Details

analyze130.0ms (3.4%)

Algorithm

1×

Search

True	Other	False	Iter
0%	100%	0%	0
0%	100%	0%	1
0%	100%	0%	2
25%	75%	0%	3
25%	62.5%	12.5%	4
25%	56.2%	18.8%	5
28.1%	50%	21.9%	6
29.7%	46.9%	23.5%	7
30.5%	45.3%	24.3%	8
30.8%	44.9%	24.3%	9
31.2%	44.5%	24.3%	10
31.3%	44.4%	24.3%	11
31.4%	44.3%	24.3%	12

Compiler

Compiled 9 to 6 computations (33.3% saved)

sample1.4s (35.8%)

Results

735.0ms	2778×	body	1024	valid
320.0ms	3879×	body	256	valid
217.0ms	1350×	body	512	valid
77.0ms	249×	body	2048	valid
0.0ms	4×	body	256	invalid

preprocess17.0ms (0.4%)

Algorithm

2×	egg-herbie

Rules

1×	`+-commutative_binary64`
1×	`sub-neg_binary64`
1×	`1-exp_binary64`
1×	`expm1-def_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	6	8
1	12	8
2	13	8
0	1	1

Stop Event

1×	saturated
1×	saturated

Calls

Call 1

Inputs
0

Outputs
0

Call 2

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

Outputs
(/.f64 (exp.f64 x) (-.f64 (exp.f64 x) 1))
(/.f64 (exp.f64 x) (expm1.f64 x))

Compiler

Compiled 9 to 6 computations (33.3% saved)

simplify6.0ms (0.2%)

Algorithm

1×	egg-herbie

Rules

1×	`+-commutative_binary64`
1×	`sub-neg_binary64`
1×	`1-exp_binary64`
1×	`expm1-def_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	6	8
1	12	8
2	13	8

Stop Event

1×

saturated

Counts

1 → 2

Calls

Call 1

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

Outputs
(/.f64 (exp.f64 x) (-.f64 (exp.f64 x) 1))
(/.f64 (exp.f64 x) (expm1.f64 x))

eval0.0ms (0%)

Compiler: Compiled 13 to 7 computations (46.2% saved)

prune1.0ms (0%)

Pruning

1 alts after pruning (1 fresh and 0 done)

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

Error

0.8b

Counts

3 → 1

Alt Table

Click to see full alt table

Status	Error	Program
▶	0.8b	(/.f64 (exp.f64 x) (expm1.f64 x))

Compiler

Compiled 6 to 4 computations (33.3% saved)

localize5.0ms (0.1%)

Local error

Found 1 expressions with local error:

New	Error	Program
✓	0.7b	(/.f64 (exp.f64 x) (expm1.f64 x))

Compiler

Compiled 11 to 4 computations (63.6% saved)

series2.0ms (0.1%)

Counts

1 → 12

Calls

3 calls:

Time	Variable		Point	Expression
1.0ms	x	@	inf	(/.f64 (exp.f64 x) (expm1.f64 x))
1.0ms	x	@	-inf	(/.f64 (exp.f64 x) (expm1.f64 x))
1.0ms	x	@	0	(/.f64 (exp.f64 x) (expm1.f64 x))

rewrite43.0ms (1.1%)

Algorithm

1×	batch-egg-rewrite

Rules

516×	`pow1_binary64`
493×	`add-sqr-sqrt_binary64`
477×	`add-log-exp_binary64`
477×	`log1p-expm1-u_binary64`
477×	`expm1-log1p-u_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	5	8
1	99	8
2	1287	8

Stop Event

1×	node limit

Counts

1 → 30

Calls

Call 1

Inputs
(/.f64 (exp.f64 x) (expm1.f64 x))

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

Outputs

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

simplify178.0ms (4.7%)

Algorithm

1×	egg-herbie

Rules

1274×	`sqr-pow_binary64`
666×	`pow-sqr_binary64`
529×	`cube-prod_binary64`
470×	`fabs-mul_binary64`
446×	`associate-l_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	19	104
1	48	104
2	94	104
3	213	104
4	327	104
5	572	104
6	1504	104
7	2330	104
8	2416	104
9	2549	104
10	2707	104
11	2961	104
12	3283	104
13	3707	104
14	4207	104
15	4809	104
16	5533	104
17	5856	104
18	6138	104
19	6358	104
20	6534	104
21	6616	104
22	7556	104

Stop Event

1×	node limit

Counts

42 → 39

Calls

Call 1

Inputs
(/.f64 1 x)
(+.f64 1/2 (/.f64 1 x))
(+.f64 1/2 (+.f64 (*.f64 1/12 x) (/.f64 1 x)))
(+.f64 1/2 (+.f64 (.f64 -1/720 (pow.f64 x 3)) (+.f64 (.f64 1/12 x) (/.f64 1 x))))
(/.f64 (exp.f64 x) (-.f64 (exp.f64 x) 1))
(/.f64 (exp.f64 x) (-.f64 (exp.f64 x) 1))
(/.f64 (exp.f64 x) (-.f64 (exp.f64 x) 1))
(/.f64 (exp.f64 x) (-.f64 (exp.f64 x) 1))
(/.f64 (exp.f64 x) (-.f64 (exp.f64 x) 1))
(/.f64 (exp.f64 x) (-.f64 (exp.f64 x) 1))
(/.f64 (exp.f64 x) (-.f64 (exp.f64 x) 1))
(/.f64 (exp.f64 x) (-.f64 (exp.f64 x) 1))

Outputs
(/.f64 1 x)
(+.f64 1/2 (/.f64 1 x))
(+.f64 (/.f64 1 x) 1/2)
(+.f64 1/2 (+.f64 (*.f64 1/12 x) (/.f64 1 x)))
(+.f64 1/2 (fma.f64 1/12 x (/.f64 1 x)))
(+.f64 1/2 (fma.f64 x 1/12 (/.f64 1 x)))
(+.f64 (/.f64 1 x) (fma.f64 x 1/12 1/2))
(+.f64 1/2 (+.f64 (.f64 -1/720 (pow.f64 x 3)) (+.f64 (.f64 1/12 x) (/.f64 1 x))))
(+.f64 1/2 (fma.f64 -1/720 (pow.f64 x 3) (fma.f64 1/12 x (/.f64 1 x))))
(+.f64 1/2 (fma.f64 -1/720 (pow.f64 x 3) (fma.f64 x 1/12 (/.f64 1 x))))
(+.f64 1/2 (fma.f64 x 1/12 (fma.f64 -1/720 (pow.f64 x 3) (/.f64 1 x))))
(+.f64 1/2 (fma.f64 x (fma.f64 x (*.f64 x -1/720) 1/12) (/.f64 1 x)))
(+.f64 (/.f64 1 x) (fma.f64 x (fma.f64 x (*.f64 x -1/720) 1/12) 1/2))
(+.f64 (/.f64 1 x) (fma.f64 -1/720 (pow.f64 x 3) (fma.f64 x 1/12 1/2)))
(+.f64 (/.f64 1 x) (fma.f64 x 1/12 (fma.f64 -1/720 (pow.f64 x 3) 1/2)))
(/.f64 (exp.f64 x) (-.f64 (exp.f64 x) 1))
(/.f64 (exp.f64 x) (expm1.f64 x))
(/.f64 (exp.f64 x) (-.f64 (exp.f64 x) 1))
(/.f64 (exp.f64 x) (expm1.f64 x))
(/.f64 (exp.f64 x) (-.f64 (exp.f64 x) 1))
(/.f64 (exp.f64 x) (expm1.f64 x))
(/.f64 (exp.f64 x) (-.f64 (exp.f64 x) 1))
(/.f64 (exp.f64 x) (expm1.f64 x))
(/.f64 (exp.f64 x) (-.f64 (exp.f64 x) 1))
(/.f64 (exp.f64 x) (expm1.f64 x))
(/.f64 (exp.f64 x) (-.f64 (exp.f64 x) 1))
(/.f64 (exp.f64 x) (expm1.f64 x))
(/.f64 (exp.f64 x) (-.f64 (exp.f64 x) 1))
(/.f64 (exp.f64 x) (expm1.f64 x))
(/.f64 (exp.f64 x) (-.f64 (exp.f64 x) 1))
(/.f64 (exp.f64 x) (expm1.f64 x))

eval7.0ms (0.2%)

Compiler: Compiled 379 to 160 computations (57.8% saved)

prune7.0ms (0.2%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	36	3	39
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	36	4	40

Error

0.6b

Counts

40 → 4

Alt Table

Click to see full alt table

Status	Error	Program
▶	18.5b	(/.f64 1 x)
✓	0.8b	(/.f64 (exp.f64 x) (expm1.f64 x))
▶	18.9b	(+.f64 1/2 (+.f64 (*.f64 1/12 x) (/.f64 1 x)))
▶	18.7b	(+.f64 (/.f64 1 x) 1/2)

Compiler

Compiled 26 to 20 computations (23.1% saved)

localize12.0ms (0.3%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.0b	(+.f64 (*.f64 1/12 x) (/.f64 1 x))
✓	0.0b	(+.f64 1/2 (+.f64 (*.f64 1/12 x) (/.f64 1 x)))
✓	0.3b	(*.f64 1/12 x)

Compiler

Compiled 27 to 20 computations (25.9% saved)

series4.0ms (0.1%)

Counts

3 → 19

Calls

9 calls:

Time	Variable		Point	Expression
1.0ms	x	@	inf	(*.f64 1/12 x)
0.0ms	x	@	0	(*.f64 1/12 x)
0.0ms	x	@	-inf	(*.f64 1/12 x)
0.0ms	x	@	inf	(+.f64 1/2 (+.f64 (*.f64 1/12 x) (/.f64 1 x)))
0.0ms	x	@	0	(+.f64 (*.f64 1/12 x) (/.f64 1 x))

rewrite80.0ms (2.1%)

Algorithm

1×	batch-egg-rewrite

Rules

936×	`prod-diff_binary64`
625×	`unpow-prod-down_binary64`
409×	`log-prod_binary64`
332×	`fma-def_binary64`
252×	`pow2_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	9	23
1	204	23
2	2715	23

Stop Event

1×	node limit

Counts

3 → 154

Calls

Call 1

Inputs
(*.f64 1/12 x)
(+.f64 1/2 (+.f64 (*.f64 1/12 x) (/.f64 1 x)))
(+.f64 (*.f64 1/12 x) (/.f64 1 x))

Outputs
((#(struct:change #<rule egg-rr> (2) ((x +.f64 0 (.f64 1/12 x))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (log.f64 (pow.f64 (cbrt.f64 (pow.f64 (exp.f64 1/12) x)) 2)) (log.f64 (cbrt.f64 (pow.f64 (exp.f64 1/12) x))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (log.f64 (sqrt.f64 (pow.f64 (exp.f64 1/12) x))) (log.f64 (sqrt.f64 (pow.f64 (exp.f64 1/12) x))))))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (exp.f64 (log1p.f64 (.f64 1/12 x))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (.f64 1/12 x) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (.f64 1/144 (.f64 x x)) 1/2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (cbrt.f64 (.f64 1/12 x)) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (sqrt.f64 (.f64 1/12 x)) 2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (.f64 1/12 x) 3) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f64 (.f64 1/144 (.f64 x x)))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (pow.f64 (exp.f64 1/12) x))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (+.f64 1 (expm1.f64 (.f64 1/12 x))))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (pow.f64 (.f64 1/12 x) 3))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (.f64 1/12 x)))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (log.f64 (.f64 1/12 x)))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (.f64 (log.f64 (.f64 1/12 x)) 1))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (*.f64 1/12 x)))))))
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Outputs

