64 (pow.f64 x -3/2) -1) (fma.f64 -1/2 (sqrt.f64 (/.f64 1 x)) -1)))))))
(+.f64 (fma.f64 (-.f64 35/16 (fma.f64 (+.f64 3/2 (.f64 (+.f64 (pow.f64 x -3/2) -1) (-.f64 -1 (pow.f64 x -1/2)))) (fma.f64 -1/2 (sqrt.f64 (/.f64 1 x)) -1) (fma.f64 (+.f64 (pow.f64 x -3/2) -1) (fma.f64 (sqrt.f64 (/.f64 1 x)) 3/8 1) (.f64 (+.f64 15/8 (fma.f64 (+.f64 (pow.f64 x -3/2) -1) (fma.f64 -1/2 (sqrt.f64 (/.f64 1 x)) -1) (.f64 (+.f64 1 (pow.f64 x -1/2)) (+.f64 3/2 (.f64 (+.f64 (pow.f64 x -3/2) -1) (-.f64 -1 (pow.f64 x -1/2))))))) (-.f64 -1 (pow.f64 x -1/2)))))) (pow.f64 x 4) (+.f64 (pow.f64 x -1/2) (neg.f64 x))) (.f64 (.f64 x x) (-.f64 (+.f64 3/2 (.f64 (+.f64 (pow.f64 x -3/2) -1) (-.f64 -1 (pow.f64 x -1/2)))) (.f64 (+.f64 15/8 (fma.f64 (+.f64 (pow.f64 x -3/2) -1) (fma.f64 -1/2 (sqrt.f64 (/.f64 1 x)) -1) (.f64 (+.f64 1 (pow.f64 x -1/2)) (+.f64 3/2 (.f64 (+.f64 (pow.f64 x -3/2) -1) (-.f64 -1 (pow.f64 x -1/2))))))) x))))
(*.f64 3/2 (sqrt.f64 (/.f64 1 (pow.f64 x 3))))
(-.f64 (+.f64 (.f64 -15/8 (sqrt.f64 (/.f64 1 (pow.f64 x 5)))) (.f64 3/2 (sqrt.f64 (/.f64 1 (pow.f64 x 3))))) (.f64 3/2 (.f64 (-.f64 2 (*.f64 1/2 (/.f64 1 x))) (sqrt.f64 (/.f64 1 (pow.f64 x 3))))))
(+.f64 (fma.f64 -15/8 (sqrt.f64 (/.f64 1 (pow.f64 x 5))) (.f64 3/2 (sqrt.f64 (/.f64 1 (pow.f64 x 3))))) (.f64 -3/2 (*.f64 (sqrt.f64 (/.f64 1 (pow.f64 x 3))) (-.f64 2 (/.f64 1/2 x)))))
(fma.f64 -15/8 (sqrt.f64 (/.f64 1 (pow.f64 x 5))) (.f64 (sqrt.f64 (/.f64 1 (pow.f64 x 3))) (-.f64 3/2 (+.f64 3 (.f64 (/.f64 -1/2 x) 3/2)))))
(fma.f64 -15/8 (sqrt.f64 (/.f64 1 (pow.f64 x 5))) (*.f64 (sqrt.f64 (/.f64 1 (pow.f64 x 3))) (-.f64 3/2 (+.f64 3 (/.f64 -3/4 x)))))
(-.f64 (+.f64 (.f64 -15/8 (sqrt.f64 (/.f64 1 (pow.f64 x 5)))) (+.f64 (.f64 35/16 (sqrt.f64 (/.f64 1 (pow.f64 x 7)))) (.f64 3/2 (sqrt.f64 (/.f64 1 (pow.f64 x 3)))))) (+.f64 (/.f64 (.f64 (-.f64 (.f64 -15/8 (sqrt.f64 (/.f64 1 x))) (.f64 3/2 (.f64 (-.f64 2 (.f64 1/2 (/.f64 1 x))) (sqrt.f64 x)))) (-.f64 2 (.f64 1/2 (/.f64 1 x)))) (pow.f64 x 2)) (+.f64 (.f64 3/2 (.f64 (-.f64 (.f64 3/8 (/.f64 1 x)) 1) (sqrt.f64 (/.f64 1 (pow.f64 x 5))))) (.f64 3/2 (.f64 (-.f64 2 (*.f64 1/2 (/.f64 1 x))) (sqrt.f64 (/.f64 1 (pow.f64 x 3))))))))
(-.f64 (fma.f64 -15/8 (sqrt.f64 (/.f64 1 (pow.f64 x 5))) (fma.f64 35/16 (sqrt.f64 (/.f64 1 (pow.f64 x 7))) (.f64 3/2 (sqrt.f64 (/.f64 1 (pow.f64 x 3)))))) (+.f64 (/.f64 (+.f64 (.f64 (sqrt.f64 (/.f64 1 x)) -15/8) (.f64 -3/2 (.f64 (-.f64 2 (/.f64 1/2 x)) (sqrt.f64 x)))) (/.f64 (.f64 x x) (-.f64 2 (/.f64 1/2 x)))) (.f64 3/2 (+.f64 (.f64 (sqrt.f64 (/.f64 1 (pow.f64 x 5))) (+.f64 (/.f64 3/8 x) -1)) (.f64 (sqrt.f64 (/.f64 1 (pow.f64 x 3))) (-.f64 2 (/.f64 1/2 x)))))))
(-.f64 (fma.f64 -15/8 (sqrt.f64 (/.f64 1 (pow.f64 x 5))) (fma.f64 3/2 (sqrt.f64 (/.f64 1 (pow.f64 x 3))) (.f64 35/16 (sqrt.f64 (/.f64 1 (pow.f64 x 7)))))) (fma.f64 3/2 (fma.f64 (sqrt.f64 (/.f64 1 (pow.f64 x 5))) (+.f64 -1 (/.f64 3/8 x)) (.f64 (sqrt.f64 (/.f64 1 (pow.f64 x 3))) (+.f64 2 (/.f64 -1/2 x)))) (.f64 (/.f64 (+.f64 2 (/.f64 -1/2 x)) x) (/.f64 (fma.f64 (sqrt.f64 (/.f64 1 x)) -15/8 (.f64 -3/2 (*.f64 (+.f64 2 (/.f64 -1/2 x)) (sqrt.f64 x)))) x))))
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(+.f64 (+.f64 1 (pow.f64 x -1/2)) (fma.f64 x (fma.f64 -1/2 (sqrt.f64 (/.f64 1 x)) -1) (/.f64 1 x)))
