Details

analyze1.0ms (0%)

Algorithm

1×

Search

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

Compiler

Compiled 13 to 11 computations (15.4% saved)

sample2.1s (20%)

Results

1.1s	2240×	body	1024	valid
748.0ms	4982×	body	256	valid
262.0ms	1034×	body	512	valid

Bogosity

preprocess24.0ms (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)

simplify17.0ms (0.2%)

Algorithm

1×	egg-herbie

Rules

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

Iterations

Useful iterations: 0 (0.0ms)

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

Stop Event

1×

saturated

Counts

1 → 2

Calls

Call 1

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

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

eval1.0ms (0%)

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

prune2.0ms (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

24.3b

Counts

3 → 1

Alt Table

Click to see full alt table

Status	Error	Program
▶	24.3b	(-.f64 (/.f64 1 (sqrt.f64 x)) (/.f64 1 (sqrt.f64 (+.f64 x 1))))

Compiler

Compiled 12 to 10 computations (16.7% saved)

localize33.0ms (0.3%)

Local error

Found 8 expressions with local error:

New	Error	Program
	3.6b	(-.f64 (/.f64 1 (sqrt.f64 x)) (/.f64 1 (sqrt.f64 (+.f64 x 1))))
	0.3b	(/.f64 1 (sqrt.f64 x))
	0.2b	(/.f64 1 (sqrt.f64 (+.f64 x 1)))
	0.0b	(sqrt.f64 (+.f64 x 1))
✓	0.0b	(sqrt.f64 (+.f64 x 1))
✓	0.2b	(/.f64 1 (sqrt.f64 (+.f64 x 1)))
✓	0.3b	(/.f64 1 (sqrt.f64 x))
✓	3.6b	(-.f64 (/.f64 1 (sqrt.f64 x)) (/.f64 1 (sqrt.f64 (+.f64 x 1))))

Compiler

Compiled 33 to 23 computations (30.3% saved)

series20.0ms (0.2%)

Counts

4 → 8

Calls

12 calls:

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

rewrite117.0ms (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))))))

simplify178.0ms (1.7%)

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)

eval118.0ms (1.1%)

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

prune145.0ms (1.4%)

Pruning

31 alts after pruning (30 fresh and 1 done)

	Pruned	Kept	Total
New	212	30	242
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	212	31	243

Error

23.6b

Counts

243 → 31

Alt Table

Click to see full alt table

Status	Error	Program
	28.0b	(-.f64 (/.f64 1 (sqrt.f64 x)) (sqrt.f64 (/.f64 1 (+.f64 1 x))))
	32.9b	(+.f64 (fma.f64 (cbrt.f64 (/.f64 1 x)) (pow.f64 x -1/6) (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))))))
	27.9b	(-.f64 (sqrt.f64 (/.f64 1 x)) (/.f64 1 (sqrt.f64 (+.f64 x 1))))
	34.6b	(fma.f64 (pow.f64 x -1/4) (pow.f64 x -1/4) (/.f64 -1 (sqrt.f64 (+.f64 1 x))))
	34.3b	(/.f64 1 (/.f64 (+.f64 (/.f64 1 x) (+.f64 (/.f64 1 (+.f64 1 x)) (pow.f64 (*.f64 x (+.f64 1 x)) -1/2))) (-.f64 (pow.f64 x -3/2) (pow.f64 (+.f64 1 x) -3/2))))
	34.2b	(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))
	35.7b	(fma.f64 (cbrt.f64 (/.f64 1 x)) (pow.f64 x -1/6) (/.f64 -1 (sqrt.f64 (+.f64 1 x))))
▶	48.9b	(-.f64 (pow.f64 (*.f64 x x) -1/4) (/.f64 1 (sqrt.f64 (+.f64 x 1))))
	35.5b	(-.f64 (/.f64 1 (sqrt.f64 x)) (+.f64 (*.f64 -1/2 x) 1))
	34.6b	(-.f64 (/.f64 1 (sqrt.f64 x)) (exp.f64 (*.f64 -1/2 (log1p.f64 x))))
▶	35.5b	(pow.f64 (pow.f64 (-.f64 (pow.f64 x -1/2) (pow.f64 (+.f64 1 x) -1/2)) 3) 1/3)
	29.8b	(-.f64 (/.f64 1 (sqrt.f64 x)) (pow.f64 (pow.f64 (+.f64 1 x) 1/4) -2))
	34.7b	(-.f64 (/.f64 1 (sqrt.f64 x)) (/.f64 1 (+.f64 (*.f64 1/2 x) 1)))
▶	35.9b	(-.f64 (/.f64 1 (sqrt.f64 x)) 1)
	24.4b	(*.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))))
	29.9b	(-.f64 (pow.f64 (pow.f64 x 1/4) -2) (/.f64 1 (sqrt.f64 (+.f64 x 1))))
	27.6b	(+.f64 (pow.f64 x -1/2) (/.f64 -1 (sqrt.f64 (+.f64 1 x))))
	30.7b	(-.f64 (/.f64 1 (sqrt.f64 x)) (pow.f64 (cbrt.f64 (+.f64 1 x)) -3/2))
	29.7b	(-.f64 (pow.f64 (pow.f64 x -1/4) 2) (/.f64 1 (sqrt.f64 (+.f64 x 1))))
▶	34.3b	(-.f64 (/.f64 1 (sqrt.f64 x)) (cbrt.f64 (pow.f64 (+.f64 1 x) -3/2)))
	24.3b	(/.f64 (-.f64 (/.f64 1 x) (/.f64 1 (+.f64 1 x))) (+.f64 (pow.f64 x -1/2) (pow.f64 (+.f64 1 x) -1/2)))
	27.7b	(-.f64 (/.f64 1 (sqrt.f64 x)) (pow.f64 (+.f64 1 x) -1/2))
	44.6b	(-.f64 (cbrt.f64 (pow.f64 x -3/2)) (/.f64 1 (sqrt.f64 (+.f64 x 1))))
	31.4b	(/.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)))))
	34.2b	(/.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))))
	34.4b	(/.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)))))))
	31.1b	(-.f64 (pow.f64 (cbrt.f64 x) -3/2) (/.f64 1 (sqrt.f64 (+.f64 x 1))))
	24.4b	(/.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)))))
	34.4b	(fma.f64 (pow.f64 (+.f64 1 x) -1/4) (neg.f64 (pow.f64 (+.f64 1 x) -1/4)) (pow.f64 x -1/2))
✓	24.3b	(-.f64 (/.f64 1 (sqrt.f64 x)) (/.f64 1 (sqrt.f64 (+.f64 x 1))))
▶	24.3b	(/.f64 (-.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)) (sqrt.f64 (*.f64 x (+.f64 1 x))))

Compiler

Compiled 1040 to 854 computations (17.9% saved)

localize20.0ms (0.2%)

Local error

Found 8 expressions with local error:

New	Error	Program
	3.6b	(-.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x))
	0.1b	(/.f64 (-.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)) (sqrt.f64 (*.f64 x (+.f64 1 x))))
	0.0b	(*.f64 x (+.f64 1 x))
	0.0b	(sqrt.f64 (+.f64 1 x))
✓	0.0b	(*.f64 x (+.f64 1 x))
✓	0.1b	(/.f64 (-.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)) (sqrt.f64 (*.f64 x (+.f64 1 x))))
✓	3.6b	(-.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x))
✓	15.4b	(sqrt.f64 (*.f64 x (+.f64 1 x)))

Compiler

Compiled 44 to 28 computations (36.4% saved)

series17.0ms (0.2%)

Counts

4 → 21

Calls

12 calls:

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

rewrite105.0ms (1%)

Algorithm

1×	batch-egg-rewrite

Rules

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

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	10	49
1	224	43
2	3303	40

Stop Event

1×	node limit

Counts

4 → 248

Calls

Call 1

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

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

simplify45.0ms (0.4%)

Algorithm

1×	egg-herbie

Rules

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

Iterations

Useful iterations: 1 (0.0ms)

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

Stop Event

1×	node limit

Counts

269 → 263

Calls

Call 1

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

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

localize8.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.3b	(/.f64 1 (sqrt.f64 x))
	0.0b	(-.f64 (/.f64 1 (sqrt.f64 x)) 1)
✓	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 (0.4%)

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

localize24.0ms (0.2%)

Local error

Found 8 expressions with local error:

New	Error	Program
	29.7b	(pow.f64 (*.f64 x x) -1/4)
	12.2b	(-.f64 (pow.f64 (*.f64 x x) -1/4) (/.f64 1 (sqrt.f64 (+.f64 x 1))))
	0.2b	(/.f64 1 (sqrt.f64 (+.f64 x 1)))
	0.0b	(sqrt.f64 (+.f64 x 1))
	0.0b	(sqrt.f64 (+.f64 x 1))
	0.2b	(/.f64 1 (sqrt.f64 (+.f64 x 1)))
✓	12.2b	(-.f64 (pow.f64 (*.f64 x x) -1/4) (/.f64 1 (sqrt.f64 (+.f64 x 1))))
✓	29.7b	(pow.f64 (*.f64 x x) -1/4)

Compiler

Compiled 37 to 24 computations (35.1% saved)

series51.0ms (0.5%)

Counts

2 → 18

Calls

6 calls:

Time	Variable		Point	Expression
38.0ms	x	@	0	(pow.f64 (*.f64 x x) -1/4)
11.0ms	x	@	inf	(pow.f64 (*.f64 x x) -1/4)
1.0ms	x	@	inf	(-.f64 (pow.f64 (*.f64 x x) -1/4) (/.f64 1 (sqrt.f64 (+.f64 x 1))))
1.0ms	x	@	-inf	(-.f64 (pow.f64 (*.f64 x x) -1/4) (/.f64 1 (sqrt.f64 (+.f64 x 1))))
0.0ms	x	@	-inf	(pow.f64 (*.f64 x x) -1/4)

rewrite124.0ms (1.2%)

Algorithm

1×	batch-egg-rewrite

Rules

545×	`prod-diff_binary64`
451×	`log-prod_binary64`
326×	`fma-def_binary64`
295×	`pow-prod-down_binary64`
271×	`pow2_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	10	25
1	228	17
2	3013	17

Stop Event

1×	node limit

Counts

2 → 129

Calls

Call 1

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

Outputs

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

((#(struct:change #<rule egg-rr> (2) ((x +.f64 (pow.f64 x -1/2) (/.f64 -1 (sqrt.f64 (+.f64 x 1))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (pow.f64 x -1/2) (*.f64 (/.f64 -1 (sqrt.f64 (+.f64 x 1))) 1))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (-.f64 (pow.f64 x -1/2) (pow.f64 (+.f64 x 1) -1/2)) (fma.f64 (/.f64 -1 (sqrt.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) -1/6)) (cbrt.f64 (/.f64 1 (+.f64 x 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)) (+.f64 (/.f64 -1 (sqrt.f64 (+.f64 x 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 -1 (pow.f64 (+.f64 x 1) -1/2) (pow.f64 (+.f64 x 1) -1/2)))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (-.f64 (pow.f64 x 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-1 (sqrt.f64 (+.f64 x 1)))) -1 (*.f64 (/.f64 -1 (sqrt.f64 (+.f64 x 1))) -1)))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (fma.f64 (cbrt.f64 (pow.f64 x -1)) (pow.f64 x -1/6) (neg.f64 (*.f64 (/.f64 -1 (sqrt.f64 (+.f64 x 1))) -1))) (fma.f64 (neg.f64 (/.f64 -1 (sqrt.f64 (+.f64 x 1)))) -1 (*.f64 (/.f64 -1 (sqrt.f64 (+.f64 x 1))) -1)))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (fma.f64 (pow.f64 x -1/4) (pow.f64 x -1/4) (neg.f64 (*.f64 (/.f64 -1 (sqrt.f64 (+.f64 x 1))) -1))) (fma.f64 (neg.f64 (/.f64 -1 (sqrt.f64 (+.f64 x 1)))) -1 (*.f64 (/.f64 -1 (sqrt.f64 (+.f64 x 1))) -1)))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (fma.f64 (pow.f64 1 -1/4) (pow.f64 x -1/2) (neg.f64 (*.f64 (/.f64 -1 (sqrt.f64 (+.f64 x 1))) -1))) (fma.f64 (neg.f64 (/.f64 -1 (sqrt.f64 (+.f64 x 1)))) -1 (*.f64 (/.f64 -1 (sqrt.f64 (+.f64 x 1))) -1)))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (fma.f64 (pow.f64 (cbrt.f64 (pow.f64 x 4)) -1/4) (pow.f64 x -1/6) (neg.f64 (*.f64 (/.f64 -1 (sqrt.f64 (+.f64 x 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(cbrt.f64 (+.f64 x 1))))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (fma.f64 (pow.f64 (cbrt.f64 (pow.f64 x 4)) -1/4) (pow.f64 x -1/6) (neg.f64 (*.f64 (pow.f64 (+.f64 x 1) -1/6) (/.f64 1 (cbrt.f64 (+.f64 x 1)))))) (fma.f64 (neg.f64 (pow.f64 (+.f64 x 1) -1/6)) (/.f64 1 (cbrt.f64 (+.f64 x 1))) (*.f64 (pow.f64 (+.f64 x 1) -1/6) (/.f64 1 (cbrt.f64 (+.f64 x 1))))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (log.f64 (pow.f64 (cbrt.f64 (exp.f64 (-.f64 (pow.f64 x -1/2) (pow.f64 (+.f64 x 1) -1/2)))) 2)) (log.f64 (cbrt.f64 (exp.f64 (-.f64 (pow.f64 x -1/2) (pow.f64 (+.f64 x 1) -1/2))))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (log.f64 (sqrt.f64 (exp.f64 (-.f64 (pow.f64 x -1/2) (pow.f64 (+.f64 x 1) -1/2))))) (log.f64 (sqrt.f64 (exp.f64 (-.f64 (pow.f64 x -1/2) (pow.f64 (+.f64 x 1) -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 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simplify47.0ms (0.4%)

Algorithm

1×	egg-herbie

Rules

940×	`fma-def_binary64`
914×	`cancel-sign-sub-inv_binary64`
602×	`unswap-sqr_binary64`
580×	`distribute-rgt-neg-in_binary64`
564×	`associate-l_binary64`