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

((#(struct:change #<rule egg-rr> (2) ((x -.f64 (exp.f64 (log1p.f64 (fma.f64 1/12 x (/.f64 1 x)))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (/.f64 (*.f64 1/144 (*.f64 x x)) (-.f64 (*.f64 1/12 x) (/.f64 1 x))) (/.f64 (pow.f64 x -2) (-.f64 (*.f64 1/12 x) (/.f64 1 x))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 1 (fma.f64 1/12 x (/.f64 1 x)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (fma.f64 1/12 x (/.f64 1 x)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 (fma.f64 1/12 x (/.f64 1 x))) (pow.f64 (cbrt.f64 (fma.f64 1/12 x (/.f64 1 x))) 2))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (cbrt.f64 (fma.f64 1/12 x (/.f64 1 x))) 2) (cbrt.f64 (fma.f64 1/12 x (/.f64 1 x))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (sqrt.f64 (fma.f64 1/12 x (/.f64 1 x))) (sqrt.f64 (fma.f64 1/12 x (/.f64 1 x))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (fma.f64 1/1728 (pow.f64 x 3) (pow.f64 x -3)) (/.f64 1 (-.f64 (fma.f64 1/144 (*.f64 x x) (pow.f64 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x))))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (+.f64 1 (expm1.f64 (fma.f64 1/12 x (/.f64 1 x)))))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (*.f64 (+.f64 1 (expm1.f64 (*.f64 1/12 x))) (exp.f64 (/.f64 1 x))))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (*.f64 (pow.f64 (exp.f64 1/12) x) (+.f64 1 (expm1.f64 (/.f64 1 x)))))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (*.f64 (+.f64 1 (expm1.f64 (*.f64 1/12 x))) (+.f64 1 (expm1.f64 (/.f64 1 x)))))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (*.f64 (+.f64 1 (expm1.f64 (/.f64 1 x))) (pow.f64 (exp.f64 1/12) x)))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (*.f64 (exp.f64 (/.f64 1 x)) (+.f64 1 (expm1.f64 (*.f64 1/12 x)))))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (*.f64 (+.f64 1 (expm1.f64 (/.f64 1 x))) (+.f64 1 (expm1.f64 (*.f64 1/12 x)))))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (pow.f64 (fma.f64 1/12 x (/.f64 1 x)) 3))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (fma.f64 1/12 x (/.f64 1 x))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (log.f64 (fma.f64 1/12 x (/.f64 1 x))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (log.f64 (fma.f64 1/12 x (/.f64 1 x))) 1))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (fma.f64 1/12 x (/.f64 1 x))))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 1/12 x (/.f64 1 x))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 x 1/12 (/.f64 1 x))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (*.f64 1/12 x) 1 (/.f64 1 x))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 1 (*.f64 1/12 x) (/.f64 1 x))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 1 (/.f64 1 x) (*.f64 1/12 x))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (/.f64 1 x) 1 (*.f64 1/12 x))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (pow.f64 (cbrt.f64 x) 2) (*.f64 (cbrt.f64 x) 1/12) (/.f64 1 x))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (/.f64 1 (cbrt.f64 x)) (cbrt.f64 (pow.f64 x -2)) (*.f64 1/12 x))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (cbrt.f64 (pow.f64 x -2)) (/.f64 1 (cbrt.f64 x)) (*.f64 1/12 x))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (cbrt.f64 (*.f64 1/12 x)) (pow.f64 (cbrt.f64 (*.f64 1/12 x)) 2) (/.f64 1 x))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (pow.f64 (cbrt.f64 (*.f64 1/12 x)) 2) (cbrt.f64 (*.f64 1/12 x)) (/.f64 1 x))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (sqrt.f64 x) (*.f64 (sqrt.f64 x) 1/12) (/.f64 1 x))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (pow.f64 x -1/2) (pow.f64 x -1/2) (*.f64 1/12 x))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (sqrt.f64 (*.f64 1/12 x)) (sqrt.f64 (*.f64 1/12 x)) (/.f64 1 x))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 -1 (/.f64 1 (neg.f64 x)) (*.f64 1/12 x))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (*.f64 1/12 (pow.f64 (cbrt.f64 x) 2)) (cbrt.f64 x) (/.f64 1 x))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (*.f64 1/12 (sqrt.f64 x)) (sqrt.f64 x) (/.f64 1 x))))))

simplify11.0ms (0.3%)

Algorithm

1×	egg-herbie

Rules

6×	`fma-def_binary64`
4×	`+-commutative_binary64`
2×	`associate-+r+_binary64`
2×	`associate-+l+_binary64`
1×	`*-commutative_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	11	157
1	19	133
2	26	133
3	28	133

Stop Event

1×

saturated

Counts

173 → 164

Calls

Call 1

Inputs
(/.f64 1 x)
(+.f64 1/2 (/.f64 1 x))
(*.f64 1/12 x)
(+.f64 1/2 (*.f64 1/12 x))
(+.f64 1/2 (+.f64 (/.f64 1 x) (*.f64 1/12 x)))
(+.f64 1/2 (+.f64 (/.f64 1 x) (*.f64 1/12 x)))
(*.f64 1/12 x)
(+.f64 1/2 (*.f64 1/12 x))
(+.f64 1/2 (+.f64 (/.f64 1 x) (*.f64 1/12 x)))
(+.f64 1/2 (+.f64 (/.f64 1 x) (*.f64 1/12 x)))
(/.f64 1 x)
(*.f64 1/12 x)
(+.f64 (/.f64 1 x) (*.f64 1/12 x))
(+.f64 (/.f64 1 x) (*.f64 1/12 x))
(+.f64 (/.f64 1 x) (*.f64 1/12 x))
(*.f64 1/12 x)
(+.f64 (/.f64 1 x) (*.f64 1/12 x))
(+.f64 (/.f64 1 x) (*.f64 1/12 x))
(+.f64 (/.f64 1 x) (*.f64 1/12 x))

Outputs
(/.f64 1 x)
(+.f64 1/2 (/.f64 1 x))
(+.f64 (/.f64 1 x) 1/2)
(*.f64 1/12 x)
(*.f64 x 1/12)
(+.f64 1/2 (*.f64 1/12 x))
(+.f64 1/2 (*.f64 x 1/12))
(fma.f64 x 1/12 1/2)
(+.f64 1/2 (+.f64 (/.f64 1 x) (*.f64 1/12 x)))
(+.f64 1/2 (+.f64 (/.f64 1 x) (*.f64 x 1/12)))
(+.f64 (/.f64 1 x) (fma.f64 x 1/12 1/2))
(+.f64 1/2 (+.f64 (/.f64 1 x) (*.f64 1/12 x)))
(+.f64 1/2 (+.f64 (/.f64 1 x) (*.f64 x 1/12)))
(+.f64 (/.f64 1 x) (fma.f64 x 1/12 1/2))
(*.f64 1/12 x)
(*.f64 x 1/12)
(+.f64 1/2 (*.f64 1/12 x))
(+.f64 1/2 (*.f64 x 1/12))
(fma.f64 x 1/12 1/2)
(+.f64 1/2 (+.f64 (/.f64 1 x) (*.f64 1/12 x)))
(+.f64 1/2 (+.f64 (/.f64 1 x) (*.f64 x 1/12)))
(+.f64 (/.f64 1 x) (fma.f64 x 1/12 1/2))
(+.f64 1/2 (+.f64 (/.f64 1 x) (*.f64 1/12 x)))
(+.f64 1/2 (+.f64 (/.f64 1 x) (*.f64 x 1/12)))
(+.f64 (/.f64 1 x) (fma.f64 x 1/12 1/2))
(/.f64 1 x)
(*.f64 1/12 x)
(*.f64 x 1/12)
(+.f64 (/.f64 1 x) (*.f64 1/12 x))
(+.f64 (/.f64 1 x) (*.f64 x 1/12))
(fma.f64 x 1/12 (/.f64 1 x))
(+.f64 (/.f64 1 x) (*.f64 1/12 x))
(+.f64 (/.f64 1 x) (*.f64 x 1/12))
(fma.f64 x 1/12 (/.f64 1 x))
(+.f64 (/.f64 1 x) (*.f64 1/12 x))
(+.f64 (/.f64 1 x) (*.f64 x 1/12))
(fma.f64 x 1/12 (/.f64 1 x))
(*.f64 1/12 x)
(*.f64 x 1/12)
(+.f64 (/.f64 1 x) (*.f64 1/12 x))
(+.f64 (/.f64 1 x) (*.f64 x 1/12))
(fma.f64 x 1/12 (/.f64 1 x))
(+.f64 (/.f64 1 x) (*.f64 1/12 x))
(+.f64 (/.f64 1 x) (*.f64 x 1/12))
(fma.f64 x 1/12 (/.f64 1 x))
(+.f64 (/.f64 1 x) (*.f64 1/12 x))
(+.f64 (/.f64 1 x) (*.f64 x 1/12))
(fma.f64 x 1/12 (/.f64 1 x))

localize5.0ms (0.1%)

Local error

Found 1 expressions with local error:

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

Compiler

Compiled 12 to 9 computations (25% saved)

series1.0ms (0%)

Counts

1 → 12

Calls

3 calls:

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

rewrite46.0ms (1.2%)

Algorithm

1×	batch-egg-rewrite

Rules

621×	`pow1_binary64`
582×	`add-log-exp_binary64`
582×	`log1p-expm1-u_binary64`
582×	`expm1-log1p-u_binary64`
572×	`add-exp-log_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	6	7
1	130	7
2	1578	7

Stop Event

1×	node limit

Counts

1 → 30

Calls

Call 1

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

Outputs

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

simplify8.0ms (0.2%)

Algorithm

1×	egg-herbie

Rules

1×	`+-commutative_binary64`
1×	`1-exp_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	6	69
1	9	69

Stop Event

1×

saturated

Counts

42 → 34

Calls

Call 1

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

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

localize4.0ms (0.1%)

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

eval75.0ms (2%)

Compiler: Compiled 2877 to 2269 computations (21.1% saved)

prune25.0ms (0.7%)

Pruning

7 alts after pruning (3 fresh and 4 done)

	Pruned	Kept	Total
New	195	3	198
Fresh	0	0	0
Picked	0	1	1
Done	0	3	3
Total	195	7	202

Error

0.6b

Counts

202 → 7

Alt Table

Click to see full alt table

Status	Error	Program
▶	38.7b	(/.f64 (-.f64 1/4 (pow.f64 x -2)) (-.f64 1/2 (/.f64 1 x)))
▶	18.7b	(-.f64 (+.f64 1 (+.f64 (/.f64 1 x) 1/2)) 1)
✓	18.5b	(/.f64 1 x)
	61.8b	1/2
✓	0.8b	(/.f64 (exp.f64 x) (expm1.f64 x))
✓	18.9b	(+.f64 1/2 (+.f64 (*.f64 1/12 x) (/.f64 1 x)))
✓	18.7b	(+.f64 (/.f64 1 x) 1/2)

Compiler

Compiled 50 to 41 computations (18% saved)

localize11.0ms (0.3%)

Local error

Found 2 expressions with local error:

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

Compiler

Compiled 28 to 23 computations (17.9% saved)

series1.0ms (0%)

Counts

1 → 12

Calls

3 calls:

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

rewrite52.0ms (1.4%)

Algorithm

1×	batch-egg-rewrite

Rules

981×	`pow1_binary64`
925×	`add-log-exp_binary64`
924×	`log1p-expm1-u_binary64`
924×	`expm1-log1p-u_binary64`
99×	`add-sqr-sqrt_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	8	13
1	192	7
2	2779	7

Stop Event

1×	node limit

Counts

1 → 54

Calls

Call 1

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

Outputs

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

simplify7.0ms (0.2%)

Algorithm

1×	egg-herbie

Rules

1×	`+-commutative_binary64`
1×	`1-exp_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	6	69
1	9	69

Stop Event

1×

saturated

Counts

66 → 56

Calls

Call 1

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

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

localize14.0ms (0.4%)

Local error

Found 1 expressions with local error:

New	Error	Program
✓	18.6b	(/.f64 (-.f64 1/4 (pow.f64 x -2)) (-.f64 1/2 (/.f64 1 x)))

Compiler

Compiled 33 to 26 computations (21.2% saved)

series3.0ms (0.1%)

Counts

1 → 12

Calls

3 calls:

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

rewrite89.0ms (2.3%)

Algorithm

1×	batch-egg-rewrite

Rules

511×	`log-prod_binary64`
303×	`pow2_binary64`
279×	`pow-prod-down_binary64`
268×	`prod-diff_binary64`
207×	`pow1/3_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	11	16
1	257	7
2	3314	7

Stop Event

1×	node limit

Counts

1 → 131

Calls

Call 1

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

Outputs

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

simplify8.0ms (0.2%)

Algorithm

1×	egg-herbie

Rules

1×	`+-commutative_binary64`
1×	`1-exp_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	6	69
1	9	69

Stop Event

1×

saturated

Counts

143 → 133

Calls

Call 1

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

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

eval167.0ms (4.4%)

Compiler: Compiled 7220 to 6043 computations (16.3% saved)

prune37.0ms (1%)

Pruning

12 alts after pruning (7 fresh and 5 done)

	Pruned	Kept	Total
New	217	6	223
Fresh	0	1	1
Picked	0	1	1
Done	1	4	5
Total	218	12	230