(+.f64 1 (+.f64 (pow.f64 x -1/2) (+.f64 (.f64 (+.f64 (.f64 3/8 (sqrt.f64 (/.f64 1 x))) 1) (pow.f64 x 2)) (+.f64 (/.f64 1 x) (.f64 (-.f64 (.f64 -1/2 (sqrt.f64 (/.f64 1 x))) 1) x)))))
(+.f64 1 (+.f64 (pow.f64 x -1/2) (fma.f64 (fma.f64 3/8 (sqrt.f64 (/.f64 1 x)) 1) (.f64 x x) (+.f64 (/.f64 1 x) (.f64 x (fma.f64 -1/2 (sqrt.f64 (/.f64 1 x)) -1))))))
(+.f64 1 (+.f64 (pow.f64 x -1/2) (fma.f64 (*.f64 x x) (fma.f64 (sqrt.f64 (/.f64 1 x)) 3/8 1) (fma.f64 x (fma.f64 -1/2 (sqrt.f64 (/.f64 1 x)) -1) (/.f64 1 x)))))
(+.f64 (pow.f64 x -1/2) (+.f64 1 (fma.f64 (*.f64 x x) (fma.f64 (sqrt.f64 (/.f64 1 x)) 3/8 1) (fma.f64 x (fma.f64 -1/2 (sqrt.f64 (/.f64 1 x)) -1) (/.f64 1 x)))))
(/.f64 1 x)
(-.f64 (*.f64 3 (/.f64 1 x)) (/.f64 1/2 (pow.f64 x 2)))
(-.f64 (/.f64 3 x) (/.f64 1/2 (*.f64 x x)))
(+.f64 (/.f64 3 x) (/.f64 -1/2 (*.f64 x x)))
(+.f64 (/.f64 3 x) (/.f64 (/.f64 -1/2 x) x))
(-.f64 (+.f64 (.f64 3/8 (/.f64 1 (pow.f64 x 3))) (+.f64 (.f64 2 (/.f64 1 x)) (/.f64 1 x))) (*.f64 3/2 (/.f64 1 (pow.f64 x 2))))
(+.f64 (/.f64 3/8 (pow.f64 x 3)) (-.f64 (/.f64 3 x) (/.f64 3/2 (*.f64 x x))))
(+.f64 (/.f64 3/8 (pow.f64 x 3)) (+.f64 (/.f64 3 x) (/.f64 -3/2 (*.f64 x x))))
(+.f64 (/.f64 3/8 (pow.f64 x 3)) (+.f64 (/.f64 3 x) (/.f64 (/.f64 -3/2 x) x)))
(-.f64 (+.f64 (.f64 11/8 (/.f64 1 (pow.f64 x 3))) (+.f64 (.f64 2 (/.f64 1 x)) (/.f64 1 x))) (+.f64 (.f64 5/16 (/.f64 1 (pow.f64 x 4))) (.f64 3/2 (/.f64 1 (pow.f64 x 2)))))
(+.f64 (/.f64 11/8 (pow.f64 x 3)) (-.f64 (/.f64 3 x) (+.f64 (/.f64 3/2 (*.f64 x x)) (/.f64 5/16 (pow.f64 x 4)))))
(+.f64 (+.f64 (/.f64 3 x) (-.f64 (/.f64 11/8 (pow.f64 x 3)) (/.f64 5/16 (pow.f64 x 4)))) (/.f64 -3/2 (*.f64 x x)))
(+.f64 (+.f64 (/.f64 11/8 (pow.f64 x 3)) (+.f64 (/.f64 3 x) (/.f64 -5/16 (pow.f64 x 4)))) (/.f64 (/.f64 -3/2 x) x))
(/.f64 -1 x)
(+.f64 (/.f64 1/2 (pow.f64 x 2)) (/.f64 1 x))
(+.f64 (/.f64 1 x) (/.f64 1/2 (*.f64 x x)))
(-.f64 (+.f64 (.f64 -1 (/.f64 (+.f64 1 (.f64 3/8 (/.f64 1 x))) (pow.f64 x 2))) (+.f64 (.f64 1/2 (/.f64 1 (pow.f64 x 2))) (.f64 2 (/.f64 1 x)))) (/.f64 1 x))
(-.f64 (fma.f64 -1 (/.f64 (+.f64 1 (/.f64 3/8 x)) (.f64 x x)) (+.f64 (/.f64 1/2 (.f64 x x)) (/.f64 2 x))) (/.f64 1 x))
(+.f64 (-.f64 (+.f64 (/.f64 1/2 (.f64 x x)) (/.f64 2 x)) (/.f64 (+.f64 1 (/.f64 3/8 x)) (.f64 x x))) (/.f64 -1 x))
(+.f64 (/.f64 (+.f64 -1 (/.f64 -3/8 x)) (.f64 x x)) (+.f64 (/.f64 1/2 (.f64 x x)) (*.f64 (/.f64 1 x) 1)))
(-.f64 (+.f64 (.f64 -1 (/.f64 (+.f64 1 (.f64 3/8 (/.f64 1 x))) (pow.f64 x 2))) (+.f64 (.f64 5/16 (/.f64 1 (pow.f64 x 4))) (+.f64 (.f64 1/2 (/.f64 1 (pow.f64 x 2))) (+.f64 (*.f64 2 (/.f64 1 x)) (/.f64 1 (pow.f64 x 3)))))) (/.f64 1 x))
(-.f64 (fma.f64 -1 (/.f64 (+.f64 1 (/.f64 3/8 x)) (.f64 x x)) (+.f64 (/.f64 5/16 (pow.f64 x 4)) (+.f64 (/.f64 1/2 (.f64 x x)) (+.f64 (/.f64 1 (pow.f64 x 3)) (/.f64 2 x))))) (/.f64 1 x))
(+.f64 (-.f64 (+.f64 (/.f64 5/16 (pow.f64 x 4)) (+.f64 (/.f64 1 (pow.f64 x 3)) (+.f64 (/.f64 1/2 (.f64 x x)) (/.f64 2 x)))) (/.f64 (+.f64 1 (/.f64 3/8 x)) (.f64 x x))) (/.f64 -1 x))
(+.f64 (/.f64 (+.f64 -1 (/.f64 -3/8 x)) (.f64 x x)) (+.f64 (/.f64 5/16 (pow.f64 x 4)) (+.f64 (+.f64 (/.f64 1 (pow.f64 x 3)) (+.f64 (/.f64 1/2 (.f64 x x)) (/.f64 2 x))) (/.f64 -1 x))))