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	30	174
1	75	172
2	181	170
3	499	164
4	1435	161
5	4417	161

Stop Event

1×	node limit

Counts

147 → 140

Calls

Call 1

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

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

localize24.0ms (0.2%)

Local error

Found 8 expressions with local error:

New	Error	Program
	11.0b	(-.f64 (/.f64 1 (sqrt.f64 x)) (cbrt.f64 (pow.f64 (+.f64 1 x) -3/2)))
	10.1b	(cbrt.f64 (pow.f64 (+.f64 1 x) -3/2))
	0.3b	(/.f64 1 (sqrt.f64 x))
	0.0b	(pow.f64 (+.f64 1 x) -3/2)
✓	0.0b	(pow.f64 (+.f64 1 x) -3/2)
	0.3b	(/.f64 1 (sqrt.f64 x))
✓	10.1b	(cbrt.f64 (pow.f64 (+.f64 1 x) -3/2))
✓	11.0b	(-.f64 (/.f64 1 (sqrt.f64 x)) (cbrt.f64 (pow.f64 (+.f64 1 x) -3/2)))

Compiler

Compiled 35 to 25 computations (28.6% saved)

series5.0ms (0%)

Counts

3 → 16

Calls

9 calls:

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

rewrite188.0ms (1.8%)

Algorithm

1×	batch-egg-rewrite

Rules

615×	`prod-diff_binary64`
442×	`log-prod_binary64`
311×	`fma-def_binary64`
288×	`pow-prod-down_binary64`
267×	`pow2_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	10	33
1	224	27
2	2900	27

Stop Event

1×	node limit

Counts

3 → 158

Calls

Call 1

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

Outputs

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

simplify67.0ms (0.6%)

Algorithm

1×	egg-herbie

Rules

661×	`unswap-sqr_binary64`
652×	`fma-def_binary64`
326×	`distribute-rgt-out_binary64`
309×	`times-frac_binary64`
235×	`associate-/l*_binary64`

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	69	413
1	177	391
2	441	325
3	1264	262
4	4460	238
5	6519	238

Stop Event

1×	node limit

Counts

174 → 186

Calls

Call 1

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

Outputs
1
(+.f64 (*.f64 -1/2 x) 1)
(fma.f64 -1/2 x 1)
(+.f64 (.f64 -1/2 x) (+.f64 1 (.f64 3/8 (pow.f64 x 2))))
(+.f64 (fma.f64 -1/2 x 1) (.f64 3/8 (.f64 x x)))
(fma.f64 -1/2 x (fma.f64 3/8 (*.f64 x x) 1))
(fma.f64 -1/2 x (fma.f64 x (*.f64 x 3/8) 1))
(fma.f64 x (fma.f64 x 3/8 -1/2) 1)
(+.f64 (.f64 -1/2 x) (+.f64 1 (+.f64 (.f64 3/8 (pow.f64 x 2)) (*.f64 -5/16 (pow.f64 x 3)))))
(+.f64 (fma.f64 -1/2 x 1) (fma.f64 3/8 (.f64 x x) (.f64 -5/16 (pow.f64 x 3))))
(+.f64 (fma.f64 -1/2 x 1) (fma.f64 -5/16 (pow.f64 x 3) (.f64 (.f64 3/8 x) x)))
(fma.f64 -1/2 x (fma.f64 x (*.f64 x 3/8) (fma.f64 -5/16 (pow.f64 x 3) 1)))
(fma.f64 x (*.f64 x (fma.f64 x -5/16 3/8)) (fma.f64 -1/2 x 1))
(fma.f64 x (fma.f64 x 3/8 -1/2) (fma.f64 -5/16 (pow.f64 x 3) 1))
1
(+.f64 1 (*.f64 -3/2 x))
(+.f64 1 (*.f64 x -3/2))
(fma.f64 x -3/2 1)
(+.f64 (.f64 15/8 (pow.f64 x 2)) (+.f64 1 (.f64 -3/2 x)))
(fma.f64 15/8 (.f64 x x) (+.f64 1 (.f64 x -3/2)))
(fma.f64 (*.f64 x x) 15/8 (fma.f64 x -3/2 1))
(fma.f64 x -3/2 (fma.f64 x (*.f64 x 15/8) 1))
(fma.f64 x (fma.f64 x 15/8 -3/2) 1)
(+.f64 (.f64 15/8 (pow.f64 x 2)) (+.f64 1 (+.f64 (.f64 -3/2 x) (*.f64 -35/16 (pow.f64 x 3)))))
(fma.f64 15/8 (.f64 x x) (+.f64 1 (fma.f64 -3/2 x (.f64 (pow.f64 x 3) -35/16))))
(+.f64 (fma.f64 (.f64 x x) 15/8 (fma.f64 x -3/2 1)) (.f64 (pow.f64 x 3) -35/16))
(fma.f64 (*.f64 x x) 15/8 (fma.f64 (pow.f64 x 3) -35/16 (fma.f64 x -3/2 1)))
(fma.f64 x (fma.f64 x 15/8 -3/2) (fma.f64 (pow.f64 x 3) -35/16 1))
(sqrt.f64 (/.f64 1 (pow.f64 x 3)))
(+.f64 (*.f64 -3/2 (sqrt.f64 (/.f64 1 (pow.f64 x 5)))) (sqrt.f64 (/.f64 1 (pow.f64 x 3))))
(fma.f64 -3/2 (sqrt.f64 (/.f64 1 (pow.f64 x 5))) (sqrt.f64 (/.f64 1 (pow.f64 x 3))))
(+.f64 (.f64 -3/2 (sqrt.f64 (/.f64 1 (pow.f64 x 5)))) (+.f64 (.f64 15/8 (sqrt.f64 (/.f64 1 (pow.f64 x 7)))) (sqrt.f64 (/.f64 1 (pow.f64 x 3)))))
(fma.f64 -3/2 (sqrt.f64 (/.f64 1 (pow.f64 x 5))) (fma.f64 15/8 (sqrt.f64 (/.f64 1 (pow.f64 x 7))) (sqrt.f64 (/.f64 1 (pow.f64 x 3)))))
(+.f64 (.f64 -35/16 (sqrt.f64 (/.f64 1 (pow.f64 x 9)))) (+.f64 (.f64 -3/2 (sqrt.f64 (/.f64 1 (pow.f64 x 5)))) (+.f64 (*.f64 15/8 (sqrt.f64 (/.f64 1 (pow.f64 x 7)))) (sqrt.f64 (/.f64 1 (pow.f64 x 3))))))
(fma.f64 -35/16 (sqrt.f64 (/.f64 1 (pow.f64 x 9))) (fma.f64 -3/2 (sqrt.f64 (/.f64 1 (pow.f64 x 5))) (fma.f64 15/8 (sqrt.f64 (/.f64 1 (pow.f64 x 7))) (sqrt.f64 (/.f64 1 (pow.f64 x 3))))))
(fma.f64 -3/2 (sqrt.f64 (/.f64 1 (pow.f64 x 5))) (fma.f64 -35/16 (sqrt.f64 (/.f64 1 (pow.f64 x 9))) (fma.f64 15/8 (sqrt.f64 (/.f64 1 (pow.f64 x 7))) (sqrt.f64 (/.f64 1 (pow.f64 x 3))))))
(fma.f64 -3/2 (sqrt.f64 (/.f64 1 (pow.f64 x 5))) (fma.f64 15/8 (sqrt.f64 (/.f64 1 (pow.f64 x 7))) (fma.f64 -35/16 (sqrt.f64 (/.f64 1 (pow.f64 x 9))) (sqrt.f64 (/.f64 1 (pow.f64 x 3))))))
(exp.f64 (.f64 -3/2 (+.f64 (.f64 -1 (log.f64 (/.f64 -1 x))) (log.f64 -1))))
(pow.f64 (exp.f64 -3/2) (fma.f64 -1 (log.f64 (/.f64 -1 x)) (log.f64 -1)))
(pow.f64 (exp.f64 -3/2) (-.f64 (log.f64 -1) (log.f64 (/.f64 -1 x))))
(*.f64 (pow.f64 (/.f64 -1 x) 3/2) (pow.f64 -1 -3/2))
(pow.f64 (exp.f64 -3/2) (log.f64 x))
(pow.f64 x -3/2)
(+.f64 (exp.f64 (.f64 -3/2 (+.f64 (.f64 -1 (log.f64 (/.f64 -1 x))) (log.f64 -1)))) (.f64 -3/2 (/.f64 (exp.f64 (.f64 -3/2 (+.f64 (*.f64 -1 (log.f64 (/.f64 -1 x))) (log.f64 -1)))) x)))
(+.f64 (pow.f64 (exp.f64 -3/2) (fma.f64 -1 (log.f64 (/.f64 -1 x)) (log.f64 -1))) (*.f64 -3/2 (/.f64 (pow.f64 (exp.f64 -3/2) (fma.f64 -1 (log.f64 (/.f64 -1 x)) (log.f64 -1))) x)))
(fma.f64 -3/2 (/.f64 (pow.f64 (exp.f64 -3/2) (-.f64 (log.f64 -1) (log.f64 (/.f64 -1 x)))) x) (pow.f64 (exp.f64 -3/2) (-.f64 (log.f64 -1) (log.f64 (/.f64 -1 x)))))
(fma.f64 -3/2 (/.f64 (.f64 (pow.f64 (/.f64 -1 x) 3/2) (pow.f64 -1 -3/2)) x) (.f64 (pow.f64 (/.f64 -1 x) 3/2) (pow.f64 -1 -3/2)))
(*.f64 (+.f64 (/.f64 -3/2 x) 1) (pow.f64 (exp.f64 -3/2) (log.f64 x)))
(*.f64 (+.f64 1 (/.f64 -3/2 x)) (pow.f64 x -3/2))
(+.f64 (.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 (exp.f64 (.f64 -3/2 (+.f64 (.f64 -1 (log.f64 (/.f64 -1 x))) (log.f64 -1)))) (.f64 -3/2 (/.f64 (exp.f64 (.f64 -3/2 (+.f64 (.f64 -1 (log.f64 (/.f64 -1 x))) (log.f64 -1)))) x))))
(fma.f64 15/8 (/.f64 (pow.f64 (exp.f64 -3/2) (fma.f64 -1 (log.f64 (/.f64 -1 x)) (log.f64 -1))) (.f64 x x)) (+.f64 (pow.f64 (exp.f64 -3/2) (fma.f64 -1 (log.f64 (/.f64 -1 x)) (log.f64 -1))) (.f64 -3/2 (/.f64 (pow.f64 (exp.f64 -3/2) (fma.f64 -1 (log.f64 (/.f64 -1 x)) (log.f64 -1))) x))))
(fma.f64 15/8 (/.f64 (pow.f64 (exp.f64 -3/2) (-.f64 (log.f64 -1) (log.f64 (/.f64 -1 x)))) (*.f64 x x)) (fma.f64 -3/2 (/.f64 (pow.f64 (exp.f64 -3/2) (-.f64 (log.f64 -1) (log.f64 (/.f64 -1 x)))) x) (pow.f64 (exp.f64 -3/2) (-.f64 (log.f64 -1) (log.f64 (/.f64 -1 x))))))
(fma.f64 (pow.f64 (/.f64 -1 x) 3/2) (pow.f64 -1 -3/2) (.f64 (/.f64 (.f64 (pow.f64 (/.f64 -1 x) 3/2) (pow.f64 -1 -3/2)) x) (+.f64 (/.f64 15/8 x) -3/2)))
(fma.f64 (/.f64 (pow.f64 (exp.f64 -3/2) (log.f64 x)) x) (+.f64 -3/2 (/.f64 15/8 x)) (pow.f64 (exp.f64 -3/2) (log.f64 x)))
(fma.f64 (/.f64 (pow.f64 x -3/2) x) (+.f64 -3/2 (/.f64 15/8 x)) (pow.f64 x -3/2))
(fma.f64 (/.f64 1 (pow.f64 x 5/2)) (+.f64 -3/2 (/.f64 15/8 x)) (pow.f64 x -3/2))
(+.f64 (.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 (exp.f64 (.f64 -3/2 (+.f64 (.f64 -1 (log.f64 (/.f64 -1 x))) (log.f64 -1)))) (.f64 -3/2 (/.f64 (exp.f64 (.f64 -3/2 (+.f64 (*.f64 -1 (log.f64 (/.f64 -1 x))) (log.f64 -1)))) x)))))
(fma.f64 15/8 (/.f64 (pow.f64 (exp.f64 -3/2) (fma.f64 -1 (log.f64 (/.f64 -1 x)) (log.f64 -1))) (.f64 x x)) (fma.f64 -35/16 (/.f64 (pow.f64 (exp.f64 -3/2) (fma.f64 -1 (log.f64 (/.f64 -1 x)) (log.f64 -1))) (pow.f64 x 3)) (+.f64 (pow.f64 (exp.f64 -3/2) (fma.f64 -1 (log.f64 (/.f64 -1 x)) (log.f64 -1))) (.f64 -3/2 (/.f64 (pow.f64 (exp.f64 -3/2) (fma.f64 -1 (log.f64 (/.f64 -1 x)) (log.f64 -1))) x)))))
(fma.f64 15/8 (/.f64 (pow.f64 (exp.f64 -3/2) (-.f64 (log.f64 -1) (log.f64 (/.f64 -1 x)))) (*.f64 x x)) (fma.f64 -35/16 (/.f64 (pow.f64 (exp.f64 -3/2) (-.f64 (log.f64 -1) (log.f64 (/.f64 -1 x)))) (pow.f64 x 3)) (fma.f64 -3/2 (/.f64 (pow.f64 (exp.f64 -3/2) (-.f64 (log.f64 -1) (log.f64 (/.f64 -1 x)))) x) (pow.f64 (exp.f64 -3/2) (-.f64 (log.f64 -1) (log.f64 (/.f64 -1 x)))))))
(fma.f64 -35/16 (/.f64 (.f64 (pow.f64 (/.f64 -1 x) 3/2) (pow.f64 -1 -3/2)) (pow.f64 x 3)) (fma.f64 (pow.f64 (/.f64 -1 x) 3/2) (pow.f64 -1 -3/2) (.f64 (/.f64 (*.f64 (pow.f64 (/.f64 -1 x) 3/2) (pow.f64 -1 -3/2)) x) (+.f64 (/.f64 15/8 x) -3/2))))
(+.f64 (pow.f64 (exp.f64 -3/2) (log.f64 x)) (.f64 (/.f64 (pow.f64 (exp.f64 -3/2) (log.f64 x)) x) (+.f64 (+.f64 -3/2 (/.f64 15/8 x)) (/.f64 -35/16 (.f64 x x)))))
(+.f64 (pow.f64 x -3/2) (.f64 (/.f64 (pow.f64 x -3/2) x) (+.f64 (/.f64 15/8 x) (+.f64 -3/2 (/.f64 -35/16 (.f64 x x))))))
(+.f64 (pow.f64 x -3/2) (.f64 (/.f64 1 (pow.f64 x 5/2)) (+.f64 (/.f64 15/8 x) (+.f64 -3/2 (/.f64 -35/16 (.f64 x x))))))

localize66.0ms (0.6%)

