Details

analyze122.0ms (3.2%)

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)

sample1.6s (43.5%)

Results

893.0ms	2700×	body	1024	valid
348.0ms	3960×	body	256	valid
283.0ms	1318×	body	512	valid
111.0ms	278×	body	2048	valid
0.0ms	1×	body	256	invalid

preprocess18.0ms (0.5%)

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))

eval1.0ms (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

1.0b

Counts

3 → 1

Alt Table

Click to see full alt table

Status	Error	Program
▶	1.0b	(/.f64 (exp.f64 x) (expm1.f64 x))

Compiler

Compiled 6 to 4 computations (33.3% saved)

localize3.0ms (0.1%)

Local error

Found 2 expressions with local error:

New	Error	Program
	1.0b	(/.f64 (exp.f64 x) (expm1.f64 x))
✓	1.0b	(/.f64 (exp.f64 x) (expm1.f64 x))

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))

rewrite37.0ms (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 log1p.f64 (expm1.f64 (/.f64 (exp.f64 x) (expm1.f64 x))))))) (#(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))))))))

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 log1p.f64 (expm1.f64 (/.f64 (exp.f64 x) (expm1.f64 x))))))) (#(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))))))))

simplify136.0ms (3.6%)

Algorithm

1×	egg-herbie

Rules

1329×	`sqr-pow_binary64`
715×	`pow-sqr_binary64`
530×	`cube-prod_binary64`
472×	`fabs-mul_binary64`
438×	`associate-l_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	19	104
1	48	104
2	94	104
3	215	104
4	331	104
5	568	104
6	1456	104
7	2283	104
8	2369	104
9	2502	104
10	2660	104
11	2890	104
12	3212	104
13	3633	104
14	4133	104
15	4728	104
16	5448	104
17	5769	104
18	6053	104
19	6277	104
20	6455	104
21	6539	104
22	7479	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 (fma.f64 x 1/12 (/.f64 1 x)) (fma.f64 -1/720 (pow.f64 x 3) 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 (fma.f64 x (*.f64 x -1/720) 1/12) 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 159 computations (58% saved)

prune7.0ms (0.2%)

Pruning

5 alts after pruning (4 fresh and 1 done)

	Pruned	Kept	Total
New	35	4	39
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	35	5	40

Error

0.8b

Counts

40 → 5

Alt Table

Click to see full alt table

Status	Error	Program
✓	1.0b	(/.f64 (exp.f64 x) (expm1.f64 x))
▶	21.4b	(+.f64 1/2 (+.f64 (.f64 -1/720 (pow.f64 x 3)) (+.f64 (.f64 1/12 x) (/.f64 1 x))))
▶	21.0b	(+.f64 1/2 (+.f64 (*.f64 1/12 x) (/.f64 1 x)))
▶	21.1b	(+.f64 1/2 (/.f64 1 x))
▶	21.2b	(/.f64 1 x)

Compiler

Compiled 42 to 33 computations (21.4% saved)

localize2.0ms (0%)

localize4.0ms (0.1%)

Local error

Found 2 expressions with local error:

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

series1.0ms (0%)

Counts

1 → 3

Calls

3 calls:

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

rewrite43.0ms (1.1%)

Algorithm

1×	batch-egg-rewrite

Rules

628×	`pow1_binary64`
588×	`add-log-exp_binary64`
588×	`log1p-expm1-u_binary64`
588×	`expm1-log1p-u_binary64`
578×	`add-exp-log_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	6	7
1	130	7
2	1589	7

Stop Event

1×	node limit

Counts

1 → 30

Calls

Call 1

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

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

Outputs

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

simplify6.0ms (0.2%)

Algorithm

1×	egg-herbie

Rules

1×	`1-exp_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	5	6
1	7	6

Stop Event

1×

saturated

Counts

33 → 32

Calls

Call 1

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

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

localize6.0ms (0.2%)

Local error

Found 6 expressions with local error:

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

series3.0ms (0.1%)

Counts

3 → 19

Calls

9 calls:

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

rewrite64.0ms (1.7%)

Algorithm

1×	batch-egg-rewrite

Rules

936×	`prod-diff_binary64`
626×	`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	2710	23

Stop Event

1×	node limit

Counts

3 → 154

Calls

Call 1

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

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

simplify13.0ms (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 1/12 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))
(/.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)))

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

localize8.0ms (0.2%)

Local error

Found 8 expressions with local error:

New	Error	Program
	0.3b	(*.f64 1/12 x)
	0.1b	(*.f64 -1/720 (pow.f64 x 3))
	0.0b	(+.f64 1/2 (+.f64 (.f64 -1/720 (pow.f64 x 3)) (+.f64 (.f64 1/12 x) (/.f64 1 x))))
	0.0b	(+.f64 (*.f64 1/12 x) (/.f64 1 x))
	0.0b	(+.f64 (*.f64 1/12 x) (/.f64 1 x))
✓	0.0b	(+.f64 1/2 (+.f64 (.f64 -1/720 (pow.f64 x 3)) (+.f64 (.f64 1/12 x) (/.f64 1 x))))
✓	0.1b	(*.f64 -1/720 (pow.f64 x 3))
	0.3b	(*.f64 1/12 x)

series4.0ms (0.1%)

Counts

2 → 11

Calls

6 calls:

Time	Variable		Point	Expression
1.0ms	x	@	-inf	(*.f64 -1/720 (pow.f64 x 3))
1.0ms	x	@	0	(*.f64 -1/720 (pow.f64 x 3))
1.0ms	x	@	inf	(*.f64 -1/720 (pow.f64 x 3))
0.0ms	x	@	inf	(+.f64 1/2 (+.f64 (.f64 -1/720 (pow.f64 x 3)) (+.f64 (.f64 1/12 x) (/.f64 1 x))))
0.0ms	x	@	0	(+.f64 1/2 (+.f64 (.f64 -1/720 (pow.f64 x 3)) (+.f64 (.f64 1/12 x) (/.f64 1 x))))

rewrite68.0ms (1.8%)

Algorithm

1×	batch-egg-rewrite

Rules

685×	`fma-def_binary64`
643×	`log-prod_binary64`
360×	`fma-neg_binary64`
267×	`expm1-udef_binary64`
267×	`log1p-udef_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	14	25
1	326	25
2	4280	25

Stop Event

1×	node limit

Counts

2 → 84

Calls

Call 1

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

Outputs

((#(struct:change #<rule egg-rr> (2) ((x +.f64 0 (*.f64 -1/720 (pow.f64 x 3)))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (log.f64 (*.f64 (cbrt.f64 (pow.f64 (exp.f64 (pow.f64 x 3)) -1/720)) (cbrt.f64 (pow.f64 (exp.f64 (pow.f64 x 3)) -1/720)))) (log.f64 (cbrt.f64 (pow.f64 (exp.f64 (pow.f64 x 3)) -1/720))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (log.f64 (sqrt.f64 (pow.f64 (exp.f64 (pow.f64 x 3)) -1/720))) (log.f64 (sqrt.f64 (pow.f64 (exp.f64 (pow.f64 x 3)) -1/720))))))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (exp.f64 (log1p.f64 (*.f64 -1/720 (pow.f64 x 3)))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (*.f64 -1/720 (pow.f64 x 3)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (*.f64 x (cbrt.f64 -1/720)) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (*.f64 (sqrt.f64 -1/720) (pow.f64 x 3/2)) 2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (*.f64 (pow.f64 (pow.f64 x 3) 3) -1/373248000) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f64 (*.f64 (pow.f64 x 6) 1/518400))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (pow.f64 (exp.f64 (pow.f64 x 3)) -1/720))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (+.f64 1 (expm1.f64 (*.f64 -1/720 (pow.f64 x 3)))))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (*.f64 (pow.f64 (pow.f64 x 3) 3) -1/373248000))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (*.f64 -1/720 (pow.f64 x 3))))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (*.f64 -1/720 (pow.f64 x 3))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (fma.f64 3 (log.f64 x) (log.f64 -1/720)))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (fma.f64 3 (log.f64 x) (log.f64 -1/720)) 1))))))