eval1.6s (17.2%)

Compiler: Compiled 33918 to 25518 computations (24.8% saved)

prune194.0ms (2%)

Pruning

20 alts after pruning (19 fresh and 1 done)

	Pruned	Kept	Total
New	1197	16	1213
Fresh	26	3	29
Picked	1	0	1
Done	4	1	5
Total	1228	20	1248

Error

4.2b

Counts

1248 → 20

Alt Table

Click to see full alt table

Status	Error	Program
▶	30.5b	(/.f64 1 (+.f64 x (sqrt.f64 x)))
	31.9b	(-.f64 (+.f64 (.f64 1/2 x) (+.f64 (pow.f64 x -1/2) (.f64 -3/8 (pow.f64 x 2)))) 1)
	30.5b	(-.f64 (/.f64 1 (sqrt.f64 x)) (/.f64 1 (+.f64 (*.f64 1/2 x) 1)))
	35.8b	(/.f64 (pow.f64 (/.f64 -1 (/.f64 -1 x)) 1/2) (/.f64 (*.f64 x x) 1/2))
▶	30.6b	(/.f64 1 (*.f64 (+.f64 (pow.f64 x -1/2) 1) x))
	36.9b	(/.f64 (+.f64 (/.f64 1 (*.f64 x x)) (/.f64 -1 (pow.f64 x 3))) (+.f64 (pow.f64 x -1/2) (pow.f64 (+.f64 1 x) -1/2)))
✓	20.5b	(/.f64 (-.f64 (/.f64 1 x) (/.f64 1 (+.f64 1 x))) (+.f64 (pow.f64 x -1/2) (pow.f64 (+.f64 1 x) -1/2)))
▶	32.1b	(pow.f64 x -1/2)
	32.1b	(sqrt.f64 (/.f64 1 x))
	31.7b	(-.f64 (pow.f64 x -1/2) 1)
▶	4.6b	(/.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)))
	42.1b	(*.f64 (-.f64 (pow.f64 x -3/2) 1) x)
	22.6b	(-.f64 (/.f64 1 (sqrt.f64 x)) (pow.f64 (+.f64 1 x) -1/2))
	62.8b	-1
	31.1b	(-.f64 (+.f64 (*.f64 1/2 x) (pow.f64 x -1/2)) 1)
	22.1b	(.f64 1 (pow.f64 (.f64 x (+.f64 1 x)) -1/2))
▶	40.1b	(*.f64 1/2 (sqrt.f64 (/.f64 1 (pow.f64 x 3))))
	33.3b	(+.f64 (pow.f64 x -1/2) (neg.f64 x))
	20.3b	(-.f64 (pow.f64 x -1/2) (pow.f64 (+.f64 1 x) -1/2))
	31.2b	(-.f64 (/.f64 1 (sqrt.f64 x)) (+.f64 (*.f64 -1/2 x) 1))

Compiler

Compiled 412 to 326 computations (20.9% saved)

localize37.0ms (0.4%)

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	(pow.f64 (+.f64 1 x) -1/2)
✓	0.1b	(/.f64 (/.f64 (+.f64 1 (-.f64 x x)) x) (+.f64 1 x))
✓	4.6b	(/.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)

series11.0ms (0.1%)