Error

0.6b

Counts

230 → 12

Alt Table

Click to see full alt table

Status	Error	Program
✓	38.7b	(/.f64 (-.f64 1/4 (pow.f64 x -2)) (-.f64 1/2 (/.f64 1 x)))
▶	38.7b	(-.f64 (+.f64 1 (/.f64 (-.f64 1/4 (pow.f64 x -2)) (-.f64 1/2 (/.f64 1 x)))) 1)
	61.8b	1/2
▶	19.6b	(fma.f64 (pow.f64 (cbrt.f64 (+.f64 (/.f64 1 x) 3/2)) 2) (cbrt.f64 (+.f64 (/.f64 1 x) 3/2)) -1)
✓	18.7b	(+.f64 (/.f64 1 x) 1/2)
▶	38.5b	(/.f64 (+.f64 (pow.f64 (+.f64 (/.f64 1 x) 3/2) 2) -1) (-.f64 (+.f64 (/.f64 1 x) 3/2) -1))
✓	18.5b	(/.f64 1 x)
	39.0b	(*.f64 (pow.f64 (cbrt.f64 (+.f64 1/2 (/.f64 -1 x))) -2) (/.f64 (-.f64 1/4 (pow.f64 x -2)) (cbrt.f64 (+.f64 1/2 (/.f64 -1 x)))))
▶	2.0b	(-.f64 (+.f64 1 (/.f64 1 x)) 1)
▶	18.7b	(+.f64 (+.f64 (/.f64 1 x) 3/2) -1)
✓	0.8b	(/.f64 (exp.f64 x) (expm1.f64 x))
✓	18.9b	(+.f64 1/2 (+.f64 (*.f64 1/12 x) (/.f64 1 x)))

Compiler

Compiled 218 to 188 computations (13.8% saved)

localize7.0ms (0.2%)

Local error

Found 1 expressions with local error:

New	Error	Program
✓	1.0b	(-.f64 (+.f64 1 (/.f64 1 x)) 1)

Compiler

Compiled 18 to 14 computations (22.2% saved)

series1.0ms (0%)

Counts

1 → 12

Calls

3 calls:

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

rewrite45.0ms (1.2%)

Algorithm

1×	batch-egg-rewrite

Rules

665×	`pow1_binary64`
626×	`add-log-exp_binary64`
626×	`log1p-expm1-u_binary64`
626×	`expm1-log1p-u_binary64`
615×	`add-exp-log_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	6	10
1	139	4
2	2008	4

Stop Event

1×	node limit

Counts

1 → 46

Calls

Call 1

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

Outputs

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

simplify10.0ms (0.3%)

Algorithm

1×	egg-herbie

Rules

1×	`1-exp_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	4	48
1	6	48

Stop Event

1×

saturated

Counts

58 → 46

Calls

Call 1

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

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

localize8.0ms (0.2%)

Local error

Found 1 expressions with local error:

New	Error	Program
✓	0.0b	(+.f64 (+.f64 (/.f64 1 x) 3/2) -1)

Compiler

Compiled 20 to 16 computations (20% saved)

series1.0ms (0%)

Counts

1 → 12

Calls

3 calls:

Time	Variable		Point	Expression
0.0ms	x	@	0	(+.f64 (+.f64 (/.f64 1 x) 3/2) -1)
0.0ms	x	@	-inf	(+.f64 (+.f64 (/.f64 1 x) 3/2) -1)
0.0ms	x	@	inf	(+.f64 (+.f64 (/.f64 1 x) 3/2) -1)

rewrite50.0ms (1.3%)

Algorithm

1×	batch-egg-rewrite

Rules

907×	`pow1_binary64`
853×	`add-log-exp_binary64`
852×	`log1p-expm1-u_binary64`
852×	`expm1-log1p-u_binary64`
840×	`add-exp-log_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	8	7
1	177	7
2	2228	7

Stop Event

1×	node limit

Counts

1 → 36

Calls

Call 1

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

Outputs

((#(struct:change #<rule egg-rr> (2) ((x -.f64 (+.f64 1 (+.f64 (/.f64 1 x) 1/2)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (/.f64 (pow.f64 (+.f64 (/.f64 1 x) 3/2) 2) (+.f64 (/.f64 1 x) 5/2)) (/.f64 1 (+.f64 (/.f64 1 x) 5/2)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 1 (+.f64 (/.f64 1 x) 1/2))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (+.f64 (/.f64 1 x) 1/2) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 (+.f64 (/.f64 1 x) 1/2)) (pow.f64 (cbrt.f64 (+.f64 (/.f64 1 x) 1/2)) 2))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (cbrt.f64 (+.f64 (/.f64 1 x) 1/2)) 2) (cbrt.f64 (+.f64 (/.f64 1 x) 1/2)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (sqrt.f64 (+.f64 (/.f64 1 x) 1/2)) (sqrt.f64 (+.f64 (/.f64 1 x) 1/2)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (+.f64 -1 (pow.f64 (+.f64 (/.f64 1 x) 3/2) 3)) (/.f64 1 (+.f64 (pow.f64 (+.f64 (/.f64 1 x) 3/2) 2) (-.f64 1 (*.f64 (+.f64 (/.f64 1 x) 3/2) -1)))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (+.f64 (pow.f64 (+.f64 (/.f64 1 x) 3/2) 2) -1) (/.f64 1 (+.f64 (/.f64 1 x) 5/2)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (+.f64 (sqrt.f64 (+.f64 (/.f64 1 x) 3/2)) 1) (-.f64 (sqrt.f64 (+.f64 (/.f64 1 x) 3/2)) 1))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 1 (/.f64 (+.f64 (pow.f64 (+.f64 (/.f64 1 x) 3/2) 2) (-.f64 1 (*.f64 (+.f64 (/.f64 1 x) 3/2) -1))) (+.f64 -1 (pow.f64 (+.f64 (/.f64 1 x) 3/2) 3))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 1 (/.f64 (+.f64 (/.f64 1 x) 5/2) (+.f64 (pow.f64 (+.f64 (/.f64 1 x) 3/2) 2) -1)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (+.f64 -1 (pow.f64 (+.f64 (/.f64 1 x) 3/2) 3)) (+.f64 (pow.f64 (+.f64 (/.f64 1 x) 3/2) 2) (-.f64 1 (*.f64 (+.f64 (/.f64 1 x) 3/2) -1))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (+.f64 -1 (pow.f64 (+.f64 (/.f64 1 x) 3/2) 3)) (+.f64 1 (-.f64 (pow.f64 (+.f64 (/.f64 1 x) 3/2) 2) (*.f64 (+.f64 (/.f64 1 x) 3/2) -1))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (+.f64 (pow.f64 (+.f64 (/.f64 1 x) 3/2) 2) -1) (+.f64 (/.f64 1 x) 5/2))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (neg.f64 (+.f64 -1 (pow.f64 (+.f64 (/.f64 1 x) 3/2) 3))) (neg.f64 (+.f64 (pow.f64 (+.f64 (/.f64 1 x) 3/2) 2) (-.f64 1 (*.f64 (+.f64 (/.f64 1 x) 3/2) -1)))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (neg.f64 (+.f64 (pow.f64 (+.f64 (/.f64 1 x) 3/2) 2) -1)) (neg.f64 (+.f64 (/.f64 1 x) 5/2)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (+.f64 (pow.f64 x -3) 1/8) (+.f64 (pow.f64 x -2) (-.f64 1/4 (*.f64 (/.f64 1 x) 1/2))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (-.f64 (pow.f64 x -2) 1/4) (-.f64 (/.f64 1 x) 1/2))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (-.f64 1 (pow.f64 (+.f64 (/.f64 1 x) 3/2) 2)) (-.f64 -1 (+.f64 (/.f64 1 x) 3/2)))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (+.f64 (/.f64 1 x) 1/2) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (+.f64 (/.f64 1 x) 1/2) 3) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (cbrt.f64 (+.f64 (/.f64 1 x) 1/2)) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (sqrt.f64 (+.f64 (/.f64 1 x) 1/2)) 2)))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f64 (pow.f64 (+.f64 (/.f64 1 x) 1/2) 2))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (exp.f64 (+.f64 (/.f64 1 x) 1/2)))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (pow.f64 (+.f64 (/.f64 1 x) 1/2) 3))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (+.f64 (/.f64 1 x) 1/2)))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (log.f64 (+.f64 (/.f64 1 x) 1/2)))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (+.f64 (/.f64 1 x) 1/2)))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 1 (/.f64 1 x) 1/2)))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 1 (+.f64 (/.f64 1 x) 3/2) -1)))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (pow.f64 (cbrt.f64 (+.f64 (/.f64 1 x) 3/2)) 2) (cbrt.f64 (+.f64 (/.f64 1 x) 3/2)) -1)))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (cbrt.f64 (pow.f64 x -2)) (/.f64 1 (cbrt.f64 x)) 1/2)))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (sqrt.f64 (+.f64 (/.f64 1 x) 3/2)) (sqrt.f64 (+.f64 (/.f64 1 x) 3/2)) -1)))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (pow.f64 x -1/2) (pow.f64 x -1/2) 1/2)))))

simplify9.0ms (0.2%)

Algorithm

1×	egg-herbie

Rules

1×	`+-commutative_binary64`
1×	`1-exp_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	6	69
1	9	69

Stop Event

1×

saturated

Counts

48 → 40

Calls

Call 1

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

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

localize23.0ms (0.6%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.0b	(-.f64 (+.f64 1 (/.f64 (-.f64 1/4 (pow.f64 x -2)) (-.f64 1/2 (/.f64 1 x)))) 1)
	18.6b	(/.f64 (-.f64 1/4 (pow.f64 x -2)) (-.f64 1/2 (/.f64 1 x)))

Compiler

Compiled 61 to 50 computations (18% saved)

series3.0ms (0.1%)

Counts

1 → 12

Calls

3 calls:

Time

Variable

Point

Expression

1.0ms

-inf

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

1.0ms

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

1.0ms

inf

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

rewrite102.0ms (2.7%)

Algorithm

1×	batch-egg-rewrite

Rules

783×	`prod-diff_binary64`
534×	`fma-def_binary64`
281×	`fma-neg_binary64`
243×	`expm1-udef_binary64`
243×	`log1p-udef_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	13	22
1	317	7
2	4453	7

Stop Event

1×	node limit

Counts

1 → 201

Calls

Call 1

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

Outputs

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

simplify10.0ms (0.3%)

Algorithm

1×	egg-herbie

Rules

1×	`+-commutative_binary64`
1×	`1-exp_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	6	69
1	9	69

Stop Event

1×

saturated

Counts

213 → 203

Calls

Call 1

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

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

localize27.0ms (0.7%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(-.f64 (+.f64 (/.f64 1 x) 3/2) -1)
✓	0.0b	(+.f64 (pow.f64 (+.f64 (/.f64 1 x) 3/2) 2) -1)
✓	0.2b	(pow.f64 (+.f64 (/.f64 1 x) 3/2) 2)
✓	18.6b	(/.f64 (+.f64 (pow.f64 (+.f64 (/.f64 1 x) 3/2) 2) -1) (-.f64 (+.f64 (/.f64 1 x) 3/2) -1))

Compiler

Compiled 54 to 46 computations (14.8% saved)

series4.0ms (0.1%)

Counts

4 → 48

Calls

12 calls:

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

rewrite86.0ms (2.2%)

Algorithm

1×	batch-egg-rewrite

Rules

535×	`log-prod_binary64`
323×	`pow2_binary64`
278×	`fma-def_binary64`
239×	`fma-neg_binary64`
222×	`pow1/3_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	12	52
1	277	37
2	3647	37