Local error

Found 6 expressions with local error:

New	Error	Program
	11.3b	(pow.f64 (pow.f64 (-.f64 (pow.f64 x -1/2) (pow.f64 (+.f64 1 x) -1/2)) 3) 1/3)
	3.6b	(-.f64 (pow.f64 x -1/2) (pow.f64 (+.f64 1 x) -1/2))
	0.2b	(pow.f64 (-.f64 (pow.f64 x -1/2) (pow.f64 (+.f64 1 x) -1/2)) 3)
✓	0.2b	(pow.f64 (-.f64 (pow.f64 x -1/2) (pow.f64 (+.f64 1 x) -1/2)) 3)
✓	3.6b	(-.f64 (pow.f64 x -1/2) (pow.f64 (+.f64 1 x) -1/2))
✓	11.3b	(pow.f64 (pow.f64 (-.f64 (pow.f64 x -1/2) (pow.f64 (+.f64 1 x) -1/2)) 3) 1/3)

Compiler

Compiled 50 to 40 computations (20% saved)

series145.0ms (1.4%)

Counts

3 → 36

Calls

9 calls:

Time	Variable		Point	Expression
11.0ms	x	@	inf	(pow.f64 (pow.f64 (-.f64 (pow.f64 x -1/2) (pow.f64 (+.f64 1 x) -1/2)) 3) 1/3)
7.0ms	x	@	-inf	(pow.f64 (pow.f64 (-.f64 (pow.f64 x -1/2) (pow.f64 (+.f64 1 x) -1/2)) 3) 1/3)
5.0ms	x	@	0	(pow.f64 (pow.f64 (-.f64 (pow.f64 x -1/2) (pow.f64 (+.f64 1 x) -1/2)) 3) 1/3)
1.0ms	x	@	-inf	(pow.f64 (-.f64 (pow.f64 x -1/2) (pow.f64 (+.f64 1 x) -1/2)) 3)
1.0ms	x	@	inf	(pow.f64 (-.f64 (pow.f64 x -1/2) (pow.f64 (+.f64 1 x) -1/2)) 3)

rewrite136.0ms (1.3%)

Algorithm

1×	batch-egg-rewrite

Rules

553×	`prod-diff_binary64`
467×	`log-prod_binary64`
319×	`fma-def_binary64`
309×	`pow-prod-down_binary64`
296×	`pow2_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	12	42
1	279	42
2	3116	42

Stop Event

1×	node limit

Counts

3 → 261

Calls

Call 1

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

Outputs

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

simplify118.0ms (1.1%)

Algorithm

1×	egg-herbie

Rules

389×	`fma-def_binary64`
361×	`cancel-sign-sub-inv_binary64`
273×	`associate-*l/_binary64`
263×	`associate-*r/_binary64`
214×	`associate-r_binary64`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	354	3709
1	1144	3277
2	4528	2790