Counts

3 → 36

Calls

9 calls:

Time	Variable		Point	Expression
5.0ms	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	(+.f64 (pow.f64 x -1/2) (pow.f64 (+.f64 1 x) -1/2))
0.0ms	x	@	inf	(+.f64 (pow.f64 x -1/2) (pow.f64 (+.f64 1 x) -1/2))

rewrite91.0ms (1%)

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	48
1	331	48
2	4279	48

Stop Event

1×	node limit

Counts

3 → 129

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))

(+.f64 (pow.f64 x -1/2) (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) (*.f64 (cbrt.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 (cbrt.f64 (/.f64 1 (*.f64 (+.f64 (pow.f64 x -1/2) (pow.f64 (+.f64 1 x) -1/2)) (*.f64 x (+.f64 1 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))))) 2))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (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))))) 2) (cbrt.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 *.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 (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 (/.f64 (/.f64 -1 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 (/.f64 1 x) (+.f64 1 x)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (pow.f64 (/.f64 1 (cbrt.f64 x)) 2) (+.f64 (pow.f64 x -1/2) (pow.f64 (+.f64 1 x) -1/2))) (/.f64 (/.f64 1 (cbrt.f64 x)) (+.f64 1 x)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (pow.f64 x -1/2) (+.f64 (pow.f64 x -1/2) (pow.f64 (+.f64 1 x) -1/2))) (/.f64 (pow.f64 x -1/2) (+.f64 1 x)))))) (#(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 (pow.f64 (cbrt.f64 (/.f64 (/.f64 1 x) (+.f64 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(+.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 (pow.f64 (*.f64 x (+.f64 1 x)) -1/2) (pow.f64 (cbrt.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 (/.f64 1 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 x) (hypot.f64 (pow.f64 x -1/4) (pow.f64 (+.f64 1 x) -1/4))) (/.f64 (/.f64 1 (+.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 (pow.f64 (cbrt.f64 (/.f64 (/.f64 1 x) (+.f64 1 x))) 2) (hypot.f64 (pow.f64 x -1/4) (pow.f64 (+.f64 1 x) -1/4))) (/.f64 (cbrt.f64 (/.f64 (/.f64 1 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 (/.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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simplify65.0ms (0.7%)

Algorithm

1×	egg-herbie

Rules

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

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	202	2211
1	656	2038
2	2390	1581

Stop Event

1×	node limit

Counts

165 → 190

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

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

localize5.0ms (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)

series7.0ms (0.1%)

Counts

2 → 4

Calls

6 calls:

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

rewrite83.0ms (0.9%)

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)))))

simplify7.0ms (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

localize63.0ms (0.7%)

Local error

Found 3 expressions with local error:

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

Compiler

Compiled 28 to 21 computations (25% saved)

series11.0ms (0.1%)

Counts

3 → 32

Calls

9 calls:

Time	Variable		Point	Expression
6.0ms	x	@	0	(*.f64 (+.f64 (pow.f64 x -1/2) 1) x)
1.0ms	x	@	-inf	(/.f64 1 (*.f64 (+.f64 (pow.f64 x -1/2) 1) x))
1.0ms	x	@	-inf	(*.f64 (+.f64 (pow.f64 x -1/2) 1) x)
1.0ms	x	@	inf	(/.f64 1 (*.f64 (+.f64 (pow.f64 x -1/2) 1) x))
1.0ms	x	@	inf	(*.f64 (+.f64 (pow.f64 x -1/2) 1) x)

rewrite82.0ms (0.9%)

Algorithm

1×	batch-egg-rewrite

Rules

840×	`pow1_binary64`
786×	`add-log-exp_binary64`
786×	`log1p-expm1-u_binary64`
786×	`expm1-log1p-u_binary64`
769×	`add-exp-log_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	8	30
1	178	30
2	2244	30

Stop Event

1×	node limit

Counts

3 → 81

Calls

Call 1

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

Outputs

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

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

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

simplify76.0ms (0.8%)

Algorithm

1×	egg-herbie

Rules

655×	`fma-neg_binary64`
487×	`fma-def_binary64`
434×	`times-frac_binary64`
312×	`unswap-sqr_binary64`
284×	`associate-l_binary64`

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	25	324
1	66	324
2	133	272
3	317	260
4	806	228
5	2299	228
6	7348	228

Stop Event

1×	node limit

Counts

113 → 91

Calls

Call 1

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

localize12.0ms (0.1%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.0b	(*.f64 1/2 (sqrt.f64 (/.f64 1 (pow.f64 x 3))))
✓	0.1b	(/.f64 1 (pow.f64 x 3))
✓	18.8b	(sqrt.f64 (/.f64 1 (pow.f64 x 3)))

Compiler

Compiled 27 to 22 computations (18.5% saved)

series5.0ms (0.1%)

Counts

3 → 0

Calls

9 calls:

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

rewrite152.0ms (1.6%)

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

eval558.0ms (5.9%)

Compiler: Compiled 10440 to 7972 computations (23.6% saved)

prune207.0ms (2.2%)

Pruning

18 alts after pruning (17 fresh and 1 done)

	Pruned	Kept	Total
New	452	6	458
Fresh	3	11	14
Picked	1	0	1
Done	4	1	5
Total	460	18	478