Stop Event

1×	node limit

Counts

4 → 197

Calls

Call 1

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

Outputs
((#(struct:change #<rule egg-rr> (2) ((x +.f64 (/.f64 1 x) 1/2)))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 3/2 (+.f64 (/.f64 1 x) -1))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (+.f64 (/.f64 1 x) 3/2) -1)))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 -1 (+.f64 (/.f64 1 x) 3/2))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 0 (+.f64 (/.f64 1 x) 1/2))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (log.f64 (pow.f64 (cbrt.f64 (exp.f64 (+.f64 (/.f64 1 x) 1/2))) 2)) (log.f64 (cbrt.f64 (exp.f64 (+.f64 (/.f64 1 x) 1/2)))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (log.f64 (sqrt.f64 (exp.f64 (+.f64 (/.f64 1 x) 1/2)))) (log.f64 (sqrt.f64 (exp.f64 (+.f64 (/.f64 1 x) 1/2)))))))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (+.f64 (/.f64 1 x) 3/2) 1)))) (#(struct:change #<rule egg-rr> (2) ((x .f64 1 (+.f64 (/.f64 1 x) 1/2))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (+.f64 (pow.f64 (+.f64 (/.f64 1 x) 3/2) 2) -1) (/.f64 1 (+.f64 (/.f64 1 x) 5/2)))))) 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((#(struct:change #<rule egg-rr> (2) ((x +.f64 1 (+.f64 (/.f64 1 x) 3/2))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (/.f64 1 x) 5/2)))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 3/2 (+.f64 (/.f64 1 x) 1))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (+.f64 (/.f64 1 x) 3/2) 1)))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 0 (+.f64 (/.f64 1 x) 5/2))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 5/2 (/.f64 1 x))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (log.f64 (pow.f64 (cbrt.f64 (exp.f64 (+.f64 (/.f64 1 x) 5/2))) 2)) (log.f64 (cbrt.f64 (exp.f64 (+.f64 (/.f64 1 x) 5/2)))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (log.f64 (sqrt.f64 (exp.f64 (+.f64 (/.f64 1 x) 5/2)))) (log.f64 (sqrt.f64 (exp.f64 (+.f64 (/.f64 1 x) 5/2)))))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 1 (+.f64 (/.f64 1 x) 5/2))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (+.f64 (pow.f64 (+.f64 (/.f64 1 x) 3/2) 2) -1) (/.f64 1 (+.f64 (/.f64 1 x) 1/2)))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (+.f64 (/.f64 1 x) 5/2) 1)))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (cbrt.f64 (+.f64 (/.f64 1 x) 5/2)) (pow.f64 (cbrt.f64 (+.f64 (/.f64 1 x) 5/2)) 2))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (pow.f64 (cbrt.f64 (+.f64 (/.f64 1 x) 5/2)) 2) (cbrt.f64 (+.f64 (/.f64 1 x) 5/2)))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (sqrt.f64 (+.f64 (/.f64 1 x) 5/2)) (sqrt.f64 (+.f64 (/.f64 1 x) 5/2)))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (+.f64 (pow.f64 (+.f64 (/.f64 1 x) 3/2) 3) 1) (/.f64 1 (+.f64 (pow.f64 (+.f64 (/.f64 1 x) 3/2) 2) (fma.f64 (+.f64 (/.f64 1 x) 3/2) -1 1))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 1 (/.f64 (+.f64 (pow.f64 (+.f64 (/.f64 1 x) 3/2) 2) (fma.f64 (+.f64 (/.f64 1 x) 3/2) -1 1)) (+.f64 (pow.f64 (+.f64 (/.f64 1 x) 3/2) 3) 1)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 1 (/.f64 (+.f64 (/.f64 1 x) 1/2) (+.f64 (pow.f64 (+.f64 (/.f64 1 x) 3/2) 2) -1)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (+.f64 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(#(struct:change #<rule egg-rr> (2) ((x pow.f64 (+.f64 (/.f64 1 x) 5/2) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (+.f64 (/.f64 1 x) 5/2) 2) 1/2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (+.f64 (/.f64 1 x) 5/2) 3) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (cbrt.f64 (+.f64 (/.f64 1 x) 5/2)) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (sqrt.f64 (+.f64 (/.f64 1 x) 5/2)) 2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (/.f64 (+.f64 (pow.f64 (+.f64 (/.f64 1 x) 3/2) 2) (fma.f64 (+.f64 (/.f64 1 x) 3/2) -1 1)) (+.f64 (pow.f64 (+.f64 (/.f64 1 x) 3/2) 3) 1)) -1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (/.f64 (+.f64 (/.f64 1 x) 1/2) (+.f64 (pow.f64 (+.f64 (/.f64 1 x) 3/2) 2) -1)) -1)))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f64 (pow.f64 (+.f64 (/.f64 1 x) 5/2) 2))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (exp.f64 (+.f64 (/.f64 1 x) 5/2)))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (+.f64 1 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2) 1)))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (pow.f64 (cbrt.f64 (+.f64 (/.f64 1 x) 3/2)) 2) (cbrt.f64 (+.f64 (/.f64 1 x) 3/2)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (/.f64 1 (cbrt.f64 x)) (cbrt.f64 (pow.f64 x -2)) 5/2)))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (cbrt.f64 (pow.f64 x -2)) (/.f64 1 (cbrt.f64 x)) 5/2)))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (sqrt.f64 (+.f64 (/.f64 1 x) 3/2)) (sqrt.f64 (+.f64 (/.f64 1 x) 3/2)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (pow.f64 x -1/2) (pow.f64 x -1/2) 5/2)))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (+.f64 27/8 (pow.f64 x -3)) (/.f64 1 (+.f64 (pow.f64 x -2) (-.f64 9/4 (/.f64 3/2 x)))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (+.f64 (pow.f64 x -2) -9/4) (/.f64 1 (+.f64 (/.f64 1 x) -3/2)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (sqrt.f64 (cbrt.f64 (pow.f64 (+.f64 (/.f64 1 x) 3/2) 4))) (sqrt.f64 (pow.f64 (cbrt.f64 (+.f64 (/.f64 1 x) 3/2)) 2)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (/.f64 1 (pow.f64 (cbrt.f64 x) 2)) (/.f64 1 (cbrt.f64 x)) 5/2)))))

simplify117.0ms (3.1%)

Algorithm

1×	egg-herbie

Rules

793×	`associate-/r/_binary64`
720×	`fma-def_binary64`
586×	`sqr-pow_binary64`
505×	`associate-/l/_binary64`
434×	`unswap-sqr_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	22	402
1	44	402
2	64	402
3	81	402
4	128	402
5	309	402
6	1071	402
7	3130	402
8	3585	402
9	3943	402
10	4236	402
11	4618	402
12	5138	402
13	6642	402
14	7919	402

Stop Event

1×	node limit

Counts

245 → 215

Calls

Call 1

Inputs
(/.f64 1 x)
(+.f64 1/2 (/.f64 1 x))
(+.f64 1/2 (/.f64 1 x))
(+.f64 1/2 (/.f64 1 x))
1/2
(+.f64 1/2 (/.f64 1 x))
(+.f64 1/2 (/.f64 1 x))
(+.f64 1/2 (/.f64 1 x))
1/2
(+.f64 1/2 (/.f64 1 x))
(+.f64 1/2 (/.f64 1 x))
(+.f64 1/2 (/.f64 1 x))
(/.f64 1 (pow.f64 x 2))
(+.f64 (/.f64 1 (pow.f64 x 2)) (*.f64 3 (/.f64 1 x)))
(+.f64 (*.f64 3 (/.f64 1 x)) (+.f64 9/4 (/.f64 1 (pow.f64 x 2))))
(+.f64 (*.f64 3 (/.f64 1 x)) (+.f64 9/4 (/.f64 1 (pow.f64 x 2))))
9/4
(+.f64 9/4 (*.f64 3 (/.f64 1 x)))
(+.f64 (*.f64 3 (/.f64 1 x)) (+.f64 9/4 (/.f64 1 (pow.f64 x 2))))
(+.f64 (*.f64 3 (/.f64 1 x)) (+.f64 9/4 (/.f64 1 (pow.f64 x 2))))
9/4
(+.f64 9/4 (*.f64 3 (/.f64 1 x)))
(+.f64 (*.f64 3 (/.f64 1 x)) (+.f64 9/4 (/.f64 1 (pow.f64 x 2))))
(+.f64 (*.f64 3 (/.f64 1 x)) (+.f64 9/4 (/.f64 1 (pow.f64 x 2))))
(/.f64 1 (pow.f64 x 2))
(+.f64 (/.f64 1 (pow.f64 x 2)) (*.f64 3 (/.f64 1 x)))
(+.f64 (*.f64 3 (/.f64 1 x)) (+.f64 5/4 (/.f64 1 (pow.f64 x 2))))
(+.f64 (*.f64 3 (/.f64 1 x)) (+.f64 5/4 (/.f64 1 (pow.f64 x 2))))
5/4
(+.f64 5/4 (*.f64 3 (/.f64 1 x)))
(+.f64 (*.f64 3 (/.f64 1 x)) (+.f64 5/4 (/.f64 1 (pow.f64 x 2))))
(+.f64 (*.f64 3 (/.f64 1 x)) (+.f64 5/4 (/.f64 1 (pow.f64 x 2))))
5/4
(+.f64 5/4 (*.f64 3 (/.f64 1 x)))
(+.f64 (*.f64 3 (/.f64 1 x)) (+.f64 5/4 (/.f64 1 (pow.f64 x 2))))
(+.f64 (*.f64 3 (/.f64 1 x)) (+.f64 5/4 (/.f64 1 (pow.f64 x 2))))
(/.f64 1 x)
(+.f64 5/2 (/.f64 1 x))
(+.f64 5/2 (/.f64 1 x))
(+.f64 5/2 (/.f64 1 x))
5/2
(+.f64 5/2 (/.f64 1 x))
(+.f64 5/2 (/.f64 1 x))
(+.f64 5/2 (/.f64 1 x))
5/2
(+.f64 5/2 (/.f64 1 x))
(+.f64 5/2 (/.f64 1 x))
(+.f64 5/2 (/.f64 1 x))

Outputs
(/.f64 1 x)
(+.f64 1/2 (/.f64 1 x))
(+.f64 (/.f64 1 x) 1/2)
(+.f64 1/2 (/.f64 1 x))
(+.f64 (/.f64 1 x) 1/2)
(+.f64 1/2 (/.f64 1 x))
(+.f64 (/.f64 1 x) 1/2)
1/2
(+.f64 1/2 (/.f64 1 x))
(+.f64 (/.f64 1 x) 1/2)
(+.f64 1/2 (/.f64 1 x))
(+.f64 (/.f64 1 x) 1/2)
(+.f64 1/2 (/.f64 1 x))
(+.f64 (/.f64 1 x) 1/2)
1/2
(+.f64 1/2 (/.f64 1 x))
(+.f64 (/.f64 1 x) 1/2)
(+.f64 1/2 (/.f64 1 x))
(+.f64 (/.f64 1 x) 1/2)
(+.f64 1/2 (/.f64 1 x))
(+.f64 (/.f64 1 x) 1/2)
(/.f64 1 (pow.f64 x 2))
(/.f64 1 (*.f64 x x))
(+.f64 (/.f64 1 (pow.f64 x 2)) (*.f64 3 (/.f64 1 x)))
(+.f64 (/.f64 1 (*.f64 x x)) (/.f64 3 x))
(+.f64 (*.f64 3 (/.f64 1 x)) (+.f64 9/4 (/.f64 1 (pow.f64 x 2))))
(+.f64 (/.f64 3 x) (+.f64 (/.f64 1 (*.f64 x x)) 9/4))
(+.f64 (/.f64 1 (*.f64 x x)) (+.f64 (/.f64 3 x) 9/4))
(+.f64 (*.f64 3 (/.f64 1 x)) (+.f64 9/4 (/.f64 1 (pow.f64 x 2))))
(+.f64 (/.f64 3 x) (+.f64 (/.f64 1 (*.f64 x x)) 9/4))
(+.f64 (/.f64 1 (*.f64 x x)) (+.f64 (/.f64 3 x) 9/4))
9/4
(+.f64 9/4 (*.f64 3 (/.f64 1 x)))
(+.f64 (/.f64 3 x) 9/4)
(+.f64 (*.f64 3 (/.f64 1 x)) (+.f64 9/4 (/.f64 1 (pow.f64 x 2))))
(+.f64 (/.f64 3 x) (+.f64 (/.f64 1 (*.f64 x x)) 9/4))
(+.f64 (/.f64 1 (*.f64 x x)) (+.f64 (/.f64 3 x) 9/4))
(+.f64 (*.f64 3 (/.f64 1 x)) (+.f64 9/4 (/.f64 1 (pow.f64 x 2))))
(+.f64 (/.f64 3 x) (+.f64 (/.f64 1 (*.f64 x x)) 9/4))
(+.f64 (/.f64 1 (*.f64 x x)) (+.f64 (/.f64 3 x) 9/4))
9/4
(+.f64 9/4 (*.f64 3 (/.f64 1 x)))
(+.f64 (/.f64 3 x) 9/4)
(+.f64 (*.f64 3 (/.f64 1 x)) (+.f64 9/4 (/.f64 1 (pow.f64 x 2))))
(+.f64 (/.f64 3 x) (+.f64 (/.f64 1 (*.f64 x x)) 9/4))
(+.f64 (/.f64 1 (*.f64 x x)) (+.f64 (/.f64 3 x) 9/4))
(+.f64 (*.f64 3 (/.f64 1 x)) (+.f64 9/4 (/.f64 1 (pow.f64 x 2))))
(+.f64 (/.f64 3 x) (+.f64 (/.f64 1 (*.f64 x x)) 9/4))
(+.f64 (/.f64 1 (*.f64 x x)) (+.f64 (/.f64 3 x) 9/4))
(/.f64 1 (pow.f64 x 2))
(/.f64 1 (*.f64 x x))
(+.f64 (/.f64 1 (pow.f64 x 2)) (*.f64 3 (/.f64 1 x)))
(+.f64 (/.f64 1 (*.f64 x x)) (/.f64 3 x))
(+.f64 (*.f64 3 (/.f64 1 x)) (+.f64 5/4 (/.f64 1 (pow.f64 x 2))))
(+.f64 (/.f64 3 x) (+.f64 (/.f64 1 (*.f64 x x)) 5/4))
(+.f64 (/.f64 1 (*.f64 x x)) (+.f64 (/.f64 3 x) 5/4))
(+.f64 (*.f64 3 (/.f64 1 x)) (+.f64 5/4 (/.f64 1 (pow.f64 x 2))))
(+.f64 (/.f64 3 x) (+.f64 (/.f64 1 (*.f64 x x)) 5/4))
(+.f64 (/.f64 1 (*.f64 x x)) (+.f64 (/.f64 3 x) 5/4))
5/4
(+.f64 5/4 (*.f64 3 (/.f64 1 x)))
(+.f64 (/.f64 3 x) 5/4)
(+.f64 (*.f64 3 (/.f64 1 x)) (+.f64 5/4 (/.f64 1 (pow.f64 x 2))))
(+.f64 (/.f64 3 x) (+.f64 (/.f64 1 (*.f64 x x)) 5/4))
(+.f64 (/.f64 1 (*.f64 x x)) (+.f64 (/.f64 3 x) 5/4))
(+.f64 (*.f64 3 (/.f64 1 x)) (+.f64 5/4 (/.f64 1 (pow.f64 x 2))))
(+.f64 (/.f64 3 x) (+.f64 (/.f64 1 (*.f64 x x)) 5/4))
(+.f64 (/.f64 1 (*.f64 x x)) (+.f64 (/.f64 3 x) 5/4))
5/4
(+.f64 5/4 (*.f64 3 (/.f64 1 x)))
(+.f64 (/.f64 3 x) 5/4)
(+.f64 (*.f64 3 (/.f64 1 x)) (+.f64 5/4 (/.f64 1 (pow.f64 x 2))))
(+.f64 (/.f64 3 x) (+.f64 (/.f64 1 (*.f64 x x)) 5/4))
(+.f64 (/.f64 1 (*.f64 x x)) (+.f64 (/.f64 3 x) 5/4))
(+.f64 (*.f64 3 (/.f64 1 x)) (+.f64 5/4 (/.f64 1 (pow.f64 x 2))))
(+.f64 (/.f64 3 x) (+.f64 (/.f64 1 (*.f64 x x)) 5/4))
(+.f64 (/.f64 1 (*.f64 x x)) (+.f64 (/.f64 3 x) 5/4))
(/.f64 1 x)
(+.f64 5/2 (/.f64 1 x))
(+.f64 (/.f64 1 x) 5/2)
(+.f64 5/2 (/.f64 1 x))
(+.f64 (/.f64 1 x) 5/2)
(+.f64 5/2 (/.f64 1 x))
(+.f64 (/.f64 1 x) 5/2)
5/2
(+.f64 5/2 (/.f64 1 x))
(+.f64 (/.f64 1 x) 5/2)
(+.f64 5/2 (/.f64 1 x))
(+.f64 (/.f64 1 x) 5/2)
(+.f64 5/2 (/.f64 1 x))
(+.f64 (/.f64 1 x) 5/2)
5/2
(+.f64 5/2 (/.f64 1 x))
(+.f64 (/.f64 1 x) 5/2)
(+.f64 5/2 (/.f64 1 x))
(+.f64 (/.f64 1 x) 5/2)
(+.f64 5/2 (/.f64 1 x))
(+.f64 (/.f64 1 x) 5/2)