Stop Event

1×	node limit

Counts

297 → 221

Calls

Call 1

Inputs
(-.f64 (pow.f64 x -1/2) 1)
(-.f64 (+.f64 (.f64 1/3 (.f64 (pow.f64 (/.f64 1 (pow.f64 (-.f64 (pow.f64 x -1/2) 1) 2)) 1/3) (.f64 (+.f64 (.f64 1/2 (pow.f64 (-.f64 (pow.f64 x -1/2) 1) 2)) (pow.f64 (-.f64 (pow.f64 x -1/2) 1) 2)) x))) (pow.f64 x -1/2)) 1)
(-.f64 (+.f64 (.f64 1/3 (.f64 (pow.f64 (/.f64 1 (pow.f64 (-.f64 (pow.f64 x -1/2) 1) 2)) 1/3) (.f64 (+.f64 (.f64 1/2 (pow.f64 (-.f64 (pow.f64 x -1/2) 1) 2)) (pow.f64 (-.f64 (pow.f64 x -1/2) 1) 2)) x))) (+.f64 (pow.f64 x -1/2) (.f64 1/3 (/.f64 (.f64 (-.f64 (+.f64 (.f64 1/2 (-.f64 (pow.f64 x -1/2) 1)) (+.f64 (.f64 (-.f64 (pow.f64 x -1/2) 1) (+.f64 1/4 (.f64 -3/4 (-.f64 (pow.f64 x -1/2) 1)))) (.f64 -3/8 (pow.f64 (-.f64 (pow.f64 x -1/2) 1) 2)))) (.f64 1/3 (.f64 (pow.f64 (/.f64 1 (-.f64 (pow.f64 x -1/2) 1)) 1/3) (pow.f64 (+.f64 (*.f64 1/2 (pow.f64 (-.f64 (pow.f64 x -1/2) 1) 2)) (pow.f64 (-.f64 (pow.f64 x -1/2) 1) 2)) 2)))) (pow.f64 x 2)) (pow.f64 (-.f64 (pow.f64 x -1/2) 1) 2))))) 1)
(-.f64 (+.f64 (.f64 1/3 (.f64 (pow.f64 (/.f64 1 (pow.f64 (-.f64 (pow.f64 x -1/2) 1) 2)) 1/3) (.f64 (+.f64 (.f64 1/2 (pow.f64 (-.f64 (pow.f64 x -1/2) 1) 2)) (pow.f64 (-.f64 (pow.f64 x -1/2) 1) 2)) x))) (+.f64 (.f64 1/3 (/.f64 (.f64 (-.f64 (+.f64 (.f64 1/2 (+.f64 1/4 (.f64 -3/4 (-.f64 (pow.f64 x -1/2) 1)))) (+.f64 (.f64 5/16 (pow.f64 (-.f64 (pow.f64 x -1/2) 1) 2)) (+.f64 (.f64 -3/8 (-.f64 (pow.f64 x -1/2) 1)) (.f64 (-.f64 (pow.f64 x -1/2) 1) (-.f64 (.f64 5/8 (-.f64 (pow.f64 x -1/2) 1)) 3/8))))) (+.f64 (.f64 1/3 (.f64 (pow.f64 (/.f64 1 (pow.f64 (-.f64 (pow.f64 x -1/2) 1) 5)) 1/3) (.f64 (-.f64 (+.f64 (.f64 1/2 (-.f64 (pow.f64 x -1/2) 1)) (+.f64 (.f64 (-.f64 (pow.f64 x -1/2) 1) (+.f64 1/4 (.f64 -3/4 (-.f64 (pow.f64 x -1/2) 1)))) (.f64 -3/8 (pow.f64 (-.f64 (pow.f64 x -1/2) 1) 2)))) (.f64 1/3 (.f64 (pow.f64 (/.f64 1 (-.f64 (pow.f64 x -1/2) 1)) 1/3) (pow.f64 (+.f64 (.f64 1/2 (pow.f64 (-.f64 (pow.f64 x -1/2) 1) 2)) (pow.f64 (-.f64 (pow.f64 x -1/2) 1) 2)) 2)))) (+.f64 (.f64 1/2 (pow.f64 (-.f64 (pow.f64 x -1/2) 1) 2)) (pow.f64 (-.f64 (pow.f64 x -1/2) 1) 2))))) (+.f64 (.f64 1/27 (/.f64 (pow.f64 (+.f64 (.f64 1/2 (pow.f64 (-.f64 (pow.f64 x -1/2) 1) 2)) (pow.f64 (-.f64 (pow.f64 x -1/2) 1) 2)) 3) (pow.f64 (-.f64 (pow.f64 x -1/2) 1) 2))) (.f64 1/3 (.f64 (pow.f64 (/.f64 1 (pow.f64 (-.f64 (pow.f64 x -1/2) 1) 5)) 1/3) (.f64 (+.f64 (.f64 1/2 (pow.f64 (-.f64 (pow.f64 x -1/2) 1) 2)) (pow.f64 (-.f64 (pow.f64 x -1/2) 1) 2)) (-.f64 (+.f64 (.f64 1/2 (-.f64 (pow.f64 x -1/2) 1)) (+.f64 (.f64 (-.f64 (pow.f64 x -1/2) 1) (+.f64 1/4 (.f64 -3/4 (-.f64 (pow.f64 x -1/2) 1)))) (.f64 -3/8 (pow.f64 (-.f64 (pow.f64 x -1/2) 1) 2)))) (.f64 1/3 (.f64 (pow.f64 (/.f64 1 (-.f64 (pow.f64 x -1/2) 1)) 1/3) (pow.f64 (+.f64 (.f64 1/2 (pow.f64 (-.f64 (pow.f64 x -1/2) 1) 2)) (pow.f64 (-.f64 (pow.f64 x -1/2) 1) 2)) 2)))))))))) (pow.f64 x 3)) (pow.f64 (-.f64 (pow.f64 x -1/2) 1) 2))) (+.f64 (pow.f64 x -1/2) (.f64 1/3 (/.f64 (.f64 (-.f64 (+.f64 (.f64 1/2 (-.f64 (pow.f64 x -1/2) 1)) (+.f64 (.f64 (-.f64 (pow.f64 x -1/2) 1) (+.f64 1/4 (.f64 -3/4 (-.f64 (pow.f64 x -1/2) 1)))) (.f64 -3/8 (pow.f64 (-.f64 (pow.f64 x -1/2) 1) 2)))) (.f64 1/3 (.f64 (pow.f64 (/.f64 1 (-.f64 (pow.f64 x -1/2) 1)) 1/3) (pow.f64 (+.f64 (*.f64 1/2 (pow.f64 (-.f64 (pow.f64 x -1/2) 1) 2)) (pow.f64 (-.f64 (pow.f64 x -1/2) 1) 2)) 2)))) (pow.f64 x 2)) (pow.f64 (-.f64 (pow.f64 x -1/2) 1) 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 1/3 (.f64 (pow.f64 (/.f64 1 (pow.f64 x 5)) 1/3) (/.f64 (+.f64 (.f64 -3/32 (sqrt.f64 (/.f64 1 (pow.f64 x 3)))) (*.f64 -3/16 (sqrt.f64 (/.f64 1 (pow.f64 x 3))))) (cbrt.f64 1/4)))))
(+.f64 (.f64 4/3 (/.f64 (-.f64 (+.f64 (.f64 29/128 (sqrt.f64 (/.f64 1 (pow.f64 x 3)))) (+.f64 (.f64 5/64 (sqrt.f64 (/.f64 1 (pow.f64 x 3)))) (.f64 9/64 (sqrt.f64 (/.f64 1 (pow.f64 x 3)))))) (.f64 1/6 (.f64 (pow.f64 (.f64 1 x) 1/6) (/.f64 (pow.f64 (+.f64 (.f64 -3/16 (sqrt.f64 (/.f64 1 (pow.f64 x 3)))) (.f64 -3/32 (sqrt.f64 (/.f64 1 (pow.f64 x 3))))) 2) (pow.f64 (cbrt.f64 1/4) 2))))) (pow.f64 x 2))) (+.f64 (.f64 1/2 (sqrt.f64 (/.f64 1 (pow.f64 x 3)))) (.f64 1/3 (.f64 (pow.f64 (/.f64 1 (pow.f64 x 5)) 1/3) (/.f64 (+.f64 (.f64 -3/32 (sqrt.f64 (/.f64 1 (pow.f64 x 3)))) (.f64 -3/16 (sqrt.f64 (/.f64 1 (pow.f64 x 3))))) (cbrt.f64 1/4))))))
(+.f64 (.f64 4/3 (/.f64 (-.f64 (+.f64 (.f64 29/128 (sqrt.f64 (/.f64 1 (pow.f64 x 3)))) (+.f64 (.f64 5/64 (sqrt.f64 (/.f64 1 (pow.f64 x 3)))) (.f64 9/64 (sqrt.f64 (/.f64 1 (pow.f64 x 3)))))) (.f64 1/6 (.f64 (pow.f64 (.f64 1 x) 1/6) (/.f64 (pow.f64 (+.f64 (.f64 -3/16 (sqrt.f64 (/.f64 1 (pow.f64 x 3)))) (.f64 -3/32 (sqrt.f64 (/.f64 1 (pow.f64 x 3))))) 2) (pow.f64 (cbrt.f64 1/4) 2))))) (pow.f64 x 2))) (+.f64 (.f64 1/2 (sqrt.f64 (/.f64 1 (pow.f64 x 3)))) (+.f64 (.f64 1/3 (.f64 (pow.f64 (/.f64 1 (pow.f64 x 5)) 1/3) (/.f64 (+.f64 (.f64 -3/32 (sqrt.f64 (/.f64 1 (pow.f64 x 3)))) (.f64 -3/16 (sqrt.f64 (/.f64 1 (pow.f64 x 3))))) (cbrt.f64 1/4)))) (.f64 4/3 (/.f64 (-.f64 (+.f64 (.f64 -87/512 (sqrt.f64 (/.f64 1 (pow.f64 x 3)))) (+.f64 (.f64 -15/128 (sqrt.f64 (/.f64 1 (pow.f64 x 3)))) (+.f64 (.f64 -35/512 (sqrt.f64 (/.f64 1 (pow.f64 x 3)))) (.f64 -65/256 (sqrt.f64 (/.f64 1 (pow.f64 x 3))))))) (+.f64 (.f64 4/27 (.f64 (pow.f64 (+.f64 (.f64 -3/16 (sqrt.f64 (/.f64 1 (pow.f64 x 3)))) (.f64 -3/32 (sqrt.f64 (/.f64 1 (pow.f64 x 3))))) 3) x)) (.f64 4/3 (.f64 (/.f64 (.f64 (-.f64 (+.f64 (.f64 29/128 (sqrt.f64 (/.f64 1 (pow.f64 x 3)))) (+.f64 (.f64 5/64 (sqrt.f64 (/.f64 1 (pow.f64 x 3)))) (.f64 9/64 (sqrt.f64 (/.f64 1 (pow.f64 x 3)))))) (.f64 1/6 (.f64 (pow.f64 (.f64 1 x) 1/6) (/.f64 (pow.f64 (+.f64 (.f64 -3/32 (sqrt.f64 (/.f64 1 (pow.f64 x 3)))) (.f64 -3/16 (sqrt.f64 (/.f64 1 (pow.f64 x 3))))) 2) (pow.f64 (cbrt.f64 1/4) 2))))) (+.f64 (.f64 -3/16 (sqrt.f64 (/.f64 1 (pow.f64 x 3)))) (.f64 -3/32 (sqrt.f64 (/.f64 1 (pow.f64 x 3)))))) (cbrt.f64 1/4)) (pow.f64 (*.f64 1 (pow.f64 x 5)) 1/6))))) (pow.f64 x 3))))))
(.f64 -1 (/.f64 (.f64 (exp.f64 (.f64 -1/2 (+.f64 (.f64 -1 (log.f64 (/.f64 -1 x))) (log.f64 -1)))) (cbrt.f64 -1/8)) x))
(+.f64 (.f64 -1 (/.f64 (.f64 (exp.f64 (.f64 -1/2 (+.f64 (.f64 -1 (log.f64 (/.f64 -1 x))) (log.f64 -1)))) (cbrt.f64 -1/8)) x)) (.f64 1/3 (.f64 (pow.f64 (/.f64 1 (.f64 (pow.f64 (exp.f64 (.f64 -1/2 (+.f64 (.f64 -1 (log.f64 (/.f64 -1 x))) (log.f64 -1)))) 2) (pow.f64 (cbrt.f64 -1/8) 2))) 1/3) (/.f64 (+.f64 (.f64 -3/16 (pow.f64 (exp.f64 (.f64 -1/2 (+.f64 (.f64 -1 (log.f64 (/.f64 -1 x))) (log.f64 -1)))) 3)) (.f64 -3/32 (pow.f64 (exp.f64 (.f64 -1/2 (+.f64 (*.f64 -1 (log.f64 (/.f64 -1 x))) (log.f64 -1)))) 3))) (pow.f64 x 2)))))
(+.f64 (.f64 -1 (/.f64 (.f64 (exp.f64 (.f64 -1/2 (+.f64 (.f64 -1 (log.f64 (/.f64 -1 x))) (log.f64 -1)))) (cbrt.f64 -1/8)) x)) (+.f64 (.f64 -1/3 (/.f64 (-.f64 (+.f64 (.f64 -1/2 (.f64 (exp.f64 (.f64 -1/2 (+.f64 (.f64 -1 (log.f64 (/.f64 -1 x))) (log.f64 -1)))) (+.f64 (.f64 5/16 (pow.f64 (exp.f64 (.f64 -1/2 (+.f64 (.f64 -1 (log.f64 (/.f64 -1 x))) (log.f64 -1)))) 2)) (.f64 9/64 (pow.f64 (exp.f64 (.f64 -1/2 (+.f64 (.f64 -1 (log.f64 (/.f64 -1 x))) (log.f64 -1)))) 2))))) (+.f64 (.f64 -9/64 (pow.f64 (exp.f64 (.f64 -1/2 (+.f64 (.f64 -1 (log.f64 (/.f64 -1 x))) (log.f64 -1)))) 3)) (.f64 -5/64 (pow.f64 (exp.f64 (.f64 -1/2 (+.f64 (.f64 -1 (log.f64 (/.f64 -1 x))) (log.f64 -1)))) 3)))) (.f64 1/3 (.f64 (pow.f64 (/.f64 1 (.f64 (exp.f64 (.f64 -1/2 (+.f64 (.f64 -1 (log.f64 (/.f64 -1 x))) (log.f64 -1)))) (cbrt.f64 -1/8))) 1/3) (pow.f64 (+.f64 (.f64 -3/16 (pow.f64 (exp.f64 (.f64 -1/2 (+.f64 (.f64 -1 (log.f64 (/.f64 -1 x))) (log.f64 -1)))) 3)) (.f64 -3/32 (pow.f64 (exp.f64 (.f64 -1/2 (+.f64 (.f64 -1 (log.f64 (/.f64 -1 x))) (log.f64 -1)))) 3))) 2)))) (.f64 (pow.f64 (exp.f64 (.f64 -1/2 (+.f64 (.f64 -1 (log.f64 (/.f64 -1 x))) (log.f64 -1)))) 2) (.f64 (pow.f64 x 3) (pow.f64 (cbrt.f64 -1/8) 2))))) (.f64 1/3 (.f64 (pow.f64 (/.f64 1 (.f64 (pow.f64 (exp.f64 (.f64 -1/2 (+.f64 (.f64 -1 (log.f64 (/.f64 -1 x))) (log.f64 -1)))) 2) (pow.f64 (cbrt.f64 -1/8) 2))) 1/3) (/.f64 (+.f64 (.f64 -3/16 (pow.f64 (exp.f64 (.f64 -1/2 (+.f64 (.f64 -1 (log.f64 (/.f64 -1 x))) (log.f64 -1)))) 3)) (.f64 -3/32 (pow.f64 (exp.f64 (.f64 -1/2 (+.f64 (*.f64 -1 (log.f64 (/.f64 -1 x))) (log.f64 -1)))) 3))) (pow.f64 x 2))))))
(+.f64 (.f64 -1 (/.f64 (.f64 (exp.f64 (.f64 -1/2 (+.f64 (.f64 -1 (log.f64 (/.f64 -1 x))) (log.f64 -1)))) (cbrt.f64 -1/8)) x)) (+.f64 (.f64 -1/3 (/.f64 (-.f64 (+.f64 (.f64 -1/2 (.f64 (exp.f64 (.f64 -1/2 (+.f64 (.f64 -1 (log.f64 (/.f64 -1 x))) (log.f64 -1)))) (+.f64 (.f64 5/16 (pow.f64 (exp.f64 (.f64 -1/2 (+.f64 (.f64 -1 (log.f64 (/.f64 -1 x))) (log.f64 -1)))) 2)) (.f64 9/64 (pow.f64 (exp.f64 (.f64 -1/2 (+.f64 (.f64 -1 (log.f64 (/.f64 -1 x))) (log.f64 -1)))) 2))))) (+.f64 (.f64 -9/64 (pow.f64 (exp.f64 (.f64 -1/2 (+.f64 (.f64 -1 (log.f64 (/.f64 -1 x))) (log.f64 -1)))) 3)) (.f64 -5/64 (pow.f64 (exp.f64 (.f64 -1/2 (+.f64 (.f64 -1 (log.f64 (/.f64 -1 x))) (log.f64 -1)))) 3)))) (.f64 1/3 (.f64 (pow.f64 (/.f64 1 (.f64 (exp.f64 (.f64 -1/2 (+.f64 (.f64 -1 (log.f64 (/.f64 -1 x))) (log.f64 -1)))) (cbrt.f64 -1/8))) 1/3) (pow.f64 (+.f64 (.f64 -3/16 (pow.f64 (exp.f64 (.f64 -1/2 (+.f64 (.f64 -1 (log.f64 (/.f64 -1 x))) (log.f64 -1)))) 3)) (.f64 -3/32 (pow.f64 (exp.f64 (.f64 -1/2 (+.f64 (.f64 -1 (log.f64 (/.f64 -1 x))) (log.f64 -1)))) 3))) 2)))) (.f64 (pow.f64 (exp.f64 (.f64 -1/2 (+.f64 (.f64 -1 (log.f64 (/.f64 -1 x))) (log.f64 -1)))) 2) (.f64 (pow.f64 x 3) (pow.f64 (cbrt.f64 -1/8) 2))))) (+.f64 (.f64 1/3 (.f64 (pow.f64 (/.f64 1 (.f64 (pow.f64 (exp.f64 (.f64 -1/2 (+.f64 (.f64 -1 (log.f64 (/.f64 -1 x))) (log.f64 -1)))) 2) (pow.f64 (cbrt.f64 -1/8) 2))) 1/3) (/.f64 (+.f64 (.f64 -3/16 (pow.f64 (exp.f64 (.f64 -1/2 (+.f64 (.f64 -1 (log.f64 (/.f64 -1 x))) (log.f64 -1)))) 3)) (.f64 -3/32 (pow.f64 (exp.f64 (.f64 -1/2 (+.f64 (.f64 -1 (log.f64 (/.f64 -1 x))) (log.f64 -1)))) 3))) (pow.f64 x 2)))) (.f64 1/3 (/.f64 (-.f64 (+.f64 (.f64 -35/512 (pow.f64 (exp.f64 (.f64 -1/2 (+.f64 (.f64 -1 (log.f64 (/.f64 -1 x))) (log.f64 -1)))) 3)) (+.f64 (.f64 -15/128 (pow.f64 (exp.f64 (.f64 -1/2 (+.f64 (.f64 -1 (log.f64 (/.f64 -1 x))) (log.f64 -1)))) 3)) (+.f64 (.f64 -3/8 (.f64 (exp.f64 (.f64 -1/2 (+.f64 (.f64 -1 (log.f64 (/.f64 -1 x))) (log.f64 -1)))) (+.f64 (.f64 5/16 (pow.f64 (exp.f64 (.f64 -1/2 (+.f64 (.f64 -1 (log.f64 (/.f64 -1 x))) (log.f64 -1)))) 2)) (.f64 9/64 (pow.f64 (exp.f64 (.f64 -1/2 (+.f64 (.f64 -1 (log.f64 (/.f64 -1 x))) (log.f64 -1)))) 2))))) (.f64 -1/2 (.f64 (exp.f64 (.f64 -1/2 (+.f64 (.f64 -1 (log.f64 (/.f64 -1 x))) (log.f64 -1)))) (+.f64 (.f64 35/128 (pow.f64 (exp.f64 (.f64 -1/2 (+.f64 (.f64 -1 (log.f64 (/.f64 -1 x))) (log.f64 -1)))) 2)) (.f64 15/64 (pow.f64 (exp.f64 (.f64 -1/2 (+.f64 (.f64 -1 (log.f64 (/.f64 -1 x))) (log.f64 -1)))) 2)))))))) (+.f64 (.f64 2/3 (.f64 (pow.f64 (/.f64 1 (.f64 (pow.f64 (exp.f64 (.f64 -1/2 (+.f64 (.f64 -1 (log.f64 (/.f64 -1 x))) (log.f64 -1)))) 5) (pow.f64 (cbrt.f64 -1/8) 5))) 1/3) (.f64 (-.f64 (+.f64 (.f64 -1/2 (.f64 (exp.f64 (.f64 -1/2 (+.f64 (.f64 -1 (log.f64 (/.f64 -1 x))) (log.f64 -1)))) (+.f64 (.f64 5/16 (pow.f64 (exp.f64 (.f64 -1/2 (+.f64 (.f64 -1 (log.f64 (/.f64 -1 x))) (log.f64 -1)))) 2)) (.f64 9/64 (pow.f64 (exp.f64 (.f64 -1/2 (+.f64 (.f64 -1 (log.f64 (/.f64 -1 x))) (log.f64 -1)))) 2))))) (+.f64 (.f64 -9/64 (pow.f64 (exp.f64 (.f64 -1/2 (+.f64 (.f64 -1 (log.f64 (/.f64 -1 x))) (log.f64 -1)))) 3)) (.f64 -5/64 (pow.f64 (exp.f64 (.f64 -1/2 (+.f64 (.f64 -1 (log.f64 (/.f64 -1 x))) (log.f64 -1)))) 3)))) (.f64 1/3 (.f64 (pow.f64 (/.f64 1 (.f64 (exp.f64 (.f64 -1/2 (+.f64 (.f64 -1 (log.f64 (/.f64 -1 x))) (log.f64 -1)))) (cbrt.f64 -1/8))) 1/3) (pow.f64 (+.f64 (.f64 -3/16 (pow.f64 (exp.f64 (.f64 -1/2 (+.f64 (.f64 -1 (log.f64 (/.f64 -1 x))) (log.f64 -1)))) 3)) (.f64 -3/32 (pow.f64 (exp.f64 (.f64 -1/2 (+.f64 (.f64 -1 (log.f64 (/.f64 -1 x))) (log.f64 -1)))) 3))) 2)))) (+.f64 (.f64 -3/16 (pow.f64 (exp.f64 (.f64 -1/2 (+.f64 (.f64 -1 (log.f64 (/.f64 -1 x))) (log.f64 -1)))) 3)) (.f64 -3/32 (pow.f64 (exp.f64 (.f64 -1/2 (+.f64 (.f64 -1 (log.f64 (/.f64 -1 x))) (log.f64 -1)))) 3)))))) (.f64 1/27 (/.f64 (pow.f64 (+.f64 (.f64 -3/16 (pow.f64 (exp.f64 (.f64 -1/2 (+.f64 (.f64 -1 (log.f64 (/.f64 -1 x))) (log.f64 -1)))) 3)) (.f64 -3/32 (pow.f64 (exp.f64 (.f64 -1/2 (+.f64 (.f64 -1 (log.f64 (/.f64 -1 x))) (log.f64 -1)))) 3))) 3) (.f64 (pow.f64 (exp.f64 (.f64 -1/2 (+.f64 (.f64 -1 (log.f64 (/.f64 -1 x))) (log.f64 -1)))) 2) (pow.f64 (cbrt.f64 -1/8) 2)))))) (.f64 (pow.f64 (exp.f64 (.f64 -1/2 (+.f64 (.f64 -1 (log.f64 (/.f64 -1 x))) (log.f64 -1)))) 2) (*.f64 (pow.f64 x 4) (pow.f64 (cbrt.f64 -1/8) 2))))))))
(-.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))))))
(pow.f64 (-.f64 (pow.f64 x -1/2) 1) 3)
(+.f64 (.f64 (+.f64 (.f64 1/2 (pow.f64 (-.f64 (pow.f64 x -1/2) 1) 2)) (pow.f64 (-.f64 (pow.f64 x -1/2) 1) 2)) x) (pow.f64 (-.f64 (pow.f64 x -1/2) 1) 3))
(+.f64 (.f64 (+.f64 (.f64 1/2 (-.f64 (pow.f64 x -1/2) 1)) (+.f64 (.f64 (-.f64 (pow.f64 x -1/2) 1) (+.f64 1/4 (.f64 -3/4 (-.f64 (pow.f64 x -1/2) 1)))) (.f64 -3/8 (pow.f64 (-.f64 (pow.f64 x -1/2) 1) 2)))) (pow.f64 x 2)) (+.f64 (.f64 (+.f64 (*.f64 1/2 (pow.f64 (-.f64 (pow.f64 x -1/2) 1) 2)) (pow.f64 (-.f64 (pow.f64 x -1/2) 1) 2)) x) (pow.f64 (-.f64 (pow.f64 x -1/2) 1) 3)))
(+.f64 (.f64 (+.f64 (.f64 1/2 (-.f64 (pow.f64 x -1/2) 1)) (+.f64 (.f64 (-.f64 (pow.f64 x -1/2) 1) (+.f64 1/4 (.f64 -3/4 (-.f64 (pow.f64 x -1/2) 1)))) (.f64 -3/8 (pow.f64 (-.f64 (pow.f64 x -1/2) 1) 2)))) (pow.f64 x 2)) (+.f64 (.f64 (+.f64 (.f64 1/2 (pow.f64 (-.f64 (pow.f64 x -1/2) 1) 2)) (pow.f64 (-.f64 (pow.f64 x -1/2) 1) 2)) x) (+.f64 (.f64 (+.f64 (.f64 5/16 (pow.f64 (-.f64 (pow.f64 x -1/2) 1) 2)) (+.f64 (.f64 1/2 (+.f64 1/4 (.f64 -3/4 (-.f64 (pow.f64 x -1/2) 1)))) (+.f64 (.f64 (-.f64 (pow.f64 x -1/2) 1) (-.f64 (.f64 5/8 (-.f64 (pow.f64 x -1/2) 1)) 3/8)) (.f64 -3/8 (-.f64 (pow.f64 x -1/2) 1))))) (pow.f64 x 3)) (pow.f64 (-.f64 (pow.f64 x -1/2) 1) 3))))
(*.f64 1/8 (sqrt.f64 (/.f64 1 (pow.f64 x 9))))
(+.f64 (.f64 -3/32 (sqrt.f64 (/.f64 1 (pow.f64 x 11)))) (+.f64 (.f64 -3/16 (sqrt.f64 (/.f64 1 (pow.f64 x 11)))) (*.f64 1/8 (sqrt.f64 (/.f64 1 (pow.f64 x 9))))))
(+.f64 (.f64 5/64 (sqrt.f64 (/.f64 1 (pow.f64 x 13)))) (+.f64 (.f64 29/128 (sqrt.f64 (/.f64 1 (pow.f64 x 13)))) (+.f64 (.f64 -3/16 (sqrt.f64 (/.f64 1 (pow.f64 x 11)))) (+.f64 (.f64 -3/32 (sqrt.f64 (/.f64 1 (pow.f64 x 11)))) (+.f64 (.f64 9/64 (sqrt.f64 (/.f64 1 (pow.f64 x 13)))) (.f64 1/8 (sqrt.f64 (/.f64 1 (pow.f64 x 9)))))))))
(+.f64 (.f64 -87/512 (sqrt.f64 (/.f64 1 (pow.f64 x 15)))) (+.f64 (.f64 5/64 (sqrt.f64 (/.f64 1 (pow.f64 x 13)))) (+.f64 (.f64 29/128 (sqrt.f64 (/.f64 1 (pow.f64 x 13)))) (+.f64 (.f64 1/8 (sqrt.f64 (/.f64 1 (pow.f64 x 9)))) (+.f64 (.f64 -65/256 (sqrt.f64 (/.f64 1 (pow.f64 x 15)))) (+.f64 (.f64 -3/16 (sqrt.f64 (/.f64 1 (pow.f64 x 11)))) (+.f64 (.f64 -3/32 (sqrt.f64 (/.f64 1 (pow.f64 x 11)))) (+.f64 (.f64 9/64 (sqrt.f64 (/.f64 1 (pow.f64 x 13)))) (+.f64 (.f64 -15/128 (sqrt.f64 (/.f64 1 (pow.f64 x 15)))) (.f64 -35/512 (sqrt.f64 (/.f64 1 (pow.f64 x 15)))))))))))))
(.f64 1/8 (/.f64 (pow.f64 (exp.f64 (.f64 -1/2 (+.f64 (*.f64 -1 (log.f64 (/.f64 -1 x))) (log.f64 -1)))) 3) (pow.f64 x 3)))
(+.f64 (.f64 -3/32 (/.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 1/8 (/.f64 (pow.f64 (exp.f64 (.f64 -1/2 (+.f64 (.f64 -1 (log.f64 (/.f64 -1 x))) (log.f64 -1)))) 3) (pow.f64 x 3))) (.f64 -3/16 (/.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 -3/32 (/.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 (/.f64 (+.f64 (.f64 -1/2 (.f64 (exp.f64 (.f64 -1/2 (+.f64 (.f64 -1 (log.f64 (/.f64 -1 x))) (log.f64 -1)))) (+.f64 (.f64 5/16 (pow.f64 (exp.f64 (.f64 -1/2 (+.f64 (.f64 -1 (log.f64 (/.f64 -1 x))) (log.f64 -1)))) 2)) (.f64 9/64 (pow.f64 (exp.f64 (.f64 -1/2 (+.f64 (.f64 -1 (log.f64 (/.f64 -1 x))) (log.f64 -1)))) 2))))) (+.f64 (.f64 -9/64 (pow.f64 (exp.f64 (.f64 -1/2 (+.f64 (.f64 -1 (log.f64 (/.f64 -1 x))) (log.f64 -1)))) 3)) (.f64 -5/64 (pow.f64 (exp.f64 (.f64 -1/2 (+.f64 (.f64 -1 (log.f64 (/.f64 -1 x))) (log.f64 -1)))) 3)))) (pow.f64 x 5))) (+.f64 (.f64 1/8 (/.f64 (pow.f64 (exp.f64 (.f64 -1/2 (+.f64 (.f64 -1 (log.f64 (/.f64 -1 x))) (log.f64 -1)))) 3) (pow.f64 x 3))) (.f64 -3/16 (/.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 -1/2 (/.f64 (.f64 (exp.f64 (.f64 -1/2 (+.f64 (.f64 -1 (log.f64 (/.f64 -1 x))) (log.f64 -1)))) (+.f64 (.f64 35/128 (pow.f64 (exp.f64 (.f64 -1/2 (+.f64 (.f64 -1 (log.f64 (/.f64 -1 x))) (log.f64 -1)))) 2)) (.f64 15/64 (pow.f64 (exp.f64 (.f64 -1/2 (+.f64 (.f64 -1 (log.f64 (/.f64 -1 x))) (log.f64 -1)))) 2)))) (pow.f64 x 6))) (+.f64 (.f64 -3/32 (/.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 -15/128 (/.f64 (pow.f64 (exp.f64 (.f64 -1/2 (+.f64 (.f64 -1 (log.f64 (/.f64 -1 x))) (log.f64 -1)))) 3) (pow.f64 x 6))) (+.f64 (.f64 -1 (/.f64 (+.f64 (.f64 -1/2 (.f64 (exp.f64 (.f64 -1/2 (+.f64 (.f64 -1 (log.f64 (/.f64 -1 x))) (log.f64 -1)))) (+.f64 (.f64 5/16 (pow.f64 (exp.f64 (.f64 -1/2 (+.f64 (.f64 -1 (log.f64 (/.f64 -1 x))) (log.f64 -1)))) 2)) (.f64 9/64 (pow.f64 (exp.f64 (.f64 -1/2 (+.f64 (.f64 -1 (log.f64 (/.f64 -1 x))) (log.f64 -1)))) 2))))) (+.f64 (.f64 -9/64 (pow.f64 (exp.f64 (.f64 -1/2 (+.f64 (.f64 -1 (log.f64 (/.f64 -1 x))) (log.f64 -1)))) 3)) (.f64 -5/64 (pow.f64 (exp.f64 (.f64 -1/2 (+.f64 (.f64 -1 (log.f64 (/.f64 -1 x))) (log.f64 -1)))) 3)))) (pow.f64 x 5))) (+.f64 (.f64 1/8 (/.f64 (pow.f64 (exp.f64 (.f64 -1/2 (+.f64 (.f64 -1 (log.f64 (/.f64 -1 x))) (log.f64 -1)))) 3) (pow.f64 x 3))) (+.f64 (.f64 -3/16 (/.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 -3/8 (/.f64 (.f64 (exp.f64 (.f64 -1/2 (+.f64 (.f64 -1 (log.f64 (/.f64 -1 x))) (log.f64 -1)))) (+.f64 (.f64 5/16 (pow.f64 (exp.f64 (.f64 -1/2 (+.f64 (.f64 -1 (log.f64 (/.f64 -1 x))) (log.f64 -1)))) 2)) (.f64 9/64 (pow.f64 (exp.f64 (.f64 -1/2 (+.f64 (.f64 -1 (log.f64 (/.f64 -1 x))) (log.f64 -1)))) 2)))) (pow.f64 x 6))) (.f64 -35/512 (/.f64 (pow.f64 (exp.f64 (.f64 -1/2 (+.f64 (.f64 -1 (log.f64 (/.f64 -1 x))) (log.f64 -1)))) 3) (pow.f64 x 6))))))))))