Error

Counts

478 → 18

Alt Table

Click to see full alt table

Status	Error	Program
▶	31.1b	(.f64 1/2 (.f64 (/.f64 1 (sqrt.f64 x)) (/.f64 1 x)))
	22.6b	(-.f64 (/.f64 1 (sqrt.f64 x)) (pow.f64 (+.f64 1 x) -1/2))
	31.9b	(-.f64 (+.f64 (.f64 1/2 x) (+.f64 (pow.f64 x -1/2) (.f64 -3/8 (pow.f64 x 2)))) 1)
	30.5b	(-.f64 (/.f64 1 (sqrt.f64 x)) (/.f64 1 (+.f64 (*.f64 1/2 x) 1)))
	31.0b	(*.f64 1/2 (pow.f64 x -3/2))
✓	32.1b	(pow.f64 x -1/2)
	32.1b	(sqrt.f64 (/.f64 1 x))
	31.7b	(-.f64 (pow.f64 x -1/2) 1)
	33.3b	(+.f64 (pow.f64 x -1/2) (neg.f64 x))
▶	31.6b	(/.f64 1/2 (pow.f64 x 3/2))
▶	0.4b	(.f64 (/.f64 1 x) (/.f64 1 (.f64 (+.f64 1 x) (+.f64 (pow.f64 x -1/2) (pow.f64 (+.f64 1 x) -1/2)))))
▶	20.3b	(-.f64 (pow.f64 x -1/2) (pow.f64 (+.f64 1 x) -1/2))
	30.8b	(/.f64 (/.f64 (/.f64 (+.f64 1 (-.f64 x x)) x) (+.f64 1 x)) (*.f64 (sqrt.f64 (/.f64 1 x)) 2))
	31.2b	(-.f64 (/.f64 1 (sqrt.f64 x)) (+.f64 (*.f64 -1/2 x) 1))
	42.1b	(*.f64 (-.f64 (pow.f64 x -3/2) 1) x)
▶	59.2b	(/.f64 1 x)
	62.8b	-1
	31.1b	(-.f64 (+.f64 (*.f64 1/2 x) (pow.f64 x -1/2)) 1)

Compiler

Compiled 332 to 265 computations (20.2% saved)

localize69.0ms (0.7%)

Local error

Found 4 expressions with local error:

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

Compiler

Compiled 74 to 57 computations (23% saved)

series11.0ms (0.1%)

Counts

3 → 36

Calls

9 calls:

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

rewrite104.0ms (1.1%)

Algorithm

1×	batch-egg-rewrite

Rules

668×	`log-prod_binary64`
467×	`fma-def_binary64`
237×	`pow1/3_binary64`
231×	`fma-neg_binary64`
227×	`expm1-udef_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	12	66
1	286	57
2	4284	57

Stop Event

1×	node limit

Counts

3 → 199

Calls

Call 1

Inputs

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

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

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

Outputs

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simplify93.0ms (1%)

Algorithm

1×	egg-herbie

Rules

647×	`associate-/r*_binary64`
613×	`associate-/l*_binary64`
545×	`distribute-rgt-in_binary64`
538×	`distribute-lft-in_binary64`
315×	`associate-*l/_binary64`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	252	3713
1	849	3293
2	3028	2414

Stop Event

1×	node limit

Counts

235 → 267

Calls

Call 1

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

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

localize3.0ms (0%)

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

localize42.0ms (0.4%)

Local error

Found 1 expressions with local error:

New	Error	Program
✓	0.8b	(/.f64 1/2 (pow.f64 x 3/2))

Compiler

Compiled 12 to 9 computations (25% saved)

series2.0ms (0%)

Counts

1 → 0

Calls

3 calls:

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

rewrite108.0ms (1.1%)

Algorithm

1×	batch-egg-rewrite

Rules

560×	`pow1_binary64`
531×	`add-log-exp_binary64`
531×	`log1p-expm1-u_binary64`
531×	`expm1-log1p-u_binary64`
520×	`add-exp-log_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	6	7
1	134	7
2	1536	7

Stop Event

1×	node limit

Counts

1 → 20

Calls

Call 1

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

Outputs

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

simplify8.0ms (0.1%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	0	0

Stop Event

1×

saturated

Counts

20 → 20

Calls

Call 1

Inputs

Outputs

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)

series27.0ms (0.3%)

Counts

2 → 0

Calls

6 calls:

Time	Variable		Point	Expression
25.0ms	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	@	0	(.f64 1/2 (.f64 (/.f64 1 (sqrt.f64 x)) (/.f64 1 x)))

rewrite190.0ms (2%)

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)))))))

simplify9.0ms (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

localize26.0ms (0.3%)

Local error

Found 2 expressions with local error:

New	Error	Program
	0.0b	(pow.f64 (+.f64 1 x) -1/2)
✓	3.0b	(-.f64 (pow.f64 x -1/2) (pow.f64 (+.f64 1 x) -1/2))

Compiler

Compiled 24 to 18 computations (25% saved)

series4.0ms (0%)

Counts

1 → 12

Calls

3 calls:

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

rewrite86.0ms (0.9%)

Algorithm

1×	batch-egg-rewrite

Rules

943×	`pow1_binary64`
884×	`add-log-exp_binary64`
883×	`log1p-expm1-u_binary64`
883×	`expm1-log1p-u_binary64`
93×	`add-sqr-sqrt_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	8	13
1	183	13
2	2412	13