localize22.0ms (0.6%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.6b	(pow.f64 (cbrt.f64 (+.f64 (/.f64 1 x) 3/2)) 2)
✓	0.7b	(cbrt.f64 (+.f64 (/.f64 1 x) 3/2))
✓	0.7b	(fma.f64 (pow.f64 (cbrt.f64 (+.f64 (/.f64 1 x) 3/2)) 2) (cbrt.f64 (+.f64 (/.f64 1 x) 3/2)) -1)

Compiler

Compiled 44 to 37 computations (15.9% saved)

series10.0ms (0.3%)

Counts

3 → 25

Calls

9 calls:

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

rewrite61.0ms (1.6%)

Algorithm

1×	batch-egg-rewrite

Rules

949×	`pow1_binary64`
890×	`add-log-exp_binary64`
888×	`log1p-expm1-u_binary64`
888×	`expm1-log1p-u_binary64`
105×	`add-sqr-sqrt_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	11	31
1	227	28
2	2496	28

Stop Event

1×	node limit

Counts

3 → 64

Calls

Call 1

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

Outputs

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

((#(struct:change #<rule egg-rr> (2) ((x -.f64 (exp.f64 (log1p.f64 (cbrt.f64 (+.f64 (/.f64 1 x) 3/2)))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 1 (cbrt.f64 (+.f64 (/.f64 1 x) 3/2)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 (+.f64 (/.f64 1 x) 3/2)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (cbrt.f64 (cbrt.f64 (+.f64 (/.f64 1 x) 3/2))) 2) (cbrt.f64 (cbrt.f64 (+.f64 (/.f64 1 x) 3/2))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 (cbrt.f64 (+.f64 (/.f64 1 x) 3/2))) (pow.f64 (cbrt.f64 (cbrt.f64 (+.f64 (/.f64 1 x) 3/2))) 2))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (+.f64 (/.f64 1 x) 3/2) 1/6) (pow.f64 (+.f64 (/.f64 1 x) 3/2) 1/6))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (sqrt.f64 (cbrt.f64 (pow.f64 (cbrt.f64 (+.f64 (/.f64 1 x) 3/2)) 4))) (sqrt.f64 (pow.f64 (cbrt.f64 (cbrt.f64 (+.f64 (/.f64 1 x) 3/2))) 2)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 1 1/3) (cbrt.f64 (+.f64 (/.f64 1 x) 3/2)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (sqrt.f64 (+.f64 (/.f64 1 x) 3/2)) 1/3) (pow.f64 (sqrt.f64 (+.f64 (/.f64 1 x) 3/2)) 1/3))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (cbrt.f64 (+.f64 27/8 (pow.f64 x -3))) (cbrt.f64 (+.f64 (pow.f64 x -2) (-.f64 9/4 (/.f64 3/2 x)))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (cbrt.f64 (+.f64 (pow.f64 x -2) -9/4)) (cbrt.f64 (+.f64 (/.f64 1 x) -3/2)))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (+.f64 (/.f64 1 x) 3/2) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (cbrt.f64 (+.f64 (/.f64 1 x) 3/2)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (cbrt.f64 (+.f64 (/.f64 1 x) 3/2)) 2) 1/2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (cbrt.f64 (cbrt.f64 (+.f64 (/.f64 1 x) 3/2))) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (+.f64 (/.f64 1 x) 3/2) 1/6) 2)))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f64 (pow.f64 (cbrt.f64 (+.f64 (/.f64 1 x) 3/2)) 2))))) (#(struct:change #<rule egg-rr> (2) ((x fabs.f64 (cbrt.f64 (+.f64 (/.f64 1 x) 3/2)))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (exp.f64 (cbrt.f64 (+.f64 (/.f64 1 x) 3/2))))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (+.f64 1 (expm1.f64 (cbrt.f64 (+.f64 (/.f64 1 x) 3/2)))))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (cbrt.f64 (+.f64 (/.f64 1 x) 3/2))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (log.f64 (cbrt.f64 (+.f64 (/.f64 1 x) 3/2))))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (cbrt.f64 (+.f64 (/.f64 1 x) 3/2))))))))

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

simplify54.0ms (1.4%)

Algorithm

1×	egg-herbie

Rules

831×	`times-frac_binary64`
776×	`associate-+l+_binary64`
569×	`associate-l_binary64`
488×	`associate-r_binary64`
425×	`associate-/r*_binary64`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	156	1316
1	522	1087
2	1950	853