Outputs
(-.f64 (pow.f64 x -1/2) 1)
(+.f64 (pow.f64 x -1/2) -1)
(-.f64 (+.f64 (.f64 1/3 (.f64 (pow.f64 (/.f64 1 (pow.f64 (-.f64 (pow.f64 x -1/2) 1) 2)) 1/3) (.f64 (+.f64 (.f64 1/2 (pow.f64 (-.f64 (pow.f64 x -1/2) 1) 2)) (pow.f64 (-.f64 (pow.f64 x -1/2) 1) 2)) x))) (pow.f64 x -1/2)) 1)
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(fma.f64 (.f64 1/3 (cbrt.f64 (/.f64 1 (pow.f64 (+.f64 (pow.f64 x -1/2) -1) 2)))) (.f64 x (*.f64 (pow.f64 (+.f64 (pow.f64 x -1/2) -1) 2) 3/2)) (+.f64 (pow.f64 x -1/2) -1))
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(fma.f64 -3/32 (/.f64 (pow.f64 (pow.f64 (exp.f64 -1/2) (-.f64 (log.f64 -1) (log.f64 (/.f64 -1 x)))) 3) (pow.f64 x 4)) (fma.f64 -3/16 (/.f64 (pow.f64 (pow.f64 (exp.f64 -1/2) (-.f64 (log.f64 -1) (log.f64 (/.f64 -1 x)))) 3) (pow.f64 x 4)) (*.f64 1/8 (/.f64 (pow.f64 (pow.f64 (exp.f64 -1/2) (-.f64 (log.f64 -1) (log.f64 (/.f64 -1 x)))) 3) (pow.f64 x 3)))))
(+.f64 (.f64 1/8 (/.f64 (pow.f64 (.f64 (pow.f64 -1 -1/2) (pow.f64 (/.f64 -1 x) 1/2)) 3) (pow.f64 x 3))) (.f64 (/.f64 (pow.f64 (.f64 (pow.f64 -1 -1/2) (pow.f64 (/.f64 -1 x) 1/2)) 3) (pow.f64 x 4)) -9/32))
(+.f64 (.f64 -3/32 (/.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 (/.f64 (+.f64 (.f64 -1/2 (.f64 (exp.f64 (.f64 -1/2 (+.f64 (.f64 -1 (log.f64 (/.f64 -1 x))) (log.f64 -1)))) (+.f64 (.f64 5/16 (pow.f64 (exp.f64 (.f64 -1/2 (+.f64 (.f64 -1 (log.f64 (/.f64 -1 x))) (log.f64 -1)))) 2)) (.f64 9/64 (pow.f64 (exp.f64 (.f64 -1/2 (+.f64 (.f64 -1 (log.f64 (/.f64 -1 x))) (log.f64 -1)))) 2))))) (+.f64 (.f64 -9/64 (pow.f64 (exp.f64 (.f64 -1/2 (+.f64 (.f64 -1 (log.f64 (/.f64 -1 x))) (log.f64 -1)))) 3)) (.f64 -5/64 (pow.f64 (exp.f64 (.f64 -1/2 (+.f64 (.f64 -1 (log.f64 (/.f64 -1 x))) (log.f64 -1)))) 3)))) (pow.f64 x 5))) (+.f64 (.f64 1/8 (/.f64 (pow.f64 (exp.f64 (.f64 -1/2 (+.f64 (.f64 -1 (log.f64 (/.f64 -1 x))) (log.f64 -1)))) 3) (pow.f64 x 3))) (.f64 -3/16 (/.f64 (pow.f64 (exp.f64 (.f64 -1/2 (+.f64 (.f64 -1 (log.f64 (/.f64 -1 x))) (log.f64 -1)))) 3) (pow.f64 x 4))))))
(fma.f64 -3/32 (/.f64 (pow.f64 (pow.f64 (exp.f64 -1/2) (fma.f64 -1 (log.f64 (/.f64 -1 x)) (log.f64 -1))) 3) (pow.f64 x 4)) (fma.f64 -1 (/.f64 (fma.f64 -1/2 (.f64 (pow.f64 (exp.f64 -1/2) (fma.f64 -1 (log.f64 (/.f64 -1 x)) (log.f64 -1))) (.f64 (pow.f64 (pow.f64 (exp.f64 -1/2) (fma.f64 -1 (log.f64 (/.f64 -1 x)) (log.f64 -1))) 2) 29/64)) (.f64 (pow.f64 (pow.f64 (exp.f64 -1/2) (fma.f64 -1 (log.f64 (/.f64 -1 x)) (log.f64 -1))) 3) -7/32)) (pow.f64 x 5)) (fma.f64 1/8 (/.f64 (pow.f64 (pow.f64 (exp.f64 -1/2) (fma.f64 -1 (log.f64 (/.f64 -1 x)) (log.f64 -1))) 3) (pow.f64 x 3)) (.f64 -3/16 (/.f64 (pow.f64 (pow.f64 (exp.f64 -1/2) (fma.f64 -1 (log.f64 (/.f64 -1 x)) (log.f64 -1))) 3) (pow.f64 x 4))))))
(fma.f64 -3/32 (/.f64 (pow.f64 (pow.f64 (exp.f64 -1/2) (-.f64 (log.f64 -1) (log.f64 (/.f64 -1 x)))) 3) (pow.f64 x 4)) (-.f64 (fma.f64 -3/16 (/.f64 (pow.f64 (pow.f64 (exp.f64 -1/2) (-.f64 (log.f64 -1) (log.f64 (/.f64 -1 x)))) 3) (pow.f64 x 4)) (.f64 1/8 (/.f64 (pow.f64 (pow.f64 (exp.f64 -1/2) (-.f64 (log.f64 -1) (log.f64 (/.f64 -1 x)))) 3) (pow.f64 x 3)))) (/.f64 (fma.f64 -1/2 (.f64 (pow.f64 (pow.f64 (exp.f64 -1/2) (-.f64 (log.f64 -1) (log.f64 (/.f64 -1 x)))) 3) 29/64) (*.f64 (pow.f64 (pow.f64 (exp.f64 -1/2) (-.f64 (log.f64 -1) (log.f64 (/.f64 -1 x)))) 3) -7/32)) (pow.f64 x 5))))
(+.f64 (-.f64 (.f64 1/8 (/.f64 (pow.f64 (.f64 (pow.f64 -1 -1/2) (pow.f64 (/.f64 -1 x) 1/2)) 3) (pow.f64 x 3))) (/.f64 (fma.f64 -1/2 (.f64 (pow.f64 (.f64 (pow.f64 -1 -1/2) (pow.f64 (/.f64 -1 x) 1/2)) 3) 29/64) (.f64 (pow.f64 (.f64 (pow.f64 -1 -1/2) (pow.f64 (/.f64 -1 x) 1/2)) 3) -7/32)) (pow.f64 x 5))) (.f64 (/.f64 (pow.f64 (.f64 (pow.f64 -1 -1/2) (pow.f64 (/.f64 -1 x) 1/2)) 3) (pow.f64 x 4)) -9/32))
(+.f64 (.f64 -1/2 (/.f64 (.f64 (exp.f64 (.f64 -1/2 (+.f64 (.f64 -1 (log.f64 (/.f64 -1 x))) (log.f64 -1)))) (+.f64 (.f64 35/128 (pow.f64 (exp.f64 (.f64 -1/2 (+.f64 (.f64 -1 (log.f64 (/.f64 -1 x))) (log.f64 -1)))) 2)) (.f64 15/64 (pow.f64 (exp.f64 (.f64 -1/2 (+.f64 (.f64 -1 (log.f64 (/.f64 -1 x))) (log.f64 -1)))) 2)))) (pow.f64 x 6))) (+.f64 (.f64 -3/32 (/.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 -15/128 (/.f64 (pow.f64 (exp.f64 (.f64 -1/2 (+.f64 (.f64 -1 (log.f64 (/.f64 -1 x))) (log.f64 -1)))) 3) (pow.f64 x 6))) (+.f64 (.f64 -1 (/.f64 (+.f64 (.f64 -1/2 (.f64 (exp.f64 (.f64 -1/2 (+.f64 (.f64 -1 (log.f64 (/.f64 -1 x))) (log.f64 -1)))) (+.f64 (.f64 5/16 (pow.f64 (exp.f64 (.f64 -1/2 (+.f64 (.f64 -1 (log.f64 (/.f64 -1 x))) (log.f64 -1)))) 2)) (.f64 9/64 (pow.f64 (exp.f64 (.f64 -1/2 (+.f64 (.f64 -1 (log.f64 (/.f64 -1 x))) (log.f64 -1)))) 2))))) (+.f64 (.f64 -9/64 (pow.f64 (exp.f64 (.f64 -1/2 (+.f64 (.f64 -1 (log.f64 (/.f64 -1 x))) (log.f64 -1)))) 3)) (.f64 -5/64 (pow.f64 (exp.f64 (.f64 -1/2 (+.f64 (.f64 -1 (log.f64 (/.f64 -1 x))) (log.f64 -1)))) 3)))) (pow.f64 x 5))) (+.f64 (.f64 1/8 (/.f64 (pow.f64 (exp.f64 (.f64 -1/2 (+.f64 (.f64 -1 (log.f64 (/.f64 -1 x))) (log.f64 -1)))) 3) (pow.f64 x 3))) (+.f64 (.f64 -3/16 (/.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 -3/8 (/.f64 (.f64 (exp.f64 (.f64 -1/2 (+.f64 (.f64 -1 (log.f64 (/.f64 -1 x))) (log.f64 -1)))) (+.f64 (.f64 5/16 (pow.f64 (exp.f64 (.f64 -1/2 (+.f64 (.f64 -1 (log.f64 (/.f64 -1 x))) (log.f64 -1)))) 2)) (.f64 9/64 (pow.f64 (exp.f64 (.f64 -1/2 (+.f64 (.f64 -1 (log.f64 (/.f64 -1 x))) (log.f64 -1)))) 2)))) (pow.f64 x 6))) (.f64 -35/512 (/.f64 (pow.f64 (exp.f64 (.f64 -1/2 (+.f64 (.f64 -1 (log.f64 (/.f64 -1 x))) (log.f64 -1)))) 3) (pow.f64 x 6))))))))))
(fma.f64 -1/2 (/.f64 (pow.f64 (exp.f64 -1/2) (fma.f64 -1 (log.f64 (/.f64 -1 x)) (log.f64 -1))) (/.f64 (pow.f64 x 6) (.f64 (pow.f64 (pow.f64 (exp.f64 -1/2) (fma.f64 -1 (log.f64 (/.f64 -1 x)) (log.f64 -1))) 2) 65/128))) (fma.f64 -3/32 (/.f64 (pow.f64 (pow.f64 (exp.f64 -1/2) (fma.f64 -1 (log.f64 (/.f64 -1 x)) (log.f64 -1))) 3) (pow.f64 x 4)) (fma.f64 -15/128 (/.f64 (pow.f64 (pow.f64 (exp.f64 -1/2) (fma.f64 -1 (log.f64 (/.f64 -1 x)) (log.f64 -1))) 3) (pow.f64 x 6)) (fma.f64 -1 (/.f64 (fma.f64 -1/2 (.f64 (pow.f64 (exp.f64 -1/2) (fma.f64 -1 (log.f64 (/.f64 -1 x)) (log.f64 -1))) (.f64 (pow.f64 (pow.f64 (exp.f64 -1/2) (fma.f64 -1 (log.f64 (/.f64 -1 x)) (log.f64 -1))) 2) 29/64)) (.f64 (pow.f64 (pow.f64 (exp.f64 -1/2) (fma.f64 -1 (log.f64 (/.f64 -1 x)) (log.f64 -1))) 3) -7/32)) (pow.f64 x 5)) (fma.f64 1/8 (/.f64 (pow.f64 (pow.f64 (exp.f64 -1/2) (fma.f64 -1 (log.f64 (/.f64 -1 x)) (log.f64 -1))) 3) (pow.f64 x 3)) (fma.f64 -3/16 (/.f64 (pow.f64 (pow.f64 (exp.f64 -1/2) (fma.f64 -1 (log.f64 (/.f64 -1 x)) (log.f64 -1))) 3) (pow.f64 x 4)) (fma.f64 -3/8 (/.f64 (pow.f64 (exp.f64 -1/2) (fma.f64 -1 (log.f64 (/.f64 -1 x)) (log.f64 -1))) (/.f64 (pow.f64 x 6) (.f64 (pow.f64 (pow.f64 (exp.f64 -1/2) (fma.f64 -1 (log.f64 (/.f64 -1 x)) (log.f64 -1))) 2) 29/64))) (.f64 -35/512 (/.f64 (pow.f64 (pow.f64 (exp.f64 -1/2) (fma.f64 -1 (log.f64 (/.f64 -1 x)) (log.f64 -1))) 3) (pow.f64 x 6))))))))))
(fma.f64 -1/2 (/.f64 (.f64 (pow.f64 (pow.f64 (exp.f64 -1/2) (-.f64 (log.f64 -1) (log.f64 (/.f64 -1 x)))) 3) 65/128) (pow.f64 x 6)) (fma.f64 -3/32 (/.f64 (pow.f64 (pow.f64 (exp.f64 -1/2) (-.f64 (log.f64 -1) (log.f64 (/.f64 -1 x)))) 3) (pow.f64 x 4)) (fma.f64 -15/128 (/.f64 (pow.f64 (pow.f64 (exp.f64 -1/2) (-.f64 (log.f64 -1) (log.f64 (/.f64 -1 x)))) 3) (pow.f64 x 6)) (-.f64 (fma.f64 1/8 (/.f64 (pow.f64 (pow.f64 (exp.f64 -1/2) (-.f64 (log.f64 -1) (log.f64 (/.f64 -1 x)))) 3) (pow.f64 x 3)) (fma.f64 -3/16 (/.f64 (pow.f64 (pow.f64 (exp.f64 -1/2) (-.f64 (log.f64 -1) (log.f64 (/.f64 -1 x)))) 3) (pow.f64 x 4)) (fma.f64 -35/512 (/.f64 (pow.f64 (pow.f64 (exp.f64 -1/2) (-.f64 (log.f64 -1) (log.f64 (/.f64 -1 x)))) 3) (pow.f64 x 6)) (/.f64 (.f64 (pow.f64 (pow.f64 (exp.f64 -1/2) (-.f64 (log.f64 -1) (log.f64 (/.f64 -1 x)))) 3) 29/64) (/.f64 (pow.f64 x 6) -3/8))))) (/.f64 (fma.f64 -1/2 (.f64 (pow.f64 (pow.f64 (exp.f64 -1/2) (-.f64 (log.f64 -1) (log.f64 (/.f64 -1 x)))) 3) 29/64) (.f64 (pow.f64 (pow.f64 (exp.f64 -1/2) (-.f64 (log.f64 -1) (log.f64 (/.f64 -1 x)))) 3) -7/32)) (pow.f64 x 5))))))
(fma.f64 -1/2 (.f64 (/.f64 (pow.f64 (.f64 (pow.f64 -1 -1/2) (pow.f64 (/.f64 -1 x) 1/2)) 3) (pow.f64 x 6)) 65/128) (fma.f64 -3/32 (/.f64 (pow.f64 (.f64 (pow.f64 -1 -1/2) (pow.f64 (/.f64 -1 x) 1/2)) 3) (pow.f64 x 4)) (fma.f64 -15/128 (/.f64 (pow.f64 (.f64 (pow.f64 -1 -1/2) (pow.f64 (/.f64 -1 x) 1/2)) 3) (pow.f64 x 6)) (-.f64 (+.f64 (fma.f64 -3/16 (/.f64 (pow.f64 (.f64 (pow.f64 -1 -1/2) (pow.f64 (/.f64 -1 x) 1/2)) 3) (pow.f64 x 4)) (.f64 -3/8 (.f64 (/.f64 (pow.f64 (.f64 (pow.f64 -1 -1/2) (pow.f64 (/.f64 -1 x) 1/2)) 3) (pow.f64 x 6)) 29/64))) (.f64 (/.f64 (pow.f64 (.f64 (pow.f64 -1 -1/2) (pow.f64 (/.f64 -1 x) 1/2)) 3) (pow.f64 x 3)) (+.f64 (/.f64 -35/512 (pow.f64 x 3)) 1/8))) (/.f64 (fma.f64 -1/2 (.f64 (pow.f64 (.f64 (pow.f64 -1 -1/2) (pow.f64 (/.f64 -1 x) 1/2)) 3) 29/64) (.f64 (pow.f64 (.f64 (pow.f64 -1 -1/2) (pow.f64 (/.f64 -1 x) 1/2)) 3) -7/32)) (pow.f64 x 5))))))