Stop Event

1×	node limit

Counts

1 → 36

Calls

Call 1

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

Outputs

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

simplify103.0ms (1.1%)

Algorithm

1×	egg-herbie

Rules

719×	`fma-def_binary64`
583×	`times-frac_binary64`
549×	`distribute-rgt-out_binary64`
375×	`unswap-sqr_binary64`
343×	`associate-/l*_binary64`

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	70	433
1	184	421
2	464	333
3	1331	281
4	5992	260

Stop Event

1×	node limit

Counts

48 → 59

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

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

eval771.0ms (8.1%)

Compiler: Compiled 14350 to 11732 computations (18.2% saved)

prune116.0ms (1.2%)

Pruning

21 alts after pruning (17 fresh and 4 done)

	Pruned	Kept	Total
New	519	9	528
Fresh	4	8	12
Picked	0	1	1
Done	2	3	5
Total	525	21	546

Error

Counts

546 → 21

Alt Table

Click to see full alt table

Status	Error	Program
	31.1b	(/.f64 (*.f64 (/.f64 1 x) 1/2) (sqrt.f64 x))
	22.6b	(-.f64 (/.f64 1 (sqrt.f64 x)) (pow.f64 (+.f64 1 x) -1/2))
	31.1b	(/.f64 (/.f64 1/2 (sqrt.f64 x)) x)
	30.5b	(-.f64 (/.f64 1 (sqrt.f64 x)) (/.f64 1 (+.f64 (*.f64 1/2 x) 1)))
	0.4b	(/.f64 (/.f64 (/.f64 1 x) (+.f64 (pow.f64 x -1/2) (pow.f64 (+.f64 1 x) -1/2))) (+.f64 1 x))
✓	32.1b	(pow.f64 x -1/2)
	26.0b	(.f64 (/.f64 1 x) (/.f64 1 (+.f64 (.f64 (sqrt.f64 (/.f64 1 x)) 3/2) (*.f64 2 (sqrt.f64 x)))))
	32.1b	(sqrt.f64 (/.f64 1 x))
	31.7b	(-.f64 (pow.f64 x -1/2) 1)
	31.7b	(.f64 (/.f64 (pow.f64 x -1/2) x) (+.f64 1/2 (+.f64 (/.f64 5/16 (.f64 x x)) (/.f64 -3/8 x))))
	31.9b	(-.f64 (+.f64 (.f64 1/2 x) (+.f64 (pow.f64 x -1/2) (.f64 -3/8 (pow.f64 x 2)))) 1)
	33.3b	(+.f64 (pow.f64 x -1/2) (neg.f64 x))
	32.3b	(*.f64 (/.f64 (pow.f64 x -1/2) x) (+.f64 1/2 (/.f64 -3/8 x)))
✓	31.6b	(/.f64 1/2 (pow.f64 x 3/2))
	42.1b	(*.f64 (-.f64 (pow.f64 x -3/2) 1) x)
✓	59.2b	(/.f64 1 x)
	62.8b	-1
	31.1b	(-.f64 (pow.f64 x -1/2) (+.f64 (*.f64 -1/2 x) 1))
	31.0b	(*.f64 (pow.f64 x -3/2) 1/2)
✓	20.3b	(-.f64 (pow.f64 x -1/2) (pow.f64 (+.f64 1 x) -1/2))
	31.2b	(-.f64 (/.f64 1 (sqrt.f64 x)) (+.f64 (*.f64 -1/2 x) 1))

Compiler

Compiled 201 to 159 computations (20.9% saved)

regimes226.0ms (2.4%)

Counts

66 → 1

Calls

Call 1

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

Calls

3 calls:

170.0ms	x
15.0ms	(-.f64 (/.f64 1 (sqrt.f64 x)) (/.f64 1 (sqrt.f64 (+.f64 x 1))))
15.0ms	(-.f64 (/.f64 1 (sqrt.f64 x)) (/.f64 1 (sqrt.f64 (+.f64 x 1))))

Results

Error	Segments	Branch
0.4b	1	`x`
0.4b	1	`(-.f64 (/.f64 1 (sqrt.f64 x)) (/.f64 1 (sqrt.f64 (+.f64 x 1))))`
0.4b	1	`(-.f64 (/.f64 1 (sqrt.f64 x)) (/.f64 1 (sqrt.f64 (+.f64 x 1))))`

Compiler

Compiled 885 to 678 computations (23.4% saved)

regimes75.0ms (0.8%)

Counts

35 → 2

Calls

Call 1

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

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

Calls

3 calls:

34.0ms	x
15.0ms	(-.f64 (/.f64 1 (sqrt.f64 x)) (/.f64 1 (sqrt.f64 (+.f64 x 1))))
13.0ms	(-.f64 (/.f64 1 (sqrt.f64 x)) (/.f64 1 (sqrt.f64 (+.f64 x 1))))

Results

Error	Segments	Branch
0.1b	2	`x`
0.1b	2	`(-.f64 (/.f64 1 (sqrt.f64 x)) (/.f64 1 (sqrt.f64 (+.f64 x 1))))`
0.1b	2	`(-.f64 (/.f64 1 (sqrt.f64 x)) (/.f64 1 (sqrt.f64 (+.f64 x 1))))`

Compiler

Compiled 336 to 250 computations (25.6% saved)

bsearch0.0ms (0%)

Algorithm

1×	left-value

Steps

Time	Left	Right
0.0ms	2.3844635955831694e-8	0.4463460181187834

Compiler

Compiled 16 to 13 computations (18.8% saved)

regimes33.0ms (0.3%)