Stop Event

1×	node limit

Counts

89 → 93

Calls

Call 1

Inputs
-1
1/2
(+.f64 1/2 (+.f64 (.f64 2/3 (.f64 (pow.f64 (.f64 1 (pow.f64 (cbrt.f64 3/2) 4)) 1/3) (/.f64 1 x))) (.f64 1/3 (.f64 (pow.f64 (.f64 1 (pow.f64 (cbrt.f64 3/2) 4)) 1/3) (/.f64 1 x)))))
(+.f64 (/.f64 (.f64 (+.f64 (.f64 -2/9 (pow.f64 (/.f64 1 (pow.f64 (cbrt.f64 3/2) 4)) 1/3)) (.f64 1/9 (pow.f64 (/.f64 1 (pow.f64 (cbrt.f64 3/2) 4)) 1/3))) (cbrt.f64 3/2)) (pow.f64 x 2)) (+.f64 1/2 (+.f64 (.f64 2/3 (.f64 (pow.f64 (.f64 1 (pow.f64 (cbrt.f64 3/2) 4)) 1/3) (/.f64 1 x))) (+.f64 (.f64 1/3 (.f64 (pow.f64 (.f64 1 (pow.f64 (cbrt.f64 3/2) 4)) 1/3) (/.f64 1 x))) (+.f64 (.f64 2/9 (.f64 (pow.f64 (/.f64 1 (cbrt.f64 3/2)) 1/3) (/.f64 1 (pow.f64 x 2)))) (.f64 -1/9 (*.f64 (pow.f64 (/.f64 1 (cbrt.f64 3/2)) 1/3) (/.f64 1 (pow.f64 x 2)))))))))
(+.f64 1/2 (+.f64 (.f64 1/3 (.f64 (pow.f64 (/.f64 1 (pow.f64 (cbrt.f64 3/2) 2)) 1/3) (/.f64 (+.f64 (.f64 -2/9 (pow.f64 (/.f64 1 (pow.f64 (cbrt.f64 3/2) 4)) 1/3)) (.f64 1/9 (pow.f64 (/.f64 1 (pow.f64 (cbrt.f64 3/2) 4)) 1/3))) (pow.f64 x 3)))) (+.f64 (.f64 -1/3 (/.f64 (+.f64 (.f64 1/27 (/.f64 1 (pow.f64 (cbrt.f64 3/2) 2))) (.f64 -2/9 (.f64 (pow.f64 1 1/3) (/.f64 1 (pow.f64 (cbrt.f64 3/2) 2))))) (pow.f64 x 3))) (+.f64 (.f64 -1/9 (.f64 (pow.f64 (/.f64 1 (cbrt.f64 3/2)) 1/3) (/.f64 1 (pow.f64 x 2)))) (+.f64 (/.f64 (.f64 (+.f64 (.f64 -2/9 (pow.f64 (/.f64 1 (pow.f64 (cbrt.f64 3/2) 4)) 1/3)) (.f64 1/9 (pow.f64 (/.f64 1 (pow.f64 (cbrt.f64 3/2) 4)) 1/3))) (cbrt.f64 3/2)) (pow.f64 x 2)) (+.f64 (.f64 2/3 (.f64 (pow.f64 (.f64 1 (pow.f64 (cbrt.f64 3/2) 4)) 1/3) (/.f64 1 x))) (+.f64 (.f64 1/3 (.f64 (pow.f64 (.f64 1 (pow.f64 (cbrt.f64 3/2) 4)) 1/3) (/.f64 1 x))) (+.f64 (.f64 -2/27 (.f64 (pow.f64 1 1/3) (/.f64 1 (.f64 (pow.f64 (cbrt.f64 3/2) 2) (pow.f64 x 3))))) (+.f64 (.f64 2/9 (.f64 (pow.f64 (/.f64 1 (cbrt.f64 3/2)) 1/3) (/.f64 1 (pow.f64 x 2)))) (/.f64 (.f64 (cbrt.f64 3/2) (+.f64 (.f64 -2/3 (/.f64 (+.f64 (.f64 1/27 (/.f64 1 (pow.f64 (cbrt.f64 3/2) 2))) (.f64 -2/9 (.f64 (pow.f64 1 1/3) (/.f64 1 (pow.f64 (cbrt.f64 3/2) 2))))) (cbrt.f64 3/2))) (.f64 -4/81 (pow.f64 1 1/3)))) (pow.f64 x 3)))))))))))
1/2
(+.f64 (.f64 -1 (/.f64 (+.f64 (.f64 -2/3 (pow.f64 (.f64 1 (pow.f64 (cbrt.f64 3/2) 4)) 1/3)) (.f64 -1/3 (pow.f64 (*.f64 1 (pow.f64 (cbrt.f64 3/2) 4)) 1/3))) x)) 1/2)
(+.f64 (/.f64 (.f64 (+.f64 (.f64 -2/9 (pow.f64 (/.f64 1 (pow.f64 (cbrt.f64 3/2) 4)) 1/3)) (.f64 1/9 (pow.f64 (/.f64 1 (pow.f64 (cbrt.f64 3/2) 4)) 1/3))) (cbrt.f64 3/2)) (pow.f64 x 2)) (+.f64 (.f64 -1 (/.f64 (+.f64 (.f64 -2/3 (pow.f64 (.f64 1 (pow.f64 (cbrt.f64 3/2) 4)) 1/3)) (.f64 -1/3 (pow.f64 (.f64 1 (pow.f64 (cbrt.f64 3/2) 4)) 1/3))) x)) (+.f64 1/2 (+.f64 (.f64 2/9 (.f64 (pow.f64 (/.f64 1 (cbrt.f64 3/2)) 1/3) (/.f64 1 (pow.f64 x 2)))) (.f64 -1/9 (.f64 (pow.f64 (/.f64 1 (cbrt.f64 3/2)) 1/3) (/.f64 1 (pow.f64 x 2))))))))
(+.f64 (/.f64 (.f64 (+.f64 (.f64 -2/9 (pow.f64 (/.f64 1 (pow.f64 (cbrt.f64 3/2) 4)) 1/3)) (.f64 1/9 (pow.f64 (/.f64 1 (pow.f64 (cbrt.f64 3/2) 4)) 1/3))) (cbrt.f64 3/2)) (pow.f64 x 2)) (+.f64 (.f64 -1 (/.f64 (+.f64 (.f64 -2/3 (pow.f64 (.f64 1 (pow.f64 (cbrt.f64 3/2) 4)) 1/3)) (.f64 -1/3 (pow.f64 (.f64 1 (pow.f64 (cbrt.f64 3/2) 4)) 1/3))) x)) (+.f64 (.f64 -1 (/.f64 (+.f64 (.f64 1/3 (-.f64 (.f64 1/27 (/.f64 1 (pow.f64 (cbrt.f64 3/2) 2))) (.f64 2/9 (.f64 (pow.f64 1 1/3) (/.f64 1 (pow.f64 (cbrt.f64 3/2) 2)))))) (+.f64 (.f64 (+.f64 (.f64 2/3 (/.f64 (-.f64 (.f64 1/27 (/.f64 1 (pow.f64 (cbrt.f64 3/2) 2))) (.f64 2/9 (.f64 (pow.f64 1 1/3) (/.f64 1 (pow.f64 (cbrt.f64 3/2) 2))))) (cbrt.f64 3/2))) (.f64 4/81 (pow.f64 1 1/3))) (cbrt.f64 3/2)) (+.f64 (.f64 -1/3 (.f64 (pow.f64 (/.f64 1 (pow.f64 (cbrt.f64 3/2) 2)) 1/3) (+.f64 (.f64 -2/9 (pow.f64 (/.f64 1 (pow.f64 (cbrt.f64 3/2) 4)) 1/3)) (.f64 1/9 (pow.f64 (/.f64 1 (pow.f64 (cbrt.f64 3/2) 4)) 1/3))))) (.f64 2/27 (.f64 (pow.f64 1 1/3) (/.f64 1 (pow.f64 (cbrt.f64 3/2) 2))))))) (pow.f64 x 3))) (+.f64 1/2 (+.f64 (.f64 2/9 (.f64 (pow.f64 (/.f64 1 (cbrt.f64 3/2)) 1/3) (/.f64 1 (pow.f64 x 2)))) (.f64 -1/9 (*.f64 (pow.f64 (/.f64 1 (cbrt.f64 3/2)) 1/3) (/.f64 1 (pow.f64 x 2)))))))))
(cbrt.f64 3/2)
(+.f64 (.f64 1/3 (.f64 (pow.f64 (/.f64 1 (pow.f64 (cbrt.f64 3/2) 2)) 1/3) (/.f64 1 x))) (cbrt.f64 3/2))
(+.f64 (.f64 1/3 (.f64 (pow.f64 (/.f64 1 (pow.f64 (cbrt.f64 3/2) 2)) 1/3) (/.f64 1 x))) (+.f64 (.f64 -1/9 (.f64 (pow.f64 (/.f64 1 (pow.f64 (cbrt.f64 3/2) 7)) 1/3) (/.f64 1 (pow.f64 x 2)))) (cbrt.f64 3/2)))
(+.f64 (.f64 1/3 (.f64 (pow.f64 (/.f64 1 (pow.f64 (cbrt.f64 3/2) 2)) 1/3) (/.f64 1 x))) (+.f64 (.f64 -1/9 (.f64 (pow.f64 (/.f64 1 (pow.f64 (cbrt.f64 3/2) 7)) 1/3) (/.f64 1 (pow.f64 x 2)))) (+.f64 (cbrt.f64 3/2) (.f64 -1/3 (/.f64 (+.f64 (.f64 1/27 (/.f64 1 (pow.f64 (cbrt.f64 3/2) 2))) (.f64 -2/9 (.f64 (pow.f64 1 1/3) (/.f64 1 (pow.f64 (cbrt.f64 3/2) 2))))) (*.f64 (pow.f64 (cbrt.f64 3/2) 2) (pow.f64 x 3)))))))
(cbrt.f64 3/2)
(+.f64 (.f64 1/3 (.f64 (pow.f64 (/.f64 1 (pow.f64 (cbrt.f64 3/2) 2)) 1/3) (/.f64 1 x))) (cbrt.f64 3/2))
(+.f64 (.f64 1/3 (.f64 (pow.f64 (/.f64 1 (pow.f64 (cbrt.f64 3/2) 2)) 1/3) (/.f64 1 x))) (+.f64 (.f64 -1/9 (.f64 (pow.f64 (/.f64 1 (pow.f64 (cbrt.f64 3/2) 7)) 1/3) (/.f64 1 (pow.f64 x 2)))) (cbrt.f64 3/2)))
(+.f64 (.f64 -1/3 (/.f64 (-.f64 (.f64 1/27 (/.f64 1 (pow.f64 (cbrt.f64 3/2) 2))) (.f64 2/9 (.f64 (pow.f64 1 1/3) (/.f64 1 (pow.f64 (cbrt.f64 3/2) 2))))) (.f64 (pow.f64 (cbrt.f64 3/2) 2) (pow.f64 x 3)))) (+.f64 (.f64 1/3 (.f64 (pow.f64 (/.f64 1 (pow.f64 (cbrt.f64 3/2) 2)) 1/3) (/.f64 1 x))) (+.f64 (.f64 -1/9 (*.f64 (pow.f64 (/.f64 1 (pow.f64 (cbrt.f64 3/2) 7)) 1/3) (/.f64 1 (pow.f64 x 2)))) (cbrt.f64 3/2))))
(pow.f64 (cbrt.f64 3/2) 2)
(+.f64 (pow.f64 (cbrt.f64 3/2) 2) (.f64 2/3 (.f64 (pow.f64 (*.f64 1 (cbrt.f64 3/2)) 1/3) (/.f64 1 x))))
(+.f64 (pow.f64 (cbrt.f64 3/2) 2) (+.f64 (.f64 1/9 (.f64 (pow.f64 (/.f64 1 (pow.f64 (cbrt.f64 3/2) 4)) 1/3) (/.f64 1 (pow.f64 x 2)))) (+.f64 (.f64 2/3 (.f64 (pow.f64 (.f64 1 (cbrt.f64 3/2)) 1/3) (/.f64 1 x))) (.f64 -2/9 (*.f64 (pow.f64 (/.f64 1 (pow.f64 (cbrt.f64 3/2) 4)) 1/3) (/.f64 1 (pow.f64 x 2)))))))
(+.f64 (pow.f64 (cbrt.f64 3/2) 2) (+.f64 (.f64 1/9 (.f64 (pow.f64 (/.f64 1 (pow.f64 (cbrt.f64 3/2) 4)) 1/3) (/.f64 1 (pow.f64 x 2)))) (+.f64 (.f64 2/3 (.f64 (pow.f64 (.f64 1 (cbrt.f64 3/2)) 1/3) (/.f64 1 x))) (+.f64 (.f64 -2/3 (/.f64 (+.f64 (.f64 1/27 (/.f64 1 (pow.f64 (cbrt.f64 3/2) 2))) (.f64 -2/9 (.f64 (pow.f64 1 1/3) (/.f64 1 (pow.f64 (cbrt.f64 3/2) 2))))) (.f64 (cbrt.f64 3/2) (pow.f64 x 3)))) (+.f64 (.f64 -2/9 (.f64 (pow.f64 (/.f64 1 (pow.f64 (cbrt.f64 3/2) 4)) 1/3) (/.f64 1 (pow.f64 x 2)))) (.f64 -4/81 (.f64 (pow.f64 1 1/3) (/.f64 1 (pow.f64 x 3)))))))))
(pow.f64 (cbrt.f64 3/2) 2)
(+.f64 (pow.f64 (cbrt.f64 3/2) 2) (.f64 2/3 (.f64 (pow.f64 (*.f64 1 (cbrt.f64 3/2)) 1/3) (/.f64 1 x))))
(+.f64 (pow.f64 (cbrt.f64 3/2) 2) (+.f64 (.f64 1/9 (.f64 (pow.f64 (/.f64 1 (pow.f64 (cbrt.f64 3/2) 4)) 1/3) (/.f64 1 (pow.f64 x 2)))) (+.f64 (.f64 2/3 (.f64 (pow.f64 (.f64 1 (cbrt.f64 3/2)) 1/3) (/.f64 1 x))) (.f64 -2/9 (*.f64 (pow.f64 (/.f64 1 (pow.f64 (cbrt.f64 3/2) 4)) 1/3) (/.f64 1 (pow.f64 x 2)))))))
(+.f64 (.f64 -1 (/.f64 (+.f64 (.f64 2/3 (/.f64 (-.f64 (.f64 1/27 (/.f64 1 (pow.f64 (cbrt.f64 3/2) 2))) (.f64 2/9 (.f64 (pow.f64 1 1/3) (/.f64 1 (pow.f64 (cbrt.f64 3/2) 2))))) (cbrt.f64 3/2))) (.f64 4/81 (pow.f64 1 1/3))) (pow.f64 x 3))) (+.f64 (pow.f64 (cbrt.f64 3/2) 2) (+.f64 (.f64 1/9 (.f64 (pow.f64 (/.f64 1 (pow.f64 (cbrt.f64 3/2) 4)) 1/3) (/.f64 1 (pow.f64 x 2)))) (+.f64 (.f64 2/3 (.f64 (pow.f64 (.f64 1 (cbrt.f64 3/2)) 1/3) (/.f64 1 x))) (.f64 -2/9 (*.f64 (pow.f64 (/.f64 1 (pow.f64 (cbrt.f64 3/2) 4)) 1/3) (/.f64 1 (pow.f64 x 2))))))))