((#(struct:change #<rule egg-rr> (2) ((x -.f64 (exp.f64 (log1p.f64 (+.f64 1/2 (fma.f64 -1/720 (pow.f64 x 3) (fma.f64 x 1/12 (pow.f64 x -1)))))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (/.f64 1/4 (-.f64 1/2 (fma.f64 -1/720 (pow.f64 x 3) (fma.f64 x 1/12 (pow.f64 x -1))))) (/.f64 (pow.f64 (fma.f64 -1/720 (pow.f64 x 3) (fma.f64 x 1/12 (pow.f64 x -1))) 2) (-.f64 1/2 (fma.f64 -1/720 (pow.f64 x 3) (fma.f64 x 1/12 (pow.f64 x -1))))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 1 (+.f64 1/2 (fma.f64 -1/720 (pow.f64 x 3) (fma.f64 x 1/12 (pow.f64 x -1)))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (+.f64 1/2 (fma.f64 -1/720 (pow.f64 x 3) (fma.f64 x 1/12 (pow.f64 x -1)))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 (+.f64 1/2 (fma.f64 -1/720 (pow.f64 x 3) (fma.f64 x 1/12 (pow.f64 x -1))))) (pow.f64 (cbrt.f64 (+.f64 1/2 (fma.f64 -1/720 (pow.f64 x 3) (fma.f64 x 1/12 (pow.f64 x -1))))) 2))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (cbrt.f64 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x 3) (fma.f64 x 1/12 (pow.f64 x -1))) (-.f64 (fma.f64 -1/720 (pow.f64 x 3) (fma.f64 x 1/12 (pow.f64 x -1))) 1/2) 1/4) (+.f64 1/8 (pow.f64 (fma.f64 -1/720 (pow.f64 x 3) (fma.f64 x 1/12 (pow.f64 x -1))) 3))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 1 (/.f64 (-.f64 1/2 (fma.f64 -1/720 (pow.f64 x 3) (fma.f64 x 1/12 (pow.f64 x -1)))) (-.f64 1/4 (pow.f64 (fma.f64 -1/720 (pow.f64 x 3) (fma.f64 x 1/12 (pow.f64 x -1))) 2))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (+.f64 1/8 (pow.f64 (fma.f64 -1/720 (pow.f64 x 3) (fma.f64 x 1/12 (pow.f64 x -1))) 3)) (fma.f64 (fma.f64 -1/720 (pow.f64 x 3) (fma.f64 x 1/12 (pow.f64 x -1))) (-.f64 (fma.f64 -1/720 (pow.f64 x 3) (fma.f64 x 1/12 (pow.f64 x -1))) 1/2) 1/4))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (+.f64 1/8 (pow.f64 (fma.f64 -1/720 (pow.f64 x 3) (fma.f64 x 1/12 (pow.f64 x -1))) 3)) (+.f64 (pow.f64 (fma.f64 -1/720 (pow.f64 x 3) (fma.f64 x 1/12 (pow.f64 x -1))) 2) (-.f64 1/4 (*.f64 1/2 (fma.f64 -1/720 (pow.f64 x 3) (fma.f64 x 1/12 (pow.f64 x -1)))))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (-.f64 1/4 (pow.f64 (fma.f64 -1/720 (pow.f64 x 3) (fma.f64 x 1/12 (pow.f64 x -1))) 2)) (-.f64 1/2 (fma.f64 -1/720 (pow.f64 x 3) (fma.f64 x 1/12 (pow.f64 x -1)))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (neg.f64 (+.f64 1/8 (pow.f64 (fma.f64 -1/720 (pow.f64 x 3) (fma.f64 x 1/12 (pow.f64 x -1))) 3))) (neg.f64 (fma.f64 (fma.f64 -1/720 (pow.f64 x 3) (fma.f64 x 1/12 (pow.f64 x -1))) (-.f64 (fma.f64 -1/720 (pow.f64 x 3) (fma.f64 x 1/12 (pow.f64 x -1))) 1/2) 1/4)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (neg.f64 (-.f64 1/4 (pow.f64 (fma.f64 -1/720 (pow.f64 x 3) (fma.f64 x 1/12 (pow.f64 x -1))) 2))) (neg.f64 (-.f64 1/2 (fma.f64 -1/720 (pow.f64 x 3) (fma.f64 x 1/12 (pow.f64 x -1))))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (+.f64 (pow.f64 (fma.f64 -1/720 (pow.f64 x 3) 1/2) 3) (pow.f64 (fma.f64 x 1/12 (pow.f64 x -1)) 3)) (fma.f64 (fma.f64 -1/720 (pow.f64 x 3) 1/2) (fma.f64 -1/720 (pow.f64 x 3) 1/2) (-.f64 (pow.f64 (fma.f64 x 1/12 (pow.f64 x -1)) 2) (*.f64 (fma.f64 -1/720 (pow.f64 x 3) 1/2) (fma.f64 x 1/12 (pow.f64 x -1))))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (-.f64 (pow.f64 (fma.f64 -1/720 (pow.f64 x 3) (fma.f64 x 1/12 (pow.f64 x -1))) 2) 1/4) (-.f64 (fma.f64 -1/720 (pow.f64 x 3) (fma.f64 x 1/12 (pow.f64 x -1))) 1/2))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (fma.f64 (fma.f64 -1/720 (pow.f64 x 3) 1/2) (fma.f64 -1/720 (pow.f64 x 3) 1/2) (neg.f64 (pow.f64 (fma.f64 x 1/12 (pow.f64 x -1)) 2))) (-.f64 (fma.f64 -1/720 (pow.f64 x 3) 1/2) (fma.f64 x 1/12 (pow.f64 x -1))))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (+.f64 1/2 (fma.f64 -1/720 (pow.f64 x 3) (fma.f64 x 1/12 (pow.f64 x -1)))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (+.f64 1/2 (fma.f64 -1/720 (pow.f64 x 3) (fma.f64 x 1/12 (pow.f64 x -1)))) 3) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (cbrt.f64 (+.f64 1/2 (fma.f64 -1/720 (pow.f64 x 3) (fma.f64 x 1/12 (pow.f64 x -1))))) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (sqrt.f64 (+.f64 1/2 (fma.f64 -1/720 (pow.f64 x 3) (fma.f64 x 1/12 (pow.f64 x -1))))) 2)))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f64 (pow.f64 (+.f64 1/2 (fma.f64 -1/720 (pow.f64 x 3) (fma.f64 x 1/12 (pow.f64 x -1)))) 2))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (exp.f64 (+.f64 1/2 (fma.f64 -1/720 (pow.f64 x 3) (fma.f64 x 1/12 (pow.f64 x -1))))))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (+.f64 1 (expm1.f64 (+.f64 1/2 (fma.f64 -1/720 (pow.f64 x 3) (fma.f64 x 1/12 (pow.f64 x -1)))))))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (*.f64 (exp.f64 (fma.f64 x 1/12 (pow.f64 x -1))) (exp.f64 (fma.f64 -1/720 (pow.f64 x 3) 1/2))))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (*.f64 (+.f64 1 (expm1.f64 (fma.f64 x 1/12 (pow.f64 x -1)))) (exp.f64 (fma.f64 -1/720 (pow.f64 x 3) 1/2))))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (*.f64 (exp.f64 (fma.f64 -1/720 (pow.f64 x 3) 1/2)) (+.f64 1 (expm1.f64 (fma.f64 x 1/12 (pow.f64 x -1))))))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (pow.f64 (+.f64 1/2 (fma.f64 -1/720 (pow.f64 x 3) (fma.f64 x 1/12 (pow.f64 x -1)))) 3))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (+.f64 1/2 (fma.f64 -1/720 (pow.f64 x 3) (fma.f64 x 1/12 (pow.f64 x -1))))))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (+.f64 1/2 (fma.f64 -1/720 (pow.f64 x 3) (fma.f64 x 1/12 (pow.f64 x -1))))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (log.f64 (+.f64 1/2 (fma.f64 -1/720 (pow.f64 x 3) (fma.f64 x 1/12 (pow.f64 x -1))))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (log.f64 (+.f64 1/2 (fma.f64 -1/720 (pow.f64 x 3) (fma.f64 x 1/12 (pow.f64 x -1))))) 1))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 -1/720 (pow.f64 x 3) (+.f64 (fma.f64 x 1/12 (pow.f64 x -1)) 1/2))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 x (*.f64 (*.f64 x x) -1/720) (+.f64 (fma.f64 x 1/12 (pow.f64 x -1)) 1/2))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (pow.f64 x 3) -1/720 (+.f64 (fma.f64 x 1/12 (pow.f64 x -1)) 1/2))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (*.f64 -1/720 (pow.f64 x 3)) 1 (+.f64 (fma.f64 x 1/12 (pow.f64 x -1)) 1/2))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 1 (*.f64 -1/720 (pow.f64 x 3)) (+.f64 (fma.f64 x 1/12 (pow.f64 x -1)) 1/2))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 1 (fma.f64 x 1/12 (pow.f64 x -1)) (fma.f64 -1/720 (pow.f64 x 3) 1/2))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 1 (fma.f64 -1/720 (pow.f64 x 3) (fma.f64 x 1/12 (pow.f64 x -1))) 1/2)))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 1 (fma.f64 -1/720 (pow.f64 x 3) (*.f64 x 1/12)) (+.f64 (pow.f64 x -1) 1/2))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 1 (fma.f64 -1/720 (pow.f64 x 3) 1/2) (fma.f64 x 1/12 (pow.f64 x -1)))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (fma.f64 x 1/12 (pow.f64 x -1)) 1 (fma.f64 -1/720 (pow.f64 x 3) 1/2))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (fma.f64 -1/720 (pow.f64 x 3) (fma.f64 x 1/12 (pow.f64 x -1))) 1 1/2)))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (*.f64 x x) (*.f64 x -1/720) (+.f64 (fma.f64 x 1/12 (pow.f64 x -1)) 1/2))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (cbrt.f64 (fma.f64 x 1/12 (pow.f64 x -1))) (pow.f64 (cbrt.f64 (fma.f64 x 1/12 (pow.f64 x -1))) 2) (fma.f64 -1/720 (pow.f64 x 3) 1/2))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (pow.f64 (cbrt.f64 (fma.f64 x 1/12 (pow.f64 x -1))) 2) (cbrt.f64 (fma.f64 x 1/12 (pow.f64 x -1))) (fma.f64 -1/720 (pow.f64 x 3) 1/2))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (*.f64 x (cbrt.f64 -1/720)) (cbrt.f64 (*.f64 (pow.f64 x 6) 1/518400)) (+.f64 (fma.f64 x 1/12 (pow.f64 x -1)) 1/2))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (cbrt.f64 (*.f64 (pow.f64 x 6) 1/518400)) (*.f64 x (cbrt.f64 -1/720)) (+.f64 (fma.f64 x 1/12 (pow.f64 x -1)) 1/2))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (cbrt.f64 (fma.f64 -1/720 (pow.f64 x 3) (fma.f64 x 1/12 (pow.f64 x -1)))) (pow.f64 (cbrt.f64 (fma.f64 -1/720 (pow.f64 x 3) (fma.f64 x 1/12 (pow.f64 x -1)))) 2) 1/2)))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (pow.f64 (cbrt.f64 (fma.f64 -1/720 (pow.f64 x 3) (fma.f64 x 1/12 (pow.f64 x -1)))) 2) (cbrt.f64 (fma.f64 -1/720 (pow.f64 x 3) (fma.f64 x 1/12 (pow.f64 x -1)))) 1/2)))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (sqrt.f64 (fma.f64 x 1/12 (pow.f64 x -1))) (sqrt.f64 (fma.f64 x 1/12 (pow.f64 x -1))) (fma.f64 -1/720 (pow.f64 x 3) 1/2))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (*.f64 (sqrt.f64 -1/720) (pow.f64 x 3/2)) (*.f64 (sqrt.f64 -1/720) (pow.f64 x 3/2)) (+.f64 (fma.f64 x 1/12 (pow.f64 x -1)) 1/2))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (sqrt.f64 (fma.f64 -1/720 (pow.f64 x 3) (fma.f64 x 1/12 (pow.f64 x -1)))) (sqrt.f64 (fma.f64 -1/720 (pow.f64 x 3) (fma.f64 x 1/12 (pow.f64 x -1)))) 1/2)))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (fma.f64 (pow.f64 (pow.f64 x 3) 3) -1/373248000 (pow.f64 (fma.f64 x 1/12 (pow.f64 x -1)) 3)) (/.f64 1 (fma.f64 (fma.f64 x 1/12 (pow.f64 x -1)) (-.f64 (fma.f64 x 1/12 (pow.f64 x -1)) (*.f64 -1/720 (pow.f64 x 3))) (*.f64 (pow.f64 x 6) 1/518400))) 1/2)))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (fma.f64 (pow.f64 x 3) 1/1728 (pow.f64 x -3)) (/.f64 1 (-.f64 (fma.f64 1/144 (*.f64 x x) (pow.f64 x -2)) (/.f64 (*.f64 x 1/12) x))) (fma.f64 -1/720 (pow.f64 x 3) 1/2))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (-.f64 (*.f64 (pow.f64 x 6) 1/518400) (pow.f64 (fma.f64 x 1/12 (pow.f64 x -1)) 2)) (/.f64 1 (-.f64 (*.f64 -1/720 (pow.f64 x 3)) (fma.f64 x 1/12 (pow.f64 x -1)))) 1/2)))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (-.f64 (*.f64 1/144 (*.f64 x x)) (pow.f64 x -2)) (/.f64 1 (-.f64 (*.f64 x 1/12) (pow.f64 x -1))) (fma.f64 -1/720 (pow.f64 x 3) 1/2))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (pow.f64 x 3/2) (*.f64 (pow.f64 x 3/2) -1/720) (+.f64 (fma.f64 x 1/12 (pow.f64 x -1)) 1/2))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (fma.f64 -1/720 (pow.f64 x 3) 1/2) 1 (fma.f64 x 1/12 (pow.f64 x -1)))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (*.f64 (cbrt.f64 (fma.f64 -1/720 (pow.f64 x 3) 1/2)) (cbrt.f64 (fma.f64 -1/720 (pow.f64 x 3) 1/2))) (cbrt.f64 (fma.f64 -1/720 (pow.f64 x 3) 1/2)) (fma.f64 x 1/12 (pow.f64 x -1)))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (*.f64 (cbrt.f64 (fma.f64 -1/720 (pow.f64 x 3) (*.f64 x 1/12))) (cbrt.f64 (fma.f64 -1/720 (pow.f64 x 3) (*.f64 x 1/12)))) (cbrt.f64 (fma.f64 -1/720 (pow.f64 x 3) (*.f64 x 1/12))) (+.f64 (pow.f64 x -1) 1/2))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (sqrt.f64 (fma.f64 -1/720 (pow.f64 x 3) 1/2)) (sqrt.f64 (fma.f64 -1/720 (pow.f64 x 3) 1/2)) (fma.f64 x 1/12 (pow.f64 x -1)))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (sqrt.f64 (fma.f64 -1/720 (pow.f64 x 3) (*.f64 x 1/12))) (sqrt.f64 (fma.f64 -1/720 (pow.f64 x 3) (*.f64 x 1/12))) (+.f64 (pow.f64 x -1) 1/2))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (*.f64 -1/720 x) (*.f64 x x) (+.f64 (fma.f64 x 1/12 (pow.f64 x -1)) 1/2))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (*.f64 -1/720 (*.f64 x x)) x (+.f64 (fma.f64 x 1/12 (pow.f64 x -1)) 1/2))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (*.f64 -1/720 (pow.f64 x 3/2)) (pow.f64 x 3/2) (+.f64 (fma.f64 x 1/12 (pow.f64 x -1)) 1/2))))))