Counts

26 → 2

Calls

Call 1

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

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

Calls

1 calls:

26.0ms

Results

Error	Segments	Branch
0.5b	2	`x`

Compiler

Compiled 208 to 151 computations (27.4% saved)

bsearch25.0ms (0.3%)

Algorithm

1×	binary-search

Steps

Time	Left	Right
25.0ms	0.6722496367662038	76041.38464840995

Compiler

Compiled 16 to 13 computations (18.8% saved)

regimes72.0ms (0.8%)

Counts

23 → 2

Calls

Call 1

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

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

Calls

1 calls:

66.0ms

Results

Error	Segments	Branch
0.6b	2	`x`

Compiler

Compiled 165 to 120 computations (27.3% saved)

bsearch25.0ms (0.3%)

Algorithm

1×	binary-search

Steps

Time	Left	Right
25.0ms	0.6722496367662038	76041.38464840995

Compiler

Compiled 16 to 13 computations (18.8% saved)

regimes25.0ms (0.3%)

Counts

20 → 2

Calls

Call 1

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

Calls

1 calls:

20.0ms

Results

Error	Segments	Branch
0.7b	2	`x`

Compiler

Compiled 129 to 93 computations (27.9% saved)

bsearch23.0ms (0.2%)

Algorithm

1×	binary-search

Steps

Time	Left	Right
23.0ms	0.6722496367662038	76041.38464840995

Compiler

Compiled 16 to 13 computations (18.8% saved)

regimes66.0ms (0.7%)

Counts

14 → 2

Calls

Call 1

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

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

Calls

1 calls:

63.0ms

Results

Error	Segments	Branch
1.0b	2	`x`

Compiler

Compiled 73 to 51 computations (30.1% saved)

bsearch21.0ms (0.2%)

Algorithm

1×	binary-search

Steps

Time	Left	Right
21.0ms	0.6722496367662038	76041.38464840995

Compiler

Compiled 16 to 13 computations (18.8% saved)

regimes12.0ms (0.1%)

Counts

7 → 2

Calls

Call 1

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

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

Calls

1 calls:

10.0ms

Results

Error	Segments	Branch
2.4b	2	`x`

Compiler

Compiled 29 to 22 computations (24.1% saved)

bsearch21.0ms (0.2%)

Algorithm

1×	binary-search

Steps

Time	Left	Right
21.0ms	0.11024660055317465	0.6722496367662038

Compiler

Compiled 16 to 13 computations (18.8% saved)

regimes6.0ms (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:

5.0ms

Results

Error	Segments	Branch
32.1b	1	`x`

Compiler

Compiled 14 to 10 computations (28.6% saved)

regimes4.0ms (0%)

Accuracy

Total -3.6b remaining (-6.1%)

Threshold costs -3.6b (-6.1%)

Counts

2 → 1

Calls

Call 1

Inputs
-1
(/.f64 1 x)

Outputs
(/.f64 1 x)

Calls

1 calls:

3.0ms

Results

Error	Segments	Branch
59.2b	1	`x`

Compiler

Compiled 7 to 5 computations (28.6% saved)

simplify14.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

15×	`+-commutative_binary64`
9×	`*-commutative_binary64`
9×	`sub-neg_binary64`
5×	`neg-sub0_binary64`
5×	`neg-mul-1_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	51	236
1	71	236
2	85	236
3	100	236
4	107	236
5	110	236
6	111	236

Stop Event

1×	fuel
1×	saturated

Calls

Call 1

Inputs
(/.f64 (/.f64 (/.f64 1 x) (+.f64 (pow.f64 x -1/2) (pow.f64 (+.f64 1 x) -1/2))) (+.f64 1 x))
(if (<=.f64 (-.f64 (/.f64 1 (sqrt.f64 x)) (/.f64 1 (sqrt.f64 (+.f64 x 1)))) 3022314549036573/75557863725914323419136) (.f64 (/.f64 (pow.f64 x -1/2) x) (+.f64 1/2 (+.f64 (/.f64 5/16 (.f64 x x)) (/.f64 -3/8 x)))) (-.f64 (pow.f64 x -1/2) (pow.f64 (+.f64 1 x) -1/2)))
(if (<=.f64 x 12400817003070367744/18446744073709551616) (-.f64 (pow.f64 x -1/2) (+.f64 (.f64 -1/2 x) 1)) (.f64 (/.f64 (pow.f64 x -1/2) x) (+.f64 1/2 (+.f64 (/.f64 5/16 (*.f64 x x)) (/.f64 -3/8 x)))))
(if (<=.f64 x 12400817003070367744/18446744073709551616) (-.f64 (pow.f64 x -1/2) (+.f64 (.f64 -1/2 x) 1)) (.f64 (/.f64 (pow.f64 x -1/2) x) (+.f64 1/2 (/.f64 -3/8 x))))
(if (<=.f64 x 12400817003070367744/18446744073709551616) (-.f64 (pow.f64 x -1/2) (+.f64 (.f64 -1/2 x) 1)) (.f64 (pow.f64 x -3/2) 1/2))
(if (<=.f64 x 12400817003070367744/18446744073709551616) (-.f64 (pow.f64 x -1/2) 1) (*.f64 (pow.f64 x -3/2) 1/2))
(if (<=.f64 x 2033690825400898560/18446744073709551616) (pow.f64 x -1/2) (*.f64 (pow.f64 x -3/2) 1/2))
(pow.f64 x -1/2)
(/.f64 1 x)
-1