eval1.8s (16.7%)

Compiler: Compiled 23271 to 18302 computations (21.4% saved)

prune217.0ms (2%)

Pruning

11 alts after pruning (11 fresh and 0 done)

	Pruned	Kept	Total
New	987	9	996
Fresh	23	2	25
Picked	1	0	1
Done	5	0	5
Total	1016	11	1027

Error

12.4b

Counts

1027 → 11

Alt Table

Click to see full alt table

Status	Error	Program
▶	39.7b	(*.f64 1/2 (sqrt.f64 (/.f64 1 (pow.f64 x 3))))
	62.7b	-1
▶	24.4b	(/.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)))))
	34.7b	(-.f64 (/.f64 1 (sqrt.f64 x)) (/.f64 1 (+.f64 (*.f64 1/2 x) 1)))
▶	23.6b	(/.f64 (/.f64 (+.f64 x (-.f64 1 x)) (+.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x))) (sqrt.f64 (*.f64 x (+.f64 1 x))))
	24.2b	(-.f64 (pow.f64 x -1/2) (pow.f64 (+.f64 x 1) -1/2))
	38.9b	(-.f64 (pow.f64 (*.f64 x x) -1/4) (/.f64 1 (fma.f64 x (fma.f64 x -1/8 1/2) 1)))
	44.6b	(-.f64 (cbrt.f64 (pow.f64 x -3/2)) (/.f64 1 (sqrt.f64 (+.f64 x 1))))
▶	35.4b	(-.f64 (+.f64 (*.f64 1/2 x) (pow.f64 x -1/2)) 1)
▶	35.8b	(-.f64 (pow.f64 x -1/2) 1)
	24.9b	(/.f64 1 (sqrt.f64 (*.f64 x (+.f64 1 x))))