simplify142.0ms (3.8%)

Algorithm

1×	egg-herbie

Rules

1332×	`sqr-pow_binary64`
715×	`pow-sqr_binary64`
530×	`cube-prod_binary64`
473×	`fabs-mul_binary64`
451×	`associate-l_binary64`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	19	126
1	47	122
2	94	118
3	208	118
4	312	118
5	564	118
6	1477	118
7	2300	118
8	2386	118
9	2519	118
10	2677	118
11	2909	118
12	3231	118
13	3652	118
14	4152	118
15	4749	118
16	5469	118
17	5792	118
18	6078	118
19	6302	118
20	6480	118
21	6562	118
22	7502	118

Stop Event

1×	node limit

Counts

95 → 96

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

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

eval176.0ms (4.6%)

Compiler: Compiled 6657 to 5308 computations (20.3% saved)

prune50.0ms (1.3%)

Pruning

8 alts after pruning (3 fresh and 5 done)

	Pruned	Kept	Total
New	374	3	377
Fresh	0	0	0
Picked	0	1	1
Done	0	4	4
Total	374	8	382

Error

0.8b

Counts

382 → 8

Alt Table

Click to see full alt table

Status	Error	Program
✓	21.4b	(+.f64 1/2 (+.f64 (.f64 -1/720 (pow.f64 x 3)) (+.f64 (.f64 1/12 x) (/.f64 1 x))))
▶	47.7b	(*.f64 (+.f64 1/8 (pow.f64 x -3)) (/.f64 1 (+.f64 1/4 (-.f64 (pow.f64 x -2) (/.f64 1/2 x)))))
▶	21.1b	(-.f64 (+.f64 1 (+.f64 1/2 (/.f64 1 x))) 1)
	61.7b	1/2
✓	1.0b	(/.f64 (exp.f64 x) (expm1.f64 x))
✓	21.0b	(+.f64 1/2 (+.f64 (*.f64 1/12 x) (/.f64 1 x)))
✓	21.1b	(+.f64 1/2 (/.f64 1 x))
✓	21.2b	(/.f64 1 x)

Compiler

Compiled 72 to 59 computations (18.1% saved)

localize5.0ms (0.1%)

Local error

Found 4 expressions with local error:

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

series1.0ms (0%)

Counts

1 → 12

Calls

3 calls:

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

rewrite51.0ms (1.3%)

Algorithm

1×	batch-egg-rewrite

Rules

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

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	8	10
1	193	7
2	2701	7

Stop Event

1×	node limit

Counts

1 → 55

Calls

Call 1

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

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

67 → 57

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)

localize9.0ms (0.2%)

Local error

Found 6 expressions with local error:

New	Error	Program
	25.5b	(*.f64 (+.f64 1/8 (pow.f64 x -3)) (/.f64 1 (+.f64 1/4 (-.f64 (pow.f64 x -2) (/.f64 1/2 x)))))
	0.8b	(/.f64 1 (+.f64 1/4 (-.f64 (pow.f64 x -2) (/.f64 1/2 x))))
	0.0b	(-.f64 (pow.f64 x -2) (/.f64 1/2 x))
✓	0.0b	(-.f64 (pow.f64 x -2) (/.f64 1/2 x))
✓	0.8b	(/.f64 1 (+.f64 1/4 (-.f64 (pow.f64 x -2) (/.f64 1/2 x))))
✓	25.5b	(*.f64 (+.f64 1/8 (pow.f64 x -3)) (/.f64 1 (+.f64 1/4 (-.f64 (pow.f64 x -2) (/.f64 1/2 x)))))

series7.0ms (0.2%)

Counts

3 → 36

Calls

9 calls:

Time	Variable		Point	Expression
2.0ms	x	@	-inf	(*.f64 (+.f64 1/8 (pow.f64 x -3)) (/.f64 1 (+.f64 1/4 (-.f64 (pow.f64 x -2) (/.f64 1/2 x)))))
1.0ms	x	@	0	(*.f64 (+.f64 1/8 (pow.f64 x -3)) (/.f64 1 (+.f64 1/4 (-.f64 (pow.f64 x -2) (/.f64 1/2 x)))))
1.0ms	x	@	inf	(*.f64 (+.f64 1/8 (pow.f64 x -3)) (/.f64 1 (+.f64 1/4 (-.f64 (pow.f64 x -2) (/.f64 1/2 x)))))
0.0ms	x	@	inf	(/.f64 1 (+.f64 1/4 (-.f64 (pow.f64 x -2) (/.f64 1/2 x))))
0.0ms	x	@	0	(/.f64 1 (+.f64 1/4 (-.f64 (pow.f64 x -2) (/.f64 1/2 x))))

rewrite81.0ms (2.1%)

Algorithm

1×	batch-egg-rewrite

Rules

806×	`prod-diff_binary64`
426×	`fma-def_binary64`
295×	`expm1-udef_binary64`
295×	`log1p-udef_binary64`
224×	`fma-neg_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	16	48
1	370	48
2	4805	48