Outputs
(/.f64 (/.f64 (/.f64 1 x) (+.f64 (pow.f64 x -1/2) (pow.f64 (+.f64 1 x) -1/2))) (+.f64 1 x))
(if (<=.f64 (-.f64 (/.f64 1 (sqrt.f64 x)) (/.f64 1 (sqrt.f64 (+.f64 x 1)))) 3022314549036573/75557863725914323419136) (.f64 (/.f64 (pow.f64 x -1/2) x) (+.f64 1/2 (+.f64 (/.f64 5/16 (.f64 x x)) (/.f64 -3/8 x)))) (-.f64 (pow.f64 x -1/2) (pow.f64 (+.f64 1 x) -1/2)))
(if (<=.f64 (-.f64 (/.f64 1 (sqrt.f64 x)) (/.f64 1 (sqrt.f64 (+.f64 1 x)))) 3022314549036573/75557863725914323419136) (.f64 (/.f64 (pow.f64 x -1/2) x) (+.f64 1/2 (+.f64 (/.f64 5/16 (.f64 x x)) (/.f64 -3/8 x)))) (-.f64 (pow.f64 x -1/2) (pow.f64 (+.f64 1 x) -1/2)))
(if (<=.f64 x 12400817003070367744/18446744073709551616) (-.f64 (pow.f64 x -1/2) (+.f64 (.f64 -1/2 x) 1)) (.f64 (/.f64 (pow.f64 x -1/2) x) (+.f64 1/2 (+.f64 (/.f64 5/16 (*.f64 x x)) (/.f64 -3/8 x)))))
(if (<=.f64 x 6055086427280453/9007199254740992) (-.f64 (pow.f64 x -1/2) (+.f64 1 (.f64 x -1/2))) (.f64 (/.f64 (pow.f64 x -1/2) x) (+.f64 1/2 (+.f64 (/.f64 5/16 (*.f64 x x)) (/.f64 -3/8 x)))))
(if (<=.f64 x 6055086427280453/9007199254740992) (+.f64 (pow.f64 x -1/2) (+.f64 -1 (.f64 x 1/2))) (.f64 (/.f64 (pow.f64 x -1/2) x) (+.f64 1/2 (+.f64 (/.f64 5/16 (*.f64 x x)) (/.f64 -3/8 x)))))
(if (<=.f64 x 12400817003070367744/18446744073709551616) (-.f64 (pow.f64 x -1/2) (+.f64 (.f64 -1/2 x) 1)) (.f64 (/.f64 (pow.f64 x -1/2) x) (+.f64 1/2 (/.f64 -3/8 x))))
(if (<=.f64 x 6055086427280453/9007199254740992) (-.f64 (pow.f64 x -1/2) (+.f64 1 (.f64 x -1/2))) (.f64 (/.f64 (pow.f64 x -1/2) x) (+.f64 1/2 (/.f64 -3/8 x))))
(if (<=.f64 x 6055086427280453/9007199254740992) (+.f64 (pow.f64 x -1/2) (+.f64 -1 (.f64 x 1/2))) (.f64 (/.f64 (pow.f64 x -1/2) x) (+.f64 1/2 (/.f64 -3/8 x))))
(if (<=.f64 x 12400817003070367744/18446744073709551616) (-.f64 (pow.f64 x -1/2) (+.f64 (.f64 -1/2 x) 1)) (.f64 (pow.f64 x -3/2) 1/2))
(if (<=.f64 x 6055086427280453/9007199254740992) (-.f64 (pow.f64 x -1/2) (+.f64 1 (.f64 x -1/2))) (.f64 1/2 (pow.f64 x -3/2)))
(if (<=.f64 x 6055086427280453/9007199254740992) (+.f64 (pow.f64 x -1/2) (+.f64 -1 (.f64 x 1/2))) (.f64 1/2 (pow.f64 x -3/2)))
(if (<=.f64 x 12400817003070367744/18446744073709551616) (-.f64 (pow.f64 x -1/2) 1) (*.f64 (pow.f64 x -3/2) 1/2))
(if (<=.f64 x 6055086427280453/9007199254740992) (+.f64 (pow.f64 x -1/2) -1) (*.f64 1/2 (pow.f64 x -3/2)))
(if (<=.f64 x 2033690825400898560/18446744073709551616) (pow.f64 x -1/2) (*.f64 (pow.f64 x -3/2) 1/2))
(if (<=.f64 x 1986026196680565/18014398509481984) (pow.f64 x -1/2) (*.f64 1/2 (pow.f64 x -3/2)))
(pow.f64 x -1/2)
(/.f64 1 x)
-1

Compiler

Compiled 172 to 133 computations (22.7% saved)

soundness126.0ms (1.3%)

Algorithm

1×	egg-herbie

Rules

719×	`fma-def_binary64`
583×	`times-frac_binary64`
549×	`distribute-rgt-out_binary64`
375×	`unswap-sqr_binary64`
343×	`associate-/l*_binary64`

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	70	433
1	184	421
2	464	333
3	1331	281
4	5992	260

Stop Event

1×	node limit

Compiler

Compiled 1006 to 854 computations (15.1% saved)

end129.0ms (1.4%)

Compiler: Compiled 163 to 123 computations (24.5% 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