Compiler

Compiled 258 to 206 computations (20.2% saved)

localize43.0ms (0.4%)

Local error

Found 8 expressions with local error:

New	Error	Program
	0.0b	(/.f64 (+.f64 x (-.f64 1 x)) (+.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x)))
	0.0b	(*.f64 x (+.f64 1 x))
	0.0b	(+.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x))
	0.0b	(sqrt.f64 (+.f64 x 1))
✓	0.0b	(/.f64 (+.f64 x (-.f64 1 x)) (+.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x)))
✓	0.1b	(/.f64 (/.f64 (+.f64 x (-.f64 1 x)) (+.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x))) (sqrt.f64 (*.f64 x (+.f64 1 x))))
✓	2.9b	(+.f64 x (-.f64 1 x))
	15.4b	(sqrt.f64 (*.f64 x (+.f64 1 x)))

Compiler

Compiled 74 to 47 computations (36.5% saved)

series18.0ms (0.2%)

Counts

3 → 13

Calls

9 calls:

Time	Variable		Point	Expression
7.0ms	x	@	-inf	(/.f64 (/.f64 (+.f64 x (-.f64 1 x)) (+.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x))) (sqrt.f64 (*.f64 x (+.f64 1 x))))
3.0ms	x	@	inf	(/.f64 (/.f64 (+.f64 x (-.f64 1 x)) (+.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x))) (sqrt.f64 (*.f64 x (+.f64 1 x))))
3.0ms	x	@	-inf	(/.f64 (+.f64 x (-.f64 1 x)) (+.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x)))
2.0ms	x	@	0	(/.f64 (/.f64 (+.f64 x (-.f64 1 x)) (+.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x))) (sqrt.f64 (*.f64 x (+.f64 1 x))))
1.0ms	x	@	inf	(/.f64 (+.f64 x (-.f64 1 x)) (+.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x)))

rewrite223.0ms (2.1%)

Algorithm

1×	batch-egg-rewrite

Rules

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

Iterations

Useful iterations: 1 (0.0ms)

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

Stop Event

1×	node limit

Counts

3 → 293

Calls

Call 1

Inputs

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

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

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

Outputs

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

simplify15.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

1×	`1-exp_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	1	13
1	4	13

Stop Event

1×

saturated

Counts

306 → 294

Calls

Call 1

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

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

localize12.0ms (0.1%)

Local error

Found 2 expressions with local error:

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

Compiler

Compiled 12 to 9 computations (25% saved)

series29.0ms (0.3%)

Counts

1 → 8

Calls

3 calls:

Time	Variable		Point	Expression
12.0ms	x	@	-inf	(-.f64 (pow.f64 x -1/2) 1)
9.0ms	x	@	inf	(-.f64 (pow.f64 x -1/2) 1)
8.0ms	x	@	0	(-.f64 (pow.f64 x -1/2) 1)

rewrite76.0ms (0.7%)

Algorithm

1×	batch-egg-rewrite

Rules

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

Iterations

Useful iterations: 0 (0.0ms)

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

Stop Event

1×	node limit

Counts

1 → 31

Calls

Call 1

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

Outputs

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

simplify48.0ms (0.5%)

Algorithm

1×	egg-herbie

Rules

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

Iterations

Useful iterations: 4 (0.0ms)

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

Stop Event

1×	node limit

Counts

39 → 33

Calls

Call 1

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

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

localize77.0ms (0.7%)

Local error

Found 4 expressions with local error:

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

Compiler

Compiled 27 to 20 computations (25.9% saved)

series2.0ms (0%)

Counts

2 → 21

Calls

6 calls:

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

rewrite75.0ms (0.7%)

Algorithm

1×	batch-egg-rewrite

Rules

410×	`fma-def_binary64`
393×	`log-prod_binary64`
304×	`prod-exp_binary64`
299×	`exp-prod_binary64`
269×	`pow-prod-down_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	9	19
1	205	19
2	2670	19

Stop Event

1×	node limit

Counts

2 → 164

Calls

Call 1

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

Outputs

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

simplify60.0ms (0.6%)

Algorithm

1×	egg-herbie

Rules

415×	`distribute-rgt-in_binary64`
381×	`distribute-lft-in_binary64`
302×	`unswap-sqr_binary64`
270×	`fma-neg_binary64`
247×	`*-commutative_binary64`

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	24	126
1	63	126
2	135	126
3	280	126
4	710	84
5	2198	84
6	7961	84

Stop Event

1×	node limit

Counts

185 → 172

Calls

Call 1

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

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

localize15.0ms (0.1%)

Local error

Found 6 expressions with local error:

New	Error	Program
	21.5b	(sqrt.f64 (/.f64 1 (pow.f64 x 3)))
	0.1b	(/.f64 1 (pow.f64 x 3))
	0.0b	(*.f64 1/2 (sqrt.f64 (/.f64 1 (pow.f64 x 3))))
✓	0.0b	(*.f64 1/2 (sqrt.f64 (/.f64 1 (pow.f64 x 3))))
✓	0.1b	(/.f64 1 (pow.f64 x 3))
✓	21.5b	(sqrt.f64 (/.f64 1 (pow.f64 x 3)))

Compiler

Compiled 27 to 22 computations (18.5% saved)

series5.0ms (0%)

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

rewrite68.0ms (0.6%)

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)))))))

simplify11.0ms (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

localize101.0ms (0.9%)

Local error

Found 8 expressions with local error:

New	Error	Program
	0.1b	(/.f64 (+.f64 (pow.f64 x -1/2) (pow.f64 (+.f64 1 x) -1/2)) (-.f64 (/.f64 1 x) (/.f64 1 (+.f64 1 x))))
	0.1b	(/.f64 1 (/.f64 (+.f64 (pow.f64 x -1/2) (pow.f64 (+.f64 1 x) -1/2)) (-.f64 (/.f64 1 x) (/.f64 1 (+.f64 1 x)))))
	0.0b	(/.f64 1 (+.f64 1 x))
	0.0b	(+.f64 (pow.f64 x -1/2) (pow.f64 (+.f64 1 x) -1/2))
✓	0.0b	(/.f64 1 (+.f64 1 x))
✓	0.1b	(/.f64 1 (/.f64 (+.f64 (pow.f64 x -1/2) (pow.f64 (+.f64 1 x) -1/2)) (-.f64 (/.f64 1 x) (/.f64 1 (+.f64 1 x)))))
✓	0.1b	(/.f64 (+.f64 (pow.f64 x -1/2) (pow.f64 (+.f64 1 x) -1/2)) (-.f64 (/.f64 1 x) (/.f64 1 (+.f64 1 x))))
✓	3.5b	(-.f64 (/.f64 1 x) (/.f64 1 (+.f64 1 x)))

Compiler

Compiled 81 to 63 computations (22.2% saved)

series9.0ms (0.1%)

Counts

4 → 48

Calls

12 calls:

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

rewrite160.0ms (1.5%)

Algorithm

1×	batch-egg-rewrite

Rules

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

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	13	79
1	319	49
2	4928	49

Stop Event

1×	node limit

Counts

4 → 362

Calls

Call 1

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

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

simplify72.0ms (0.7%)

Algorithm

1×	egg-herbie

Rules

458×	`associate--r+_binary64`
362×	`associate--l+_binary64`
340×	`distribute-rgt-in_binary64`
320×	`associate-/r*_binary64`
301×	`associate-l_binary64`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	224	2083
1	765	1966
2	2450	1685

Stop Event

1×	node limit

Counts

410 → 437

Calls

Call 1

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

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

eval1.1s (10%)

Compiler: Compiled 26848 to 20131 computations (25% saved)

prune304.0ms (2.9%)

Pruning

16 alts after pruning (14 fresh and 2 done)

	Pruned	Kept	Total
New	1043	11	1054
Fresh	3	3	6
Picked	1	0	1
Done	2	2	4
Total	1049	16	1065

Error

0.0b

Counts

1065 → 16

Alt Table

Click to see full alt table

Status	Error	Program
	62.7b	-1
▶	62.4b	(-.f64 (*.f64 1/2 x) 1)
	26.8b	(*.f64 1/2 (pow.f64 x -3/2))
	26.9b	(.f64 1/2 (.f64 (/.f64 1 (sqrt.f64 x)) (/.f64 1 x)))
	22.6b	(/.f64 1 (fma.f64 x (.f64 (sqrt.f64 (/.f64 1 x)) 3/2) (.f64 2 (pow.f64 x 3/2))))
▶	49.4b	(/.f64 (/.f64 (+.f64 x (-.f64 1 x)) (+.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x))) x)
▶	27.1b	(*.f64 1/2 (pow.f64 (/.f64 1 (sqrt.f64 x)) 3))
	34.7b	(-.f64 (/.f64 1 (sqrt.f64 x)) (/.f64 1 (+.f64 (*.f64 1/2 x) 1)))
	49.3b	(/.f64 (/.f64 (+.f64 x (-.f64 1 x)) (+.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x))) (+.f64 x 1/2))
	24.2b	(/.f64 1 (*.f64 1 (/.f64 1 (-.f64 (pow.f64 x -1/2) (pow.f64 (+.f64 1 x) -1/2)))))
▶	4.8b	(/.f64 1 (/.f64 (+.f64 (pow.f64 x -1/2) (pow.f64 (+.f64 1 x) -1/2)) (/.f64 (/.f64 (+.f64 1 (-.f64 x x)) x) (+.f64 1 x))))
✓	35.4b	(-.f64 (+.f64 (*.f64 1/2 x) (pow.f64 x -1/2)) 1)
	34.2b	(/.f64 1 (+.f64 x (sqrt.f64 x)))
✓	35.8b	(-.f64 (pow.f64 x -1/2) 1)
	24.2b	(-.f64 (pow.f64 x -1/2) (pow.f64 (+.f64 x 1) -1/2))
▶	51.0b	(*.f64 1/2 (-.f64 (+.f64 1 (pow.f64 x -3/2)) 1))

Compiler

Compiled 342 to 273 computations (20.2% saved)

localize56.0ms (0.5%)

Local error

Found 8 expressions with local error:

New	Error	Program
	4.4b	(/.f64 (+.f64 (pow.f64 x -1/2) (pow.f64 (+.f64 1 x) -1/2)) (/.f64 (/.f64 (+.f64 1 (-.f64 x x)) x) (+.f64 1 x)))
	0.5b	(/.f64 1 (/.f64 (+.f64 (pow.f64 x -1/2) (pow.f64 (+.f64 1 x) -1/2)) (/.f64 (/.f64 (+.f64 1 (-.f64 x x)) x) (+.f64 1 x))))
	0.1b	(/.f64 (/.f64 (+.f64 1 (-.f64 x x)) x) (+.f64 1 x))
	0.0b	(+.f64 (pow.f64 x -1/2) (pow.f64 (+.f64 1 x) -1/2))
✓	0.0b	(+.f64 (pow.f64 x -1/2) (pow.f64 (+.f64 1 x) -1/2))
✓	0.1b	(/.f64 (/.f64 (+.f64 1 (-.f64 x x)) x) (+.f64 1 x))
✓	0.5b	(/.f64 1 (/.f64 (+.f64 (pow.f64 x -1/2) (pow.f64 (+.f64 1 x) -1/2)) (/.f64 (/.f64 (+.f64 1 (-.f64 x x)) x) (+.f64 1 x))))
✓	4.4b	(/.f64 (+.f64 (pow.f64 x -1/2) (pow.f64 (+.f64 1 x) -1/2)) (/.f64 (/.f64 (+.f64 1 (-.f64 x x)) x) (+.f64 1 x)))

Compiler

Compiled 94 to 60 computations (36.2% saved)

series56.0ms (0.5%)

Counts

4 → 48

Calls

12 calls:

Time	Variable		Point	Expression
33.0ms	x	@	inf	(/.f64 (+.f64 (pow.f64 x -1/2) (pow.f64 (+.f64 1 x) -1/2)) (/.f64 (/.f64 (+.f64 1 (-.f64 x x)) x) (+.f64 1 x)))
6.0ms	x	@	-inf	(/.f64 1 (/.f64 (+.f64 (pow.f64 x -1/2) (pow.f64 (+.f64 1 x) -1/2)) (/.f64 (/.f64 (+.f64 1 (-.f64 x x)) x) (+.f64 1 x))))
4.0ms	x	@	inf	(/.f64 1 (/.f64 (+.f64 (pow.f64 x -1/2) (pow.f64 (+.f64 1 x) -1/2)) (/.f64 (/.f64 (+.f64 1 (-.f64 x x)) x) (+.f64 1 x))))
3.0ms	x	@	0	(/.f64 1 (/.f64 (+.f64 (pow.f64 x -1/2) (pow.f64 (+.f64 1 x) -1/2)) (/.f64 (/.f64 (+.f64 1 (-.f64 x x)) x) (+.f64 1 x))))
2.0ms	x	@	-inf	(/.f64 (+.f64 (pow.f64 x -1/2) (pow.f64 (+.f64 1 x) -1/2)) (/.f64 (/.f64 (+.f64 1 (-.f64 x x)) x) (+.f64 1 x)))

rewrite160.0ms (1.5%)

Algorithm

1×	batch-egg-rewrite

Rules

943×	`prod-diff_binary64`
461×	`fma-def_binary64`
243×	`expm1-udef_binary64`
243×	`log1p-udef_binary64`
217×	`fma-neg_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	14	76
1	358	70
2	4690	70

Stop Event

1×	node limit

Counts

4 → 191

Calls

Call 1

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

simplify243.0ms (2.3%)

Algorithm

1×	egg-herbie

Rules

960×	`times-frac_binary64`
504×	`associate-/r*_binary64`
487×	`distribute-rgt-in_binary64`
477×	`distribute-lft-in_binary64`
475×	`associate-/l*_binary64`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	235	2708
1	776	2502
2	2799	1925