Stop Event

1×	node limit

Counts

3 → 175

Calls

Call 1

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

Outputs

((#(struct:change #<rule egg-rr> (2) ((x +.f64 (*.f64 1/8 (/.f64 1 (+.f64 (+.f64 1/4 (pow.f64 x -2)) (/.f64 -1/2 x)))) (*.f64 (pow.f64 x -3) (/.f64 1 (+.f64 (+.f64 1/4 (pow.f64 x -2)) (/.f64 -1/2 x)))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (*.f64 (pow.f64 x -3) (/.f64 1 (+.f64 (+.f64 1/4 (pow.f64 x -2)) (/.f64 -1/2 x)))) (*.f64 1/8 (/.f64 1 (+.f64 (+.f64 1/4 (pow.f64 x -2)) (/.f64 -1/2 x)))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (*.f64 (/.f64 1 (+.f64 (+.f64 1/4 (pow.f64 x -2)) (/.f64 -1/2 x))) 1/8) (*.f64 (/.f64 1 (+.f64 (+.f64 1/4 (pow.f64 x -2)) (/.f64 -1/2 x))) (pow.f64 x -3)))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (*.f64 (/.f64 1 (+.f64 (+.f64 1/4 (pow.f64 x -2)) (/.f64 -1/2 x))) (pow.f64 x -3)) (*.f64 (/.f64 1 (+.f64 (+.f64 1/4 (pow.f64 x -2)) (/.f64 -1/2 x))) 1/8))))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (exp.f64 (log1p.f64 (/.f64 (+.f64 1/8 (pow.f64 x -3)) (+.f64 (+.f64 1/4 (pow.f64 x -2)) (/.f64 -1/2 x))))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (+.f64 1/8 (pow.f64 x -3)) (+.f64 (+.f64 1/4 (pow.f64 x -2)) (/.f64 -1/2 x)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 1 (/.f64 (+.f64 (+.f64 1/4 (pow.f64 x -2)) (/.f64 -1/2 x)) (+.f64 1/8 (pow.f64 x -3))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (cbrt.f64 (pow.f64 (+.f64 1/8 (pow.f64 x -3)) 2)) (/.f64 (+.f64 (+.f64 1/4 (pow.f64 x -2)) (/.f64 -1/2 x)) (cbrt.f64 (+.f64 1/8 (pow.f64 x -3)))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (sqrt.f64 (+.f64 1/8 (pow.f64 x -3))) (/.f64 (+.f64 (+.f64 1/4 (pow.f64 x -2)) (/.f64 -1/2 x)) (sqrt.f64 (+.f64 1/8 (pow.f64 x -3)))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (+.f64 1/512 (pow.f64 x -9)) (*.f64 (+.f64 (+.f64 1/4 (pow.f64 x -2)) (/.f64 -1/2 x)) (fma.f64 (pow.f64 x -3) (-.f64 (pow.f64 x -3) 1/8) 1/64)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (-.f64 1/64 (pow.f64 x -6)) (*.f64 (+.f64 (+.f64 1/4 (pow.f64 x -2)) (/.f64 -1/2 x)) (-.f64 1/8 (pow.f64 x -3))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (neg.f64 (+.f64 1/8 (pow.f64 x -3))) (neg.f64 (+.f64 (+.f64 1/4 (pow.f64 x -2)) (/.f64 -1/2 x))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (*.f64 (+.f64 1/512 (pow.f64 x -9)) 1) (*.f64 (fma.f64 (pow.f64 x -3) (-.f64 (pow.f64 x -3) 1/8) 1/64) (+.f64 (+.f64 1/4 (pow.f64 x -2)) (/.f64 -1/2 x))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (*.f64 (-.f64 1/64 (pow.f64 x -6)) 1) (*.f64 (-.f64 1/8 (pow.f64 x -3)) (+.f64 (+.f64 1/4 (pow.f64 x -2)) (/.f64 -1/2 x))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (*.f64 (+.f64 1/512 (pow.f64 x -9)) -1) (*.f64 (fma.f64 (pow.f64 x -3) (-.f64 (pow.f64 x -3) 1/8) 1/64) (neg.f64 (+.f64 (+.f64 1/4 (pow.f64 x -2)) (/.f64 -1/2 x)))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (*.f64 (-.f64 1/64 (pow.f64 x -6)) -1) (*.f64 (-.f64 1/8 (pow.f64 x -3)) (neg.f64 (+.f64 (+.f64 1/4 (pow.f64 x -2)) (/.f64 -1/2 x)))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (*.f64 -1 (+.f64 1/512 (pow.f64 x -9))) (*.f64 (neg.f64 (+.f64 (+.f64 1/4 (pow.f64 x -2)) (/.f64 -1/2 x))) (fma.f64 (pow.f64 x -3) (-.f64 (pow.f64 x -3) 1/8) 1/64)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (*.f64 -1 (-.f64 1/64 (pow.f64 x -6))) (*.f64 (neg.f64 (+.f64 (+.f64 1/4 (pow.f64 x -2)) (/.f64 -1/2 x))) (-.f64 1/8 (pow.f64 x -3))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (/.f64 (+.f64 1/8 (pow.f64 x -3)) (sqrt.f64 (+.f64 (+.f64 1/4 (pow.f64 x -2)) (/.f64 -1/2 x)))) (sqrt.f64 (+.f64 (+.f64 1/4 (pow.f64 x -2)) (/.f64 -1/2 x))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (/.f64 (+.f64 1/8 (pow.f64 x -3)) 1) (+.f64 (+.f64 1/4 (pow.f64 x -2)) (/.f64 -1/2 x)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (/.f64 (+.f64 1/8 (pow.f64 x -3)) (cbrt.f64 (pow.f64 (+.f64 (+.f64 1/4 (pow.f64 x -2)) (/.f64 -1/2 x)) 2))) (cbrt.f64 (+.f64 (+.f64 1/4 (pow.f64 x -2)) (/.f64 -1/2 x))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (*.f64 (+.f64 1/512 (pow.f64 x -9)) (/.f64 1 (+.f64 (+.f64 1/4 (pow.f64 x -2)) (/.f64 -1/2 x)))) (fma.f64 (pow.f64 x -3) (-.f64 (pow.f64 x -3) 1/8) 1/64))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (*.f64 (-.f64 1/64 (pow.f64 x -6)) (/.f64 1 (+.f64 (+.f64 1/4 (pow.f64 x -2)) (/.f64 -1/2 x)))) (-.f64 1/8 (pow.f64 x -3)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (*.f64 -1 (+.f64 1/8 (pow.f64 x -3))) (neg.f64 (+.f64 (+.f64 1/4 (pow.f64 x -2)) (/.f64 -1/2 x))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (*.f64 (+.f64 1/8 (pow.f64 x -3)) -1) (neg.f64 (+.f64 (+.f64 1/4 (pow.f64 x -2)) (/.f64 -1/2 x))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (*.f64 (/.f64 1 (+.f64 (+.f64 1/4 (pow.f64 x -2)) (/.f64 -1/2 x))) (+.f64 1/512 (pow.f64 x -9))) (fma.f64 (pow.f64 x -3) (-.f64 (pow.f64 x -3) 1/8) 1/64))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (*.f64 (/.f64 1 (+.f64 (+.f64 1/4 (pow.f64 x -2)) (/.f64 -1/2 x))) (-.f64 1/64 (pow.f64 x -6))) (-.f64 1/8 (pow.f64 x -3)))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (/.f64 (+.f64 1/8 (pow.f64 x -3)) (+.f64 (+.f64 1/4 (pow.f64 x -2)) (/.f64 -1/2 x))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (/.f64 (+.f64 1/8 (pow.f64 x -3)) (+.f64 (+.f64 1/4 (pow.f64 x -2)) (/.f64 -1/2 x))) 3) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (cbrt.f64 (/.f64 (+.f64 1/8 (pow.f64 x -3)) (+.f64 (+.f64 1/4 (pow.f64 x -2)) (/.f64 -1/2 x)))) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (sqrt.f64 (/.f64 (+.f64 1/8 (pow.f64 x -3)) (+.f64 (+.f64 1/4 (pow.f64 x -2)) (/.f64 -1/2 x)))) 2)))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f64 (pow.f64 (/.f64 (+.f64 1/8 (pow.f64 x -3)) (+.f64 (+.f64 1/4 (pow.f64 x -2)) (/.f64 -1/2 x))) 2))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (exp.f64 (/.f64 (+.f64 1/8 (pow.f64 x -3)) (+.f64 (+.f64 1/4 (pow.f64 x -2)) (/.f64 -1/2 x)))))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (+.f64 1 (expm1.f64 (/.f64 (+.f64 1/8 (pow.f64 x -3)) (+.f64 (+.f64 1/4 (pow.f64 x -2)) (/.f64 -1/2 x))))))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (pow.f64 (/.f64 (+.f64 1/8 (pow.f64 x -3)) (+.f64 (+.f64 1/4 (pow.f64 x -2)) (/.f64 -1/2 x))) 3))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (/.f64 (pow.f64 (+.f64 1/8 (pow.f64 x -3)) 3) (pow.f64 (+.f64 (+.f64 1/4 (pow.f64 x -2)) (/.f64 -1/2 x)) 3)))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (*.f64 (pow.f64 (+.f64 1/8 (pow.f64 x -3)) 3) (pow.f64 (/.f64 1 (+.f64 (+.f64 1/4 (pow.f64 x -2)) (/.f64 -1/2 x))) 3)))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (*.f64 (pow.f64 (/.f64 1 (+.f64 (+.f64 1/4 (pow.f64 x -2)) (/.f64 -1/2 x))) 3) (pow.f64 (+.f64 1/8 (pow.f64 x -3)) 3)))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (/.f64 (+.f64 1/8 (pow.f64 x -3)) (+.f64 (+.f64 1/4 (pow.f64 x -2)) (/.f64 -1/2 x)))))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (/.f64 (+.f64 1/8 (pow.f64 x -3)) (+.f64 (+.f64 1/4 (pow.f64 x -2)) (/.f64 -1/2 x)))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (log.f64 (/.f64 (+.f64 1/8 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(-.f64 (pow.f64 x -1) (sqrt.f64 (/.f64 1/2 x))) (+.f64 (/.f64 -1/2 x) (/.f64 1/2 x)))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (neg.f64 (cbrt.f64 (*.f64 1/4 (pow.f64 x -2)))) (cbrt.f64 (/.f64 1/2 x)) (pow.f64 x -2))))))

simplify37.0ms (1%)

Algorithm

1×	egg-herbie

Rules

671×	`times-frac_binary64`
492×	`unswap-sqr_binary64`
425×	`fma-def_binary64`
321×	`*-commutative_binary64`
320×	`associate-l_binary64`

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	43	361
1	115	357
2	288	357
3	821	357
4	2931	356