Outputs
-1
1/2
(+.f64 1/2 (+.f64 (.f64 2/3 (.f64 (pow.f64 (.f64 1 (pow.f64 (cbrt.f64 3/2) 4)) 1/3) (/.f64 1 x))) (.f64 1/3 (.f64 (pow.f64 (.f64 1 (pow.f64 (cbrt.f64 3/2) 4)) 1/3) (/.f64 1 x)))))
(+.f64 1/2 (.f64 (.f64 (cbrt.f64 (pow.f64 (cbrt.f64 3/2) 4)) (/.f64 1 x)) 1))
(+.f64 1/2 (/.f64 (cbrt.f64 (pow.f64 (cbrt.f64 3/2) 4)) x))
(+.f64 1/2 (/.f64 (cbrt.f64 (*.f64 3/2 (cbrt.f64 3/2))) x))
(+.f64 (/.f64 (.f64 (+.f64 (.f64 -2/9 (pow.f64 (/.f64 1 (pow.f64 (cbrt.f64 3/2) 4)) 1/3)) (.f64 1/9 (pow.f64 (/.f64 1 (pow.f64 (cbrt.f64 3/2) 4)) 1/3))) (cbrt.f64 3/2)) (pow.f64 x 2)) (+.f64 1/2 (+.f64 (.f64 2/3 (.f64 (pow.f64 (.f64 1 (pow.f64 (cbrt.f64 3/2) 4)) 1/3) (/.f64 1 x))) (+.f64 (.f64 1/3 (.f64 (pow.f64 (.f64 1 (pow.f64 (cbrt.f64 3/2) 4)) 1/3) (/.f64 1 x))) (+.f64 (.f64 2/9 (.f64 (pow.f64 (/.f64 1 (cbrt.f64 3/2)) 1/3) (/.f64 1 (pow.f64 x 2)))) (.f64 -1/9 (*.f64 (pow.f64 (/.f64 1 (cbrt.f64 3/2)) 1/3) (/.f64 1 (pow.f64 x 2)))))))))
(+.f64 (/.f64 (.f64 (cbrt.f64 (/.f64 1 (pow.f64 (cbrt.f64 3/2) 4))) -1/9) (/.f64 (.f64 x x) (cbrt.f64 3/2))) (+.f64 1/2 (+.f64 (.f64 (.f64 (cbrt.f64 (pow.f64 (cbrt.f64 3/2) 4)) (/.f64 1 x)) 1) (.f64 (.f64 (cbrt.f64 (/.f64 1 (cbrt.f64 3/2))) (/.f64 1 (*.f64 x x))) 1/9))))
(+.f64 (/.f64 (cbrt.f64 (/.f64 1 (pow.f64 (cbrt.f64 3/2) 4))) (/.f64 (/.f64 x (/.f64 (cbrt.f64 3/2) x)) -1/9)) (+.f64 (/.f64 (cbrt.f64 (pow.f64 (cbrt.f64 3/2) 4)) x) (fma.f64 (/.f64 (cbrt.f64 (/.f64 1 (cbrt.f64 3/2))) (*.f64 x x)) 1/9 1/2)))
(+.f64 (fma.f64 (/.f64 (cbrt.f64 (/.f64 1 (cbrt.f64 3/2))) (.f64 x x)) 1/9 1/2) (fma.f64 (/.f64 (cbrt.f64 (/.f64 2/3 (cbrt.f64 3/2))) (/.f64 x -1/9)) (/.f64 (cbrt.f64 3/2) x) (/.f64 (cbrt.f64 (.f64 3/2 (cbrt.f64 3/2))) x)))
(+.f64 1/2 (+.f64 (.f64 1/3 (.f64 (pow.f64 (/.f64 1 (pow.f64 (cbrt.f64 3/2) 2)) 1/3) (/.f64 (+.f64 (.f64 -2/9 (pow.f64 (/.f64 1 (pow.f64 (cbrt.f64 3/2) 4)) 1/3)) (.f64 1/9 (pow.f64 (/.f64 1 (pow.f64 (cbrt.f64 3/2) 4)) 1/3))) (pow.f64 x 3)))) (+.f64 (.f64 -1/3 (/.f64 (+.f64 (.f64 1/27 (/.f64 1 (pow.f64 (cbrt.f64 3/2) 2))) (.f64 -2/9 (.f64 (pow.f64 1 1/3) (/.f64 1 (pow.f64 (cbrt.f64 3/2) 2))))) (pow.f64 x 3))) (+.f64 (.f64 -1/9 (.f64 (pow.f64 (/.f64 1 (cbrt.f64 3/2)) 1/3) (/.f64 1 (pow.f64 x 2)))) (+.f64 (/.f64 (.f64 (+.f64 (.f64 -2/9 (pow.f64 (/.f64 1 (pow.f64 (cbrt.f64 3/2) 4)) 1/3)) (.f64 1/9 (pow.f64 (/.f64 1 (pow.f64 (cbrt.f64 3/2) 4)) 1/3))) (cbrt.f64 3/2)) (pow.f64 x 2)) (+.f64 (.f64 2/3 (.f64 (pow.f64 (.f64 1 (pow.f64 (cbrt.f64 3/2) 4)) 1/3) (/.f64 1 x))) (+.f64 (.f64 1/3 (.f64 (pow.f64 (.f64 1 (pow.f64 (cbrt.f64 3/2) 4)) 1/3) (/.f64 1 x))) (+.f64 (.f64 -2/27 (.f64 (pow.f64 1 1/3) (/.f64 1 (.f64 (pow.f64 (cbrt.f64 3/2) 2) (pow.f64 x 3))))) (+.f64 (.f64 2/9 (.f64 (pow.f64 (/.f64 1 (cbrt.f64 3/2)) 1/3) (/.f64 1 (pow.f64 x 2)))) (/.f64 (.f64 (cbrt.f64 3/2) (+.f64 (.f64 -2/3 (/.f64 (+.f64 (.f64 1/27 (/.f64 1 (pow.f64 (cbrt.f64 3/2) 2))) (.f64 -2/9 (.f64 (pow.f64 1 1/3) (/.f64 1 (pow.f64 (cbrt.f64 3/2) 2))))) (cbrt.f64 3/2))) (.f64 -4/81 (pow.f64 1 1/3)))) (pow.f64 x 3)))))))))))
(+.f64 1/2 (fma.f64 1/3 (.f64 (cbrt.f64 (/.f64 1 (pow.f64 (cbrt.f64 3/2) 2))) (/.f64 (.f64 (cbrt.f64 (/.f64 1 (pow.f64 (cbrt.f64 3/2) 4))) -1/9) (pow.f64 x 3))) (fma.f64 -1/3 (/.f64 (+.f64 (/.f64 1/27 (pow.f64 (cbrt.f64 3/2) 2)) (.f64 -2/9 (/.f64 1 (pow.f64 (cbrt.f64 3/2) 2)))) (pow.f64 x 3)) (fma.f64 -1/9 (.f64 (cbrt.f64 (/.f64 1 (cbrt.f64 3/2))) (/.f64 1 (.f64 x x))) (+.f64 (/.f64 (.f64 (cbrt.f64 (/.f64 1 (pow.f64 (cbrt.f64 3/2) 4))) -1/9) (/.f64 (.f64 x x) (cbrt.f64 3/2))) (+.f64 (.f64 (.f64 (cbrt.f64 (pow.f64 (cbrt.f64 3/2) 4)) (/.f64 1 x)) 1) (fma.f64 -2/27 (/.f64 1 (.f64 (pow.f64 (cbrt.f64 3/2) 2) (pow.f64 x 3))) (fma.f64 2/9 (.f64 (cbrt.f64 (/.f64 1 (cbrt.f64 3/2))) (/.f64 1 (.f64 x x))) (/.f64 (cbrt.f64 3/2) (/.f64 (pow.f64 x 3) (fma.f64 -2/3 (/.f64 (+.f64 (/.f64 1/27 (pow.f64 (cbrt.f64 3/2) 2)) (*.f64 -2/9 (/.f64 1 (pow.f64 (cbrt.f64 3/2) 2)))) (cbrt.f64 3/2)) -4/81)))))))))))
(+.f64 1/2 (fma.f64 1/3 (.f64 (cbrt.f64 (/.f64 1 (pow.f64 (cbrt.f64 3/2) 2))) (/.f64 (cbrt.f64 (/.f64 1 (pow.f64 (cbrt.f64 3/2) 4))) (/.f64 (pow.f64 x 3) -1/9))) (fma.f64 -1/3 (/.f64 (.f64 (/.f64 1 (pow.f64 (cbrt.f64 3/2) 2)) -5/27) (pow.f64 x 3)) (+.f64 (+.f64 (/.f64 (cbrt.f64 (pow.f64 (cbrt.f64 3/2) 4)) x) (+.f64 (/.f64 -2/27 (.f64 (pow.f64 (cbrt.f64 3/2) 2) (pow.f64 x 3))) (fma.f64 2/9 (/.f64 (cbrt.f64 (/.f64 1 (cbrt.f64 3/2))) (.f64 x x)) (.f64 (/.f64 (cbrt.f64 3/2) (pow.f64 x 3)) (fma.f64 -2/3 (/.f64 (.f64 (/.f64 1 (pow.f64 (cbrt.f64 3/2) 2)) -5/27) (cbrt.f64 3/2)) -4/81))))) (fma.f64 (/.f64 (cbrt.f64 (/.f64 1 (cbrt.f64 3/2))) (*.f64 x x)) -1/9 (/.f64 (cbrt.f64 (/.f64 1 (pow.f64 (cbrt.f64 3/2) 4))) (/.f64 (/.f64 x (/.f64 (cbrt.f64 3/2) x)) -1/9)))))))
(+.f64 (/.f64 (.f64 (.f64 (cbrt.f64 (/.f64 1 (pow.f64 (cbrt.f64 3/2) 2))) (cbrt.f64 (/.f64 2/3 (cbrt.f64 3/2)))) -1/27) (pow.f64 x 3)) (+.f64 1/2 (fma.f64 -1/3 (/.f64 (/.f64 -5/27 (pow.f64 (cbrt.f64 3/2) 2)) (pow.f64 x 3)) (fma.f64 (/.f64 (cbrt.f64 (/.f64 1 (cbrt.f64 3/2))) (.f64 x x)) -1/9 (+.f64 (+.f64 (/.f64 (/.f64 -2/27 (pow.f64 (cbrt.f64 3/2) 2)) (pow.f64 x 3)) (fma.f64 2/9 (/.f64 (cbrt.f64 (/.f64 1 (cbrt.f64 3/2))) (.f64 x x)) (/.f64 (cbrt.f64 3/2) (/.f64 (pow.f64 x 3) 8/243)))) (fma.f64 (/.f64 (cbrt.f64 (/.f64 2/3 (cbrt.f64 3/2))) (/.f64 x -1/9)) (/.f64 (cbrt.f64 3/2) x) (/.f64 (cbrt.f64 (*.f64 3/2 (cbrt.f64 3/2))) x)))))))
1/2
(+.f64 (.f64 -1 (/.f64 (+.f64 (.f64 -2/3 (pow.f64 (.f64 1 (pow.f64 (cbrt.f64 3/2) 4)) 1/3)) (.f64 -1/3 (pow.f64 (*.f64 1 (pow.f64 (cbrt.f64 3/2) 4)) 1/3))) x)) 1/2)
(+.f64 1/2 (.f64 (.f64 (cbrt.f64 (pow.f64 (cbrt.f64 3/2) 4)) (/.f64 1 x)) 1))
(+.f64 1/2 (/.f64 (cbrt.f64 (pow.f64 (cbrt.f64 3/2) 4)) x))
(+.f64 1/2 (/.f64 (cbrt.f64 (*.f64 3/2 (cbrt.f64 3/2))) x))
(+.f64 (/.f64 (.f64 (+.f64 (.f64 -2/9 (pow.f64 (/.f64 1 (pow.f64 (cbrt.f64 3/2) 4)) 1/3)) (.f64 1/9 (pow.f64 (/.f64 1 (pow.f64 (cbrt.f64 3/2) 4)) 1/3))) (cbrt.f64 3/2)) (pow.f64 x 2)) (+.f64 (.f64 -1 (/.f64 (+.f64 (.f64 -2/3 (pow.f64 (.f64 1 (pow.f64 (cbrt.f64 3/2) 4)) 1/3)) (.f64 -1/3 (pow.f64 (.f64 1 (pow.f64 (cbrt.f64 3/2) 4)) 1/3))) x)) (+.f64 1/2 (+.f64 (.f64 2/9 (.f64 (pow.f64 (/.f64 1 (cbrt.f64 3/2)) 1/3) (/.f64 1 (pow.f64 x 2)))) (.f64 -1/9 (.f64 (pow.f64 (/.f64 1 (cbrt.f64 3/2)) 1/3) (/.f64 1 (pow.f64 x 2))))))))
(+.f64 (/.f64 (.f64 (cbrt.f64 (/.f64 1 (pow.f64 (cbrt.f64 3/2) 4))) -1/9) (/.f64 (.f64 x x) (cbrt.f64 3/2))) (+.f64 1/2 (+.f64 (.f64 (.f64 (cbrt.f64 (pow.f64 (cbrt.f64 3/2) 4)) (/.f64 1 x)) 1) (.f64 (.f64 (cbrt.f64 (/.f64 1 (cbrt.f64 3/2))) (/.f64 1 (*.f64 x x))) 1/9))))
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(+.f64 (.f64 -1 (/.f64 (+.f64 (.f64 2/3 (/.f64 (-.f64 (.f64 1/27 (/.f64 1 (pow.f64 (cbrt.f64 3/2) 2))) (.f64 2/9 (.f64 (pow.f64 1 1/3) (/.f64 1 (pow.f64 (cbrt.f64 3/2) 2))))) (cbrt.f64 3/2))) (.f64 4/81 (pow.f64 1 1/3))) (pow.f64 x 3))) (+.f64 (pow.f64 (cbrt.f64 3/2) 2) (+.f64 (.f64 1/9 (.f64 (pow.f64 (/.f64 1 (pow.f64 (cbrt.f64 3/2) 4)) 1/3) (/.f64 1 (pow.f64 x 2)))) (+.f64 (.f64 2/3 (.f64 (pow.f64 (.f64 1 (cbrt.f64 3/2)) 1/3) (/.f64 1 x))) (.f64 -2/9 (*.f64 (pow.f64 (/.f64 1 (pow.f64 (cbrt.f64 3/2) 4)) 1/3) (/.f64 1 (pow.f64 x 2))))))))
(fma.f64 -1 (/.f64 (fma.f64 2/3 (/.f64 (+.f64 (/.f64 1/27 (pow.f64 (cbrt.f64 3/2) 2)) (.f64 -2/9 (/.f64 1 (pow.f64 (cbrt.f64 3/2) 2)))) (cbrt.f64 3/2)) 4/81) (pow.f64 x 3)) (+.f64 (pow.f64 (cbrt.f64 3/2) 2) (fma.f64 1/9 (.f64 (cbrt.f64 (/.f64 1 (pow.f64 (cbrt.f64 3/2) 4))) (/.f64 1 (.f64 x x))) (fma.f64 2/3 (.f64 (/.f64 1 x) (cbrt.f64 (cbrt.f64 3/2))) (.f64 -2/9 (.f64 (cbrt.f64 (/.f64 1 (pow.f64 (cbrt.f64 3/2) 4))) (/.f64 1 (*.f64 x x))))))))
(-.f64 (+.f64 (pow.f64 (cbrt.f64 3/2) 2) (fma.f64 1/9 (/.f64 (cbrt.f64 (/.f64 1 (pow.f64 (cbrt.f64 3/2) 4))) (.f64 x x)) (fma.f64 2/3 (/.f64 (cbrt.f64 (cbrt.f64 3/2)) x) (.f64 -2/9 (/.f64 (cbrt.f64 (/.f64 1 (pow.f64 (cbrt.f64 3/2) 4))) (.f64 x x)))))) (/.f64 (fma.f64 2/3 (/.f64 (.f64 (/.f64 1 (pow.f64 (cbrt.f64 3/2) 2)) -5/27) (cbrt.f64 3/2)) 4/81) (pow.f64 x 3)))
(+.f64 (+.f64 (.f64 (/.f64 (cbrt.f64 (/.f64 2/3 (cbrt.f64 3/2))) (.f64 x x)) -1/9) (fma.f64 2/3 (/.f64 (cbrt.f64 (cbrt.f64 3/2)) x) (pow.f64 (cbrt.f64 3/2) 2))) (/.f64 8/243 (pow.f64 x 3)))

eval530.0ms (13.9%)