Stop Event

1×	node limit

Counts

239 → 275

Calls

Call 1

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

localize12.0ms (0.1%)

Compiler: Compiled 12 to 9 computations (25% saved)

localize46.0ms (0.4%)

Local error

Found 2 expressions with local error:

New	Error	Program
	1.7b	(-.f64 (+.f64 1 (pow.f64 x -3/2)) 1)
✓	1.7b	(-.f64 (+.f64 1 (pow.f64 x -3/2)) 1)

Compiler

Compiled 29 to 24 computations (17.2% saved)

series3.0ms (0%)

Counts

1 → 12

Calls

3 calls:

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

rewrite83.0ms (0.8%)

Algorithm

1×	batch-egg-rewrite

Rules

735×	`pow1_binary64`
699×	`add-log-exp_binary64`
698×	`log1p-expm1-u_binary64`
698×	`expm1-log1p-u_binary64`
687×	`add-exp-log_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	7	10
1	162	4
2	2169	4

Stop Event

1×	node limit

Counts

1 → 42

Calls

Call 1

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

Outputs

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

simplify59.0ms (0.6%)

Algorithm

1×	egg-herbie

Rules

634×	`fma-def_binary64`
606×	`div-sub_binary64`
491×	`associate-r_binary64`
463×	`fma-neg_binary64`
430×	`associate-l_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	16	108
1	41	108
2	86	108
3	182	108
4	481	108
5	1394	108
6	5981	108

Stop Event

1×	node limit

Counts

54 → 44

Calls

Call 1

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

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

localize11.0ms (0.1%)

Local error

Found 6 expressions with local error:

New	Error	Program
	0.4b	(pow.f64 (/.f64 1 (sqrt.f64 x)) 3)
	0.3b	(/.f64 1 (sqrt.f64 x))
	0.0b	(*.f64 1/2 (pow.f64 (/.f64 1 (sqrt.f64 x)) 3))
✓	0.0b	(*.f64 1/2 (pow.f64 (/.f64 1 (sqrt.f64 x)) 3))
	0.3b	(/.f64 1 (sqrt.f64 x))
✓	0.4b	(pow.f64 (/.f64 1 (sqrt.f64 x)) 3)

Compiler

Compiled 25 to 17 computations (32% saved)

series7.0ms (0.1%)

Counts

2 → 0

Calls

6 calls:

Time	Variable		Point	Expression
3.0ms	x	@	-inf	(pow.f64 (/.f64 1 (sqrt.f64 x)) 3)
1.0ms	x	@	0	(pow.f64 (/.f64 1 (sqrt.f64 x)) 3)
1.0ms	x	@	-inf	(*.f64 1/2 (pow.f64 (/.f64 1 (sqrt.f64 x)) 3))
1.0ms	x	@	inf	(pow.f64 (/.f64 1 (sqrt.f64 x)) 3)
0.0ms	x	@	0	(*.f64 1/2 (pow.f64 (/.f64 1 (sqrt.f64 x)) 3))

rewrite63.0ms (0.6%)

Algorithm

1×	batch-egg-rewrite

Rules

722×	`pow1_binary64`
678×	`add-log-exp_binary64`
676×	`log1p-expm1-u_binary64`
676×	`expm1-log1p-u_binary64`
661×	`add-exp-log_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	9	21
1	190	13
2	2003	13

Stop Event

1×	node limit

Counts

2 → 39

Calls

Call 1

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

Outputs

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

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

39 → 39

Calls

Call 1

Inputs

Outputs

localize23.0ms (0.2%)

Local error

Found 8 expressions with local error:

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

Compiler

Compiled 55 to 34 computations (38.2% saved)

series6.0ms (0.1%)

Counts

2 → 2

Calls

6 calls:

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

rewrite79.0ms (0.7%)

Algorithm

1×	batch-egg-rewrite

Rules

720×	`fma-def_binary64`
654×	`log-prod_binary64`
359×	`fma-neg_binary64`
275×	`log-div_binary64`
225×	`expm1-udef_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	11	34
1	263	25
2	4188	25

Stop Event

1×	node limit

Counts

2 → 99

Calls

Call 1

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

Outputs

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

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

simplify8.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

1×	`1-exp_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	4	5
1	6	5

Stop Event

1×

saturated

Counts

101 → 101

Calls

Call 1

Inputs
(/.f64 1 x)
1

Outputs
(/.f64 1 x)
1

eval437.0ms (4.1%)

Compiler: Compiled 18420 to 13307 computations (27.8% saved)

prune104.0ms (1%)

Pruning

17 alts after pruning (14 fresh and 3 done)

	Pruned	Kept	Total
New	731	11	742
Fresh	6	3	9
Picked	1	0	1
Done	3	3	6
Total	741	17	758

Error

Counts

758 → 17

Alt Table

Click to see full alt table

Status	Error	Program
	32.6b	(.f64 1/2 (pow.f64 (.f64 x x) -3/4))
	34.2b	(/.f64 1 (+.f64 x (sqrt.f64 x)))
	26.9b	(.f64 1/2 (.f64 (pow.f64 x -1/2) (/.f64 1 x)))
	59.4b	(/.f64 1 x)
	25.2b	(/.f64 1 (/.f64 (+.f64 (*.f64 -1/2 x) (+.f64 (pow.f64 x -1/2) 1)) (/.f64 (/.f64 (+.f64 1 (-.f64 x x)) x) (+.f64 1 x))))
	34.7b	(-.f64 (/.f64 1 (sqrt.f64 x)) (/.f64 1 (+.f64 (*.f64 1/2 x) 1)))
	26.9b	(*.f64 1/2 (/.f64 (/.f64 1 x) (sqrt.f64 x)))
	27.2b	(/.f64 1 (/.f64 (*.f64 2 (sqrt.f64 (/.f64 1 x))) (/.f64 (/.f64 (+.f64 1 (-.f64 x x)) x) (+.f64 1 x))))
	26.1b	(/.f64 (/.f64 1 (+.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x))) x)
✓	35.8b	(-.f64 (pow.f64 x -1/2) 1)
	62.7b	-1
	50.2b	(/.f64 (/.f64 (+.f64 x (-.f64 1 x)) 1) x)
	26.8b	(*.f64 1/2 (pow.f64 x -3/2))
✓	35.4b	(-.f64 (+.f64 (*.f64 1/2 x) (pow.f64 x -1/2)) 1)
	24.2b	(-.f64 (pow.f64 x -1/2) (pow.f64 (+.f64 x 1) -1/2))
✓	51.0b	(*.f64 1/2 (-.f64 (+.f64 1 (pow.f64 x -3/2)) 1))
	0.7b	(/.f64 1 (.f64 (+.f64 x 1) (.f64 (+.f64 (pow.f64 x -1/2) (pow.f64 (+.f64 x 1) -1/2)) x)))

Compiler

Compiled 180 to 141 computations (21.7% saved)

regimes158.0ms (1.5%)

Counts

62 → 1

Calls

Call 1

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

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

Calls

3 calls:

91.0ms	x
27.0ms	(-.f64 (/.f64 1 (sqrt.f64 x)) (/.f64 1 (sqrt.f64 (+.f64 x 1))))
14.0ms	(-.f64 (/.f64 1 (sqrt.f64 x)) (/.f64 1 (sqrt.f64 (+.f64 x 1))))

Results

Error	Segments	Branch
0.7b	1	`x`
0.7b	1	`(-.f64 (/.f64 1 (sqrt.f64 x)) (/.f64 1 (sqrt.f64 (+.f64 x 1))))`
0.7b	1	`(-.f64 (/.f64 1 (sqrt.f64 x)) (/.f64 1 (sqrt.f64 (+.f64 x 1))))`

Compiler

Compiled 854 to 651 computations (23.8% saved)

regimes218.0ms (2%)

Counts

33 → 2

Calls

Call 1

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

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

Calls

3 calls:

169.0ms	x
27.0ms	(-.f64 (/.f64 1 (sqrt.f64 x)) (/.f64 1 (sqrt.f64 (+.f64 x 1))))
11.0ms	(-.f64 (/.f64 1 (sqrt.f64 x)) (/.f64 1 (sqrt.f64 (+.f64 x 1))))

Results

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

Compiler

Compiled 334 to 246 computations (26.3% saved)

bsearch1.0ms (0%)

Algorithm

1×	left-value

Steps

Time	Left	Right
0.0ms	7.177282856582479e-16	0.04093203249160843

Compiler

Compiled 16 to 13 computations (18.8% saved)

regimes30.0ms (0.3%)

Counts

23 → 2

Calls

Call 1

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

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

Calls

1 calls:

23.0ms

Results

Error	Segments	Branch
0.5b	2	`x`

Compiler

Compiled 195 to 142 computations (27.2% saved)

bsearch59.0ms (0.6%)

Algorithm

1×	binary-search

Steps

Time	Left	Right
59.0ms	0.003961232274139698	4.823624679729216

Compiler

Compiled 16 to 13 computations (18.8% saved)

regimes20.0ms (0.2%)

Counts

15 → 2

Calls

Call 1

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

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

Calls

1 calls:

16.0ms

Results

Error	Segments	Branch
0.6b	2	`x`

Compiler

Compiled 95 to 68 computations (28.4% saved)

bsearch25.0ms (0.2%)

Algorithm

1×	binary-search

Steps

Time	Left	Right
24.0ms	0.003961232274139698	4.823624679729216

Compiler

Compiled 16 to 13 computations (18.8% saved)

regimes8.0ms (0.1%)

Counts

6 → 1

Calls

Call 1

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

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

Calls

1 calls:

5.0ms

Results

Error	Segments	Branch
26.8b	1	`x`

Compiler

Compiled 31 to 23 computations (25.8% saved)

regimes5.0ms (0%)

Counts

4 → 1

Calls

Call 1

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

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

Calls

1 calls:

4.0ms

Results

Error	Segments	Branch
50.2b	1	`x`

Compiler

Compiled 21 to 15 computations (28.6% saved)

regimes5.0ms (0%)

Accuracy

Total -3.5b remaining (-6%)

Threshold costs -3.5b (-6%)

Counts

3 → 1

Calls

Call 1

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

Outputs
(/.f64 1 x)

Calls

1 calls:

3.0ms

Results

Error	Segments	Branch
59.4b	1	`x`

Compiler

Compiled 12 to 9 computations (25% saved)

simplify31.0ms (0.3%)

Algorithm

1×	egg-herbie

Rules

12×	`+-commutative_binary64`
8×	`sub-neg_binary64`
7×	`*-commutative_binary64`
3×	`neg-sub0_binary64`
3×	`neg-mul-1_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	39	135
1	59	135
2	71	135
3	77	135
4	80	135

Stop Event

1×	fuel
1×	saturated

Calls

Call 1

Inputs
(/.f64 1 (.f64 (+.f64 x 1) (.f64 (+.f64 (pow.f64 x -1/2) (pow.f64 (+.f64 x 1) -1/2)) x)))
(if (<=.f64 (-.f64 (/.f64 1 (sqrt.f64 x)) (/.f64 1 (sqrt.f64 (+.f64 x 1)))) 2535301200456459/2535301200456458802993406410752) (*.f64 1/2 (pow.f64 x -3/2)) (-.f64 (pow.f64 x -1/2) (pow.f64 (+.f64 x 1) -1/2)))
(if (<=.f64 x 4566989873598343/1152921504606846976) (-.f64 (+.f64 (.f64 1/2 x) (pow.f64 x -1/2)) 1) (.f64 1/2 (pow.f64 x -3/2)))
(if (<=.f64 x 4566989873598343/1152921504606846976) (-.f64 (pow.f64 x -1/2) 1) (*.f64 1/2 (pow.f64 x -3/2)))
(*.f64 1/2 (pow.f64 x -3/2))
(/.f64 (/.f64 (+.f64 x (-.f64 1 x)) 1) x)
(/.f64 1 x)
-1

Outputs
(/.f64 1 (.f64 (+.f64 x 1) (.f64 (+.f64 (pow.f64 x -1/2) (pow.f64 (+.f64 x 1) -1/2)) x)))
(/.f64 1 (.f64 (+.f64 1 x) (.f64 x (+.f64 (pow.f64 x -1/2) (pow.f64 (+.f64 1 x) -1/2)))))
(if (<=.f64 (-.f64 (/.f64 1 (sqrt.f64 x)) (/.f64 1 (sqrt.f64 (+.f64 x 1)))) 2535301200456459/2535301200456458802993406410752) (*.f64 1/2 (pow.f64 x -3/2)) (-.f64 (pow.f64 x -1/2) (pow.f64 (+.f64 x 1) -1/2)))
(if (<=.f64 (-.f64 (/.f64 1 (sqrt.f64 x)) (/.f64 1 (sqrt.f64 (+.f64 1 x)))) 2535301200456459/2535301200456458802993406410752) (*.f64 1/2 (pow.f64 x -3/2)) (-.f64 (pow.f64 x -1/2) (pow.f64 (+.f64 1 x) -1/2)))
(if (<=.f64 x 4566989873598343/1152921504606846976) (-.f64 (+.f64 (.f64 1/2 x) (pow.f64 x -1/2)) 1) (.f64 1/2 (pow.f64 x -3/2)))
(if (<=.f64 x 4566989873598343/1152921504606846976) (+.f64 (+.f64 (pow.f64 x -1/2) (.f64 x 1/2)) -1) (.f64 1/2 (pow.f64 x -3/2)))
(if (<=.f64 x 4566989873598343/1152921504606846976) (-.f64 (pow.f64 x -1/2) 1) (*.f64 1/2 (pow.f64 x -3/2)))
(if (<=.f64 x 4566989873598343/1152921504606846976) (+.f64 (pow.f64 x -1/2) -1) (*.f64 1/2 (pow.f64 x -3/2)))
(*.f64 1/2 (pow.f64 x -3/2))
(/.f64 (/.f64 (+.f64 x (-.f64 1 x)) 1) x)
(/.f64 (+.f64 x (-.f64 1 x)) x)
(/.f64 1 x)
-1

Compiler

Compiled 101 to 80 computations (20.8% saved)

soundness0.0ms (0%)

end112.0ms (1.1%)

Compiler: Compiled 94 to 73 computations (22.3% 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