Stop Event

1×	node limit

Counts

211 → 199

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))
(pow.f64 x 2)
(+.f64 (*.f64 1/2 (pow.f64 x 3)) (pow.f64 x 2))
(+.f64 (.f64 1/2 (pow.f64 x 3)) (+.f64 (pow.f64 x 2) (.f64 -1/8 (pow.f64 x 5))))
(+.f64 (.f64 1/2 (pow.f64 x 3)) (+.f64 (.f64 -1/16 (pow.f64 x 6)) (+.f64 (pow.f64 x 2) (*.f64 -1/8 (pow.f64 x 5)))))
4
(+.f64 4 (*.f64 8 (/.f64 1 x)))
(-.f64 (+.f64 4 (.f64 8 (/.f64 1 x))) (.f64 32 (/.f64 1 (pow.f64 x 3))))
(-.f64 (+.f64 4 (.f64 8 (/.f64 1 x))) (+.f64 (.f64 32 (/.f64 1 (pow.f64 x 3))) (*.f64 64 (/.f64 1 (pow.f64 x 4)))))
4
(+.f64 4 (*.f64 8 (/.f64 1 x)))
(-.f64 (+.f64 4 (.f64 8 (/.f64 1 x))) (.f64 32 (/.f64 1 (pow.f64 x 3))))
(-.f64 (+.f64 4 (.f64 8 (/.f64 1 x))) (+.f64 (.f64 32 (/.f64 1 (pow.f64 x 3))) (*.f64 64 (/.f64 1 (pow.f64 x 4)))))
(/.f64 1 (pow.f64 x 2))
(-.f64 (/.f64 1 (pow.f64 x 2)) (*.f64 1/2 (/.f64 1 x)))
(-.f64 (/.f64 1 (pow.f64 x 2)) (*.f64 1/2 (/.f64 1 x)))
(-.f64 (/.f64 1 (pow.f64 x 2)) (*.f64 1/2 (/.f64 1 x)))
(/.f64 -1/2 x)
(-.f64 (/.f64 1 (pow.f64 x 2)) (*.f64 1/2 (/.f64 1 x)))
(-.f64 (/.f64 1 (pow.f64 x 2)) (*.f64 1/2 (/.f64 1 x)))
(-.f64 (/.f64 1 (pow.f64 x 2)) (*.f64 1/2 (/.f64 1 x)))
(/.f64 -1/2 x)
(-.f64 (/.f64 1 (pow.f64 x 2)) (*.f64 1/2 (/.f64 1 x)))
(-.f64 (/.f64 1 (pow.f64 x 2)) (*.f64 1/2 (/.f64 1 x)))
(-.f64 (/.f64 1 (pow.f64 x 2)) (*.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)
(pow.f64 x 2)
(*.f64 x x)
(+.f64 (*.f64 1/2 (pow.f64 x 3)) (pow.f64 x 2))
(fma.f64 1/2 (pow.f64 x 3) (*.f64 x x))
(fma.f64 x x (*.f64 1/2 (pow.f64 x 3)))
(.f64 x (fma.f64 1/2 (.f64 x x) x))
(+.f64 (.f64 1/2 (pow.f64 x 3)) (+.f64 (pow.f64 x 2) (.f64 -1/8 (pow.f64 x 5))))
(+.f64 (fma.f64 1/2 (pow.f64 x 3) (.f64 x x)) (.f64 -1/8 (pow.f64 x 5)))
(fma.f64 1/2 (pow.f64 x 3) (fma.f64 x x (*.f64 -1/8 (pow.f64 x 5))))
(fma.f64 x x (fma.f64 -1/8 (pow.f64 x 5) (*.f64 1/2 (pow.f64 x 3))))
(+.f64 (.f64 1/2 (pow.f64 x 3)) (+.f64 (.f64 -1/16 (pow.f64 x 6)) (+.f64 (pow.f64 x 2) (*.f64 -1/8 (pow.f64 x 5)))))
(fma.f64 1/2 (pow.f64 x 3) (fma.f64 -1/16 (pow.f64 x 6) (+.f64 (.f64 x x) (.f64 -1/8 (pow.f64 x 5)))))
(fma.f64 1/2 (pow.f64 x 3) (fma.f64 -1/16 (pow.f64 x 6) (fma.f64 x x (*.f64 -1/8 (pow.f64 x 5)))))
(fma.f64 1/2 (pow.f64 x 3) (fma.f64 -1/8 (pow.f64 x 5) (fma.f64 x x (*.f64 -1/16 (pow.f64 x 6)))))
(fma.f64 (pow.f64 x 3) (fma.f64 (pow.f64 x 3) -1/16 1/2) (fma.f64 -1/8 (pow.f64 x 5) (*.f64 x x)))
(fma.f64 x x (fma.f64 1/2 (pow.f64 x 3) (.f64 (pow.f64 x 5) (+.f64 -1/8 (.f64 x -1/16)))))
4
(+.f64 4 (*.f64 8 (/.f64 1 x)))
(+.f64 4 (/.f64 8 x))
(-.f64 (+.f64 4 (.f64 8 (/.f64 1 x))) (.f64 32 (/.f64 1 (pow.f64 x 3))))
(+.f64 4 (-.f64 (/.f64 8 x) (/.f64 32 (pow.f64 x 3))))
(+.f64 4 (+.f64 (/.f64 8 x) (/.f64 -32 (pow.f64 x 3))))
(-.f64 (/.f64 8 x) (-.f64 (/.f64 32 (pow.f64 x 3)) 4))
(-.f64 (+.f64 4 (.f64 8 (/.f64 1 x))) (+.f64 (.f64 32 (/.f64 1 (pow.f64 x 3))) (*.f64 64 (/.f64 1 (pow.f64 x 4)))))
(-.f64 (+.f64 4 (/.f64 8 x)) (+.f64 (/.f64 32 (pow.f64 x 3)) (/.f64 64 (pow.f64 x 4))))
(+.f64 4 (+.f64 (+.f64 (/.f64 8 x) (/.f64 -32 (pow.f64 x 3))) (/.f64 -64 (pow.f64 x 4))))
(-.f64 (-.f64 (/.f64 8 x) (/.f64 32 (pow.f64 x 3))) (+.f64 (/.f64 64 (pow.f64 x 4)) -4))
(+.f64 4 (+.f64 (/.f64 8 x) (*.f64 (/.f64 1 (pow.f64 x 3)) (+.f64 -32 (/.f64 -64 x)))))
4
(+.f64 4 (*.f64 8 (/.f64 1 x)))
(+.f64 4 (/.f64 8 x))
(-.f64 (+.f64 4 (.f64 8 (/.f64 1 x))) (.f64 32 (/.f64 1 (pow.f64 x 3))))
(+.f64 4 (-.f64 (/.f64 8 x) (/.f64 32 (pow.f64 x 3))))
(+.f64 4 (+.f64 (/.f64 8 x) (/.f64 -32 (pow.f64 x 3))))
(-.f64 (/.f64 8 x) (-.f64 (/.f64 32 (pow.f64 x 3)) 4))
(-.f64 (+.f64 4 (.f64 8 (/.f64 1 x))) (+.f64 (.f64 32 (/.f64 1 (pow.f64 x 3))) (*.f64 64 (/.f64 1 (pow.f64 x 4)))))
(-.f64 (+.f64 4 (/.f64 8 x)) (+.f64 (/.f64 32 (pow.f64 x 3)) (/.f64 64 (pow.f64 x 4))))
(+.f64 4 (+.f64 (+.f64 (/.f64 8 x) (/.f64 -32 (pow.f64 x 3))) (/.f64 -64 (pow.f64 x 4))))
(-.f64 (-.f64 (/.f64 8 x) (/.f64 32 (pow.f64 x 3))) (+.f64 (/.f64 64 (pow.f64 x 4)) -4))
(+.f64 4 (+.f64 (/.f64 8 x) (*.f64 (/.f64 1 (pow.f64 x 3)) (+.f64 -32 (/.f64 -64 x)))))
(/.f64 1 (pow.f64 x 2))
(/.f64 1 (*.f64 x x))
(-.f64 (/.f64 1 (pow.f64 x 2)) (*.f64 1/2 (/.f64 1 x)))
(-.f64 (/.f64 1 (*.f64 x x)) (/.f64 1/2 x))
(+.f64 (/.f64 1 (*.f64 x x)) (/.f64 -1/2 x))
(-.f64 (/.f64 1 (pow.f64 x 2)) (*.f64 1/2 (/.f64 1 x)))
(-.f64 (/.f64 1 (*.f64 x x)) (/.f64 1/2 x))
(+.f64 (/.f64 1 (*.f64 x x)) (/.f64 -1/2 x))
(-.f64 (/.f64 1 (pow.f64 x 2)) (*.f64 1/2 (/.f64 1 x)))
(-.f64 (/.f64 1 (*.f64 x x)) (/.f64 1/2 x))
(+.f64 (/.f64 1 (*.f64 x x)) (/.f64 -1/2 x))
(/.f64 -1/2 x)
(-.f64 (/.f64 1 (pow.f64 x 2)) (*.f64 1/2 (/.f64 1 x)))
(-.f64 (/.f64 1 (*.f64 x x)) (/.f64 1/2 x))
(+.f64 (/.f64 1 (*.f64 x x)) (/.f64 -1/2 x))
(-.f64 (/.f64 1 (pow.f64 x 2)) (*.f64 1/2 (/.f64 1 x)))
(-.f64 (/.f64 1 (*.f64 x x)) (/.f64 1/2 x))
(+.f64 (/.f64 1 (*.f64 x x)) (/.f64 -1/2 x))
(-.f64 (/.f64 1 (pow.f64 x 2)) (*.f64 1/2 (/.f64 1 x)))
(-.f64 (/.f64 1 (*.f64 x x)) (/.f64 1/2 x))
(+.f64 (/.f64 1 (*.f64 x x)) (/.f64 -1/2 x))
(/.f64 -1/2 x)
(-.f64 (/.f64 1 (pow.f64 x 2)) (*.f64 1/2 (/.f64 1 x)))
(-.f64 (/.f64 1 (*.f64 x x)) (/.f64 1/2 x))
(+.f64 (/.f64 1 (*.f64 x x)) (/.f64 -1/2 x))
(-.f64 (/.f64 1 (pow.f64 x 2)) (*.f64 1/2 (/.f64 1 x)))
(-.f64 (/.f64 1 (*.f64 x x)) (/.f64 1/2 x))
(+.f64 (/.f64 1 (*.f64 x x)) (/.f64 -1/2 x))
(-.f64 (/.f64 1 (pow.f64 x 2)) (*.f64 1/2 (/.f64 1 x)))
(-.f64 (/.f64 1 (*.f64 x x)) (/.f64 1/2 x))
(+.f64 (/.f64 1 (*.f64 x x)) (/.f64 -1/2 x))