Compiler: Compiled 23359 to 20090 computations (14% saved)

prune104.0ms (2.7%)

Pruning

12 alts after pruning (7 fresh and 5 done)

	Pruned	Kept	Total
New	754	7	761
Fresh	2	0	2
Picked	1	0	1
Done	4	5	9
Total	761	12	773

Error

0.6b

Counts

773 → 12

Alt Table

Click to see full alt table

Status	Error	Program
✓	0.8b	(/.f64 (exp.f64 x) (expm1.f64 x))
	38.7b	(/.f64 (+.f64 (+.f64 (/.f64 1 (*.f64 x x)) (+.f64 (/.f64 3 x) 9/4)) -1) (-.f64 (+.f64 (/.f64 1 x) 3/2) -1))
✓	18.7b	(+.f64 (/.f64 1 x) 1/2)
	62.4b	(/.f64 (+.f64 (pow.f64 (+.f64 (/.f64 1 x) 3/2) 2) -1) 5/2)
✓	18.5b	(/.f64 1 x)
	2.0b	(+.f64 (+.f64 (/.f64 1 x) -1) 1)
✓	18.7b	(+.f64 (+.f64 (/.f64 1 x) 3/2) -1)
	38.5b	(/.f64 (+.f64 (*.f64 (+.f64 (/.f64 1 x) 3/2) (+.f64 (/.f64 1 x) 3/2)) -1) (-.f64 (+.f64 (/.f64 1 x) 3/2) -1))
	21.8b	(/.f64 (-.f64 1 (*.f64 (+.f64 (/.f64 1 x) -1) (+.f64 (/.f64 1 x) -1))) (-.f64 1 (+.f64 (/.f64 1 x) -1)))
	62.0b	-1
✓	18.9b	(+.f64 1/2 (+.f64 (*.f64 1/12 x) (/.f64 1 x)))
	61.8b	1/2

Compiler

Compiled 124 to 105 computations (15.3% saved)

regimes32.0ms (0.9%)

Counts

21 → 1

Calls

Call 1

Inputs
-1
1/2
1/2
(/.f64 1 x)
(+.f64 (/.f64 1 x) 1/2)
(+.f64 (+.f64 (/.f64 1 x) -1) 1)
(-.f64 (+.f64 1 (/.f64 1 x)) 1)
(+.f64 (+.f64 (/.f64 1 x) 3/2) -1)
(-.f64 (+.f64 1 (+.f64 (/.f64 1 x) 1/2)) 1)
(+.f64 1/2 (+.f64 (*.f64 1/12 x) (/.f64 1 x)))
(/.f64 (+.f64 (+.f64 (/.f64 1 (*.f64 x x)) (+.f64 (/.f64 3 x) 9/4)) -1) (-.f64 (+.f64 (/.f64 1 x) 3/2) -1))
(/.f64 (+.f64 (*.f64 (+.f64 (/.f64 1 x) 3/2) (+.f64 (/.f64 1 x) 3/2)) -1) (-.f64 (+.f64 (/.f64 1 x) 3/2) -1))
(/.f64 (-.f64 1 (*.f64 (+.f64 (/.f64 1 x) -1) (+.f64 (/.f64 1 x) -1))) (-.f64 1 (+.f64 (/.f64 1 x) -1)))
(/.f64 (+.f64 (pow.f64 (+.f64 (/.f64 1 x) 3/2) 2) -1) 5/2)
(/.f64 (-.f64 1/4 (pow.f64 x -2)) (-.f64 1/2 (/.f64 1 x)))
(-.f64 (+.f64 1 (/.f64 (-.f64 1/4 (pow.f64 x -2)) (-.f64 1/2 (/.f64 1 x)))) 1)
(/.f64 (+.f64 (pow.f64 (+.f64 (/.f64 1 x) 3/2) 2) -1) (-.f64 (+.f64 (/.f64 1 x) 3/2) -1))
(/.f64 (exp.f64 x) (expm1.f64 x))
(/.f64 (exp.f64 x) (-.f64 (exp.f64 x) 1))
(fma.f64 (pow.f64 (cbrt.f64 (+.f64 (/.f64 1 x) 3/2)) 2) (cbrt.f64 (+.f64 (/.f64 1 x) 3/2)) -1)
(*.f64 (pow.f64 (cbrt.f64 (+.f64 1/2 (/.f64 -1 x))) -2) (/.f64 (-.f64 1/4 (pow.f64 x -2)) (cbrt.f64 (+.f64 1/2 (/.f64 -1 x)))))

Outputs
(/.f64 (exp.f64 x) (expm1.f64 x))

Calls

5 calls:

12.0ms	x
3.0ms	(/.f64 (exp.f64 x) (-.f64 (exp.f64 x) 1))
3.0ms	(/.f64 (exp.f64 x) (-.f64 (exp.f64 x) 1))
3.0ms	(exp.f64 x)
3.0ms	(exp.f64 x)

Results

Error	Segments	Branch
0.8b	1	`x`
0.8b	1	`(/.f64 (exp.f64 x) (-.f64 (exp.f64 x) 1))`
0.8b	1	`(/.f64 (exp.f64 x) (-.f64 (exp.f64 x) 1))`
0.8b	1	`(exp.f64 x)`
0.8b	1	`(exp.f64 x)`

Compiler

Compiled 241 to 196 computations (18.7% saved)

regimes23.0ms (0.6%)

Counts

17 → 1

Calls

Call 1

Inputs
-1
1/2
1/2
(/.f64 1 x)
(+.f64 (/.f64 1 x) 1/2)
(+.f64 (+.f64 (/.f64 1 x) -1) 1)
(-.f64 (+.f64 1 (/.f64 1 x)) 1)
(+.f64 (+.f64 (/.f64 1 x) 3/2) -1)
(-.f64 (+.f64 1 (+.f64 (/.f64 1 x) 1/2)) 1)
(+.f64 1/2 (+.f64 (*.f64 1/12 x) (/.f64 1 x)))
(/.f64 (+.f64 (+.f64 (/.f64 1 (*.f64 x x)) (+.f64 (/.f64 3 x) 9/4)) -1) (-.f64 (+.f64 (/.f64 1 x) 3/2) -1))
(/.f64 (+.f64 (*.f64 (+.f64 (/.f64 1 x) 3/2) (+.f64 (/.f64 1 x) 3/2)) -1) (-.f64 (+.f64 (/.f64 1 x) 3/2) -1))
(/.f64 (-.f64 1 (*.f64 (+.f64 (/.f64 1 x) -1) (+.f64 (/.f64 1 x) -1))) (-.f64 1 (+.f64 (/.f64 1 x) -1)))
(/.f64 (+.f64 (pow.f64 (+.f64 (/.f64 1 x) 3/2) 2) -1) 5/2)
(/.f64 (-.f64 1/4 (pow.f64 x -2)) (-.f64 1/2 (/.f64 1 x)))
(-.f64 (+.f64 1 (/.f64 (-.f64 1/4 (pow.f64 x -2)) (-.f64 1/2 (/.f64 1 x)))) 1)
(/.f64 (+.f64 (pow.f64 (+.f64 (/.f64 1 x) 3/2) 2) -1) (-.f64 (+.f64 (/.f64 1 x) 3/2) -1))

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

Calls

1 calls:

17.0ms

Results

Error	Segments	Branch
2.0b	1	`x`

Compiler

Compiled 170 to 144 computations (15.3% saved)

regimes6.0ms (0.2%)

Counts

5 → 1

Calls

Call 1

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

Outputs
(/.f64 1 x)

Calls

1 calls:

5.0ms

Results

Error	Segments	Branch
18.5b	1	`x`

Compiler

Compiled 14 to 11 computations (21.4% saved)

regimes5.0ms (0.1%)

Accuracy

Total -1.1b remaining (-1.8%)

Threshold costs -1.1b (-1.8%)

Counts

3 → 1

Calls

Call 1

Inputs
-1
1/2
1/2

Outputs
1/2

Calls

1 calls:

4.0ms

Results

Error	Segments	Branch
61.8b	1	`x`

Compiler

Compiled 6 to 5 computations (16.7% saved)

simplify4.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

2×	`+-commutative_binary64`
1×	`1-exp_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	11	24
1	15	24

Stop Event

1×	fuel
1×	saturated

Calls

Call 1

Inputs
(/.f64 (exp.f64 x) (expm1.f64 x))
(+.f64 (+.f64 (/.f64 1 x) -1) 1)
(/.f64 1 x)
1/2
-1

Outputs
(/.f64 (exp.f64 x) (expm1.f64 x))
(+.f64 (+.f64 (/.f64 1 x) -1) 1)
(+.f64 1 (+.f64 (/.f64 1 x) -1))
(/.f64 1 x)
1/2
-1

Compiler

Compiled 22 to 18 computations (18.2% saved)

soundness7.0ms (0.2%)

Algorithm

1×	egg-herbie

Rules

1×	`+-commutative_binary64`
1×	`sub-neg_binary64`
1×	`1-exp_binary64`
1×	`expm1-def_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	6	8
1	12	8
2	13	8

Stop Event

1×

saturated

Compiler

Compiled 14 to 9 computations (35.7% saved)

end29.0ms (0.8%)

Compiler: Compiled 18 to 14 computations (22.2% saved)

Details

analyze130.0ms (3.4%)

sample1.4s (35.8%)

preprocess17.0ms (0.4%)

simplify6.0ms (0.2%)

eval0.0ms (0%)

prune1.0ms (0%)

localize5.0ms (0.1%)

series2.0ms (0.1%)

rewrite43.0ms (1.1%)

simplify178.0ms (4.7%)

eval7.0ms (0.2%)

prune7.0ms (0.2%)

localize12.0ms (0.3%)

series4.0ms (0.1%)

rewrite80.0ms (2.1%)

simplify11.0ms (0.3%)

localize5.0ms (0.1%)

series1.0ms (0%)

rewrite46.0ms (1.2%)

simplify8.0ms (0.2%)

localize4.0ms (0.1%)

eval75.0ms (2%)

prune25.0ms (0.7%)

localize11.0ms (0.3%)

series1.0ms (0%)

rewrite52.0ms (1.4%)

simplify7.0ms (0.2%)

localize14.0ms (0.4%)

series3.0ms (0.1%)

rewrite89.0ms (2.3%)

simplify8.0ms (0.2%)

eval167.0ms (4.4%)

prune37.0ms (1%)

localize7.0ms (0.2%)

series1.0ms (0%)

rewrite45.0ms (1.2%)

simplify10.0ms (0.3%)

localize8.0ms (0.2%)

series1.0ms (0%)

rewrite50.0ms (1.3%)

simplify9.0ms (0.2%)

localize23.0ms (0.6%)

series3.0ms (0.1%)

rewrite102.0ms (2.7%)

simplify10.0ms (0.3%)

localize27.0ms (0.7%)

series4.0ms (0.1%)

rewrite86.0ms (2.2%)

simplify117.0ms (3.1%)

localize22.0ms (0.6%)

series10.0ms (0.3%)

rewrite61.0ms (1.6%)

simplify54.0ms (1.4%)

eval530.0ms (13.9%)

prune104.0ms (2.7%)

regimes32.0ms (0.9%)

regimes23.0ms (0.6%)

regimes6.0ms (0.2%)

regimes5.0ms (0.1%)

simplify4.0ms (0.1%)

soundness7.0ms (0.2%)

end29.0ms (0.8%)

Profiling