eval142.0ms (3.7%)

Compiler: Compiled 6144 to 5074 computations (17.4% saved)

prune37.0ms (1%)

Pruning

10 alts after pruning (5 fresh and 5 done)

	Pruned	Kept	Total
New	283	5	288
Fresh	1	0	1
Picked	1	0	1
Done	1	5	6
Total	286	10	296

Error

0.8b

Counts

296 → 10

Alt Table

Click to see full alt table

Status	Error	Program
▶	3.0b	(-.f64 (+.f64 1 (/.f64 1 x)) 1)
▶	21.1b	(+.f64 -1 (+.f64 (/.f64 1 x) 3/2))
▶	62.7b	(*.f64 (+.f64 1/8 (pow.f64 x -3)) (+.f64 4 (/.f64 8 x)))
	61.7b	1/2
✓	1.0b	(/.f64 (exp.f64 x) (expm1.f64 x))
▶	62.4b	(*.f64 (+.f64 1/8 (pow.f64 x -3)) (/.f64 1 (+.f64 1/4 (/.f64 -1/2 x))))
✓	21.4b	(+.f64 1/2 (+.f64 (.f64 -1/720 (pow.f64 x 3)) (+.f64 (.f64 1/12 x) (/.f64 1 x))))
✓	21.0b	(+.f64 1/2 (+.f64 (*.f64 1/12 x) (/.f64 1 x)))
✓	21.1b	(+.f64 1/2 (/.f64 1 x))
✓	21.2b	(/.f64 1 x)

Compiler

Compiled 86 to 71 computations (17.4% saved)

localize9.0ms (0.2%)

Local error

Found 6 expressions with local error:

New	Error	Program
	7.1b	(*.f64 (+.f64 1/8 (pow.f64 x -3)) (/.f64 1 (+.f64 1/4 (/.f64 -1/2 x))))
	0.1b	(/.f64 1 (+.f64 1/4 (/.f64 -1/2 x)))
	0.0b	(+.f64 1/4 (/.f64 -1/2 x))
✓	0.0b	(+.f64 1/4 (/.f64 -1/2 x))
✓	0.1b	(/.f64 1 (+.f64 1/4 (/.f64 -1/2 x)))
✓	7.1b	(*.f64 (+.f64 1/8 (pow.f64 x -3)) (/.f64 1 (+.f64 1/4 (/.f64 -1/2 x))))

series3.0ms (0.1%)

Counts

3 → 36

Calls

9 calls:

Time	Variable		Point	Expression
1.0ms	x	@	0	(*.f64 (+.f64 1/8 (pow.f64 x -3)) (/.f64 1 (+.f64 1/4 (/.f64 -1/2 x))))
0.0ms	x	@	inf	(*.f64 (+.f64 1/8 (pow.f64 x -3)) (/.f64 1 (+.f64 1/4 (/.f64 -1/2 x))))
0.0ms	x	@	-inf	(*.f64 (+.f64 1/8 (pow.f64 x -3)) (/.f64 1 (+.f64 1/4 (/.f64 -1/2 x))))
0.0ms	x	@	inf	(/.f64 1 (+.f64 1/4 (/.f64 -1/2 x)))
0.0ms	x	@	0	(/.f64 1 (+.f64 1/4 (/.f64 -1/2 x)))

rewrite66.0ms (1.7%)

Algorithm

1×	batch-egg-rewrite

Rules

562×	`log-prod_binary64`
345×	`pow2_binary64`
238×	`pow1/3_binary64`
237×	`expm1-udef_binary64`
237×	`log1p-udef_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	13	33
1	297	33
2	3685	33

Stop Event

1×	node limit

Counts

3 → 135

Calls

Call 1

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

Outputs

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x))) 1/8))))))

((#(struct:change #<rule egg-rr> (2) ((x +.f64 0 (/.f64 1 (+.f64 1/4 (/.f64 -1/2 x))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (log.f64 (pow.f64 (cbrt.f64 (exp.f64 (/.f64 1 (+.f64 1/4 (/.f64 -1/2 x))))) 2)) (log.f64 (cbrt.f64 (exp.f64 (/.f64 1 (+.f64 1/4 (/.f64 -1/2 x)))))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (log.f64 (sqrt.f64 (exp.f64 (/.f64 1 (+.f64 1/4 (/.f64 -1/2 x)))))) (log.f64 (sqrt.f64 (exp.f64 (/.f64 1 (+.f64 1/4 (/.f64 -1/2 x)))))))))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (exp.f64 (log1p.f64 (/.f64 1 (+.f64 1/4 (/.f64 -1/2 x))))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 1 (/.f64 1 (+.f64 1/4 (/.f64 -1/2 x))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 1 (+.f64 1/4 (/.f64 -1/2 x))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 1 (cbrt.f64 (+.f64 1/4 (/.f64 -1/2 x)))) (cbrt.f64 (pow.f64 (+.f64 1/4 (/.f64 -1/2 x)) -2)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 (pow.f64 (+.f64 1/4 (/.f64 -1/2 x)) -2)) (/.f64 1 (cbrt.f64 (+.f64 1/4 (/.f64 -1/2 x)))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (+.f64 1/4 (/.f64 -1/2 x)) -1/2) (pow.f64 (+.f64 1/4 (/.f64 -1/2 x)) -1/2))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 -1 (/.f64 1 (+.f64 (neg.f64 (/.f64 -1/2 x)) -1/4)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (cbrt.f64 (+.f64 1/4 (/.f64 -1/2 x))) -2) (/.f64 1 (cbrt.f64 (+.f64 1/4 (/.f64 -1/2 x)))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 1 (fma.f64 -1/8 (pow.f64 x -3) 1/64)) (fma.f64 (/.f64 -1/2 x) (-.f64 (/.f64 -1/2 x) 1/4) 1/16))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 1 (-.f64 1/16 (pow.f64 (/.f64 -1/2 x) 2))) (-.f64 1/4 (/.f64 -1/2 x)))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (+.f64 1/4 (/.f64 -1/2 x)) -1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (/.f64 1 (+.f64 1/4 (/.f64 -1/2 x))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (+.f64 1/4 (/.f64 -1/2 x)) 3) -1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (+.f64 1/4 (/.f64 -1/2 x)) -2) 1/2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (+.f64 1/4 (/.f64 -1/2 x)) -3) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (cbrt.f64 (+.f64 1/4 (/.f64 -1/2 x))) -3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (/.f64 1 (cbrt.f64 (+.f64 1/4 (/.f64 -1/2 x)))) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (sqrt.f64 (+.f64 1/4 (/.f64 -1/2 x))) -2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (+.f64 1/4 (/.f64 -1/2 x)) -1/2) 2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (neg.f64 (+.f64 (neg.f64 (/.f64 -1/2 x)) -1/4)) -1)))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f64 (pow.f64 (+.f64 1/4 (/.f64 -1/2 x)) -2))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (exp.f64 (/.f64 1 (+.f64 1/4 (/.f64 -1/2 x)))))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (+.f64 1 (expm1.f64 (/.f64 1 (+.f64 1/4 (/.f64 -1/2 x))))))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (pow.f64 (+.f64 1/4 (/.f64 -1/2 x)) -3))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (/.f64 1 (+.f64 1/4 (/.f64 -1/2 x)))))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (/.f64 1 (+.f64 1/4 (/.f64 -1/2 x)))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (neg.f64 (log.f64 (+.f64 1/4 (/.f64 -1/2 x)))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (log.f64 (+.f64 1/4 (/.f64 -1/2 x))) -1))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (neg.f64 (log.f64 (+.f64 1/4 (/.f64 -1/2 x)))) 1))))))

((#(struct:change #<rule egg-rr> (2) ((x -.f64 (exp.f64 (log1p.f64 (+.f64 1/4 (/.f64 -1/2 x)))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (/.f64 1/16 (-.f64 1/4 (/.f64 -1/2 x))) (/.f64 (pow.f64 (/.f64 -1/2 x) 2) (-.f64 1/4 (/.f64 -1/2 x))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 1 (+.f64 1/4 (/.f64 -1/2 x)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (+.f64 1/4 (/.f64 -1/2 x)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 (+.f64 1/4 (/.f64 -1/2 x))) (pow.f64 (cbrt.f64 (+.f64 1/4 (/.f64 -1/2 x))) 2))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (cbrt.f64 (+.f64 1/4 (/.f64 -1/2 x))) 2) (cbrt.f64 (+.f64 1/4 (/.f64 -1/2 x))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (sqrt.f64 (+.f64 1/4 (/.f64 -1/2 x))) (sqrt.f64 (+.f64 1/4 (/.f64 -1/2 x))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (fma.f64 -1/8 (pow.f64 x -3) 1/64) (/.f64 1 (fma.f64 (/.f64 -1/2 x) (-.f64 (/.f64 -1/2 x) 1/4) 1/16)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (-.f64 1/16 (pow.f64 (/.f64 -1/2 x) 2)) (/.f64 1 (-.f64 1/4 (/.f64 -1/2 x))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 1 (/.f64 1 (+.f64 1/4 (/.f64 -1/2 x))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 1 (/.f64 (fma.f64 (/.f64 -1/2 x) (-.f64 (/.f64 -1/2 x) 1/4) 1/16) (fma.f64 -1/8 (pow.f64 x -3) 1/64)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 1 (/.f64 (-.f64 1/4 (/.f64 -1/2 x)) (-.f64 1/16 (pow.f64 (/.f64 -1/2 x) 2))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (+.f64 1/4 (/.f64 -1/2 x)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (pow.f64 (cbrt.f64 (+.f64 1/4 (/.f64 -1/2 x))) 2) (/.f64 1 (cbrt.f64 (+.f64 1/4 (/.f64 -1/2 x)))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (sqrt.f64 (+.f64 1/4 (/.f64 -1/2 x))) (pow.f64 (+.f64 1/4 (/.f64 -1/2 x)) -1/2))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (+.f64 (neg.f64 (/.f64 -1/2 x)) -1/4) -1)))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (fma.f64 -1/8 (pow.f64 x -3) 1/64) (fma.f64 (/.f64 -1/2 x) (-.f64 (/.f64 -1/2 x) 1/4) 1/16))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (fma.f64 -1/8 (pow.f64 x -3) 1/64) (+.f64 (pow.f64 (/.f64 -1/2 x) 2) (-.f64 1/16 (/.f64 -1/8 x))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (-.f64 1/16 (pow.f64 (/.f64 -1/2 x) 2)) (-.f64 1/4 (/.f64 -1/2 x)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (neg.f64 (fma.f64 -1/8 (pow.f64 x -3) 1/64)) (neg.f64 (fma.f64 (/.f64 -1/2 x) (-.f64 (/.f64 -1/2 x) 1/4) 1/16)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (neg.f64 (-.f64 1/16 (pow.f64 (/.f64 -1/2 x) 2))) (neg.f64 (-.f64 1/4 (/.f64 -1/2 x))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (-.f64 (pow.f64 (/.f64 -1/2 x) 2) 1/16) (-.f64 (/.f64 -1/2 x) 1/4))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (+.f64 1/4 (/.f64 -1/2 x)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (/.f64 1 (+.f64 1/4 (/.f64 -1/2 x))) -1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (+.f64 1/4 (/.f64 -1/2 x)) 2) 1/2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (+.f64 1/4 (/.f64 -1/2 x)) 3) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (+.f64 1/4 (/.f64 -1/2 x)) -3) -1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (cbrt.f64 (+.f64 1/4 (/.f64 -1/2 x))) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (/.f64 1 (cbrt.f64 (+.f64 1/4 (/.f64 -1/2 x)))) -3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (sqrt.f64 (+.f64 1/4 (/.f64 -1/2 x))) 2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (+.f64 1/4 (/.f64 -1/2 x)) -1/2) -2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (/.f64 (fma.f64 (/.f64 -1/2 x) (-.f64 (/.f64 -1/2 x) 1/4) 1/16) (fma.f64 -1/8 (pow.f64 x -3) 1/64)) -1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (/.f64 (-.f64 1/4 (/.f64 -1/2 x)) (-.f64 1/16 (pow.f64 (/.f64 -1/2 x) 2))) -1)))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f64 (pow.f64 (+.f64 1/4 (/.f64 -1/2 x)) 2))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (exp.f64 (+.f64 1/4 (/.f64 -1/2 x))))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (+.f64 1 (expm1.f64 (+.f64 1/4 (/.f64 -1/2 x)))))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (pow.f64 (+.f64 1/4 (/.f64 -1/2 x)) 3))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (+.f64 1/4 (/.f64 -1/2 x))))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (+.f64 1/4 (/.f64 -1/2 x))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (log.f64 (+.f64 1/4 (/.f64 -1/2 x))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (log.f64 (+.f64 1/4 (/.f64 -1/2 x))) 1))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 1 (/.f64 -1/2 x) 1/4)))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 -1/2 (/.f64 1 x) 1/4)))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (/.f64 -1/2 x) 1 1/4)))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (cbrt.f64 (/.f64 -1/2 x)) (cbrt.f64 (pow.f64 (/.f64 -1/2 x) 2)) 1/4)))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (cbrt.f64 (pow.f64 (/.f64 -1/2 x) 2)) (cbrt.f64 (/.f64 -1/2 x)) 1/4)))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 1/2 (/.f64 1 (neg.f64 x)) 1/4)))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (sqrt.f64 (/.f64 -1/2 x)) (sqrt.f64 (/.f64 -1/2 x)) 1/4)))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (/.f64 1 x) -1/2 1/4)))))

simplify41.0ms (1.1%)

Algorithm

1×	egg-herbie

Rules

671×	`fma-neg_binary64`
557×	`associate-/r*_binary64`
543×	`cancel-sign-sub-inv_binary64`
466×	`fma-def_binary64`
346×	`associate-/l/_binary64`

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	56	383
1	155	376
2	392	367
3	1043	366
4	3118	366

Stop Event

1×	node limit

Counts

171 → 168

Calls

Call 1

Inputs
(/.f64 -2 (pow.f64 x 2))
(neg.f64 (+.f64 (*.f64 2 (/.f64 1 (pow.f64 x 2))) (/.f64 1 x)))
(neg.f64 (+.f64 1/2 (+.f64 (*.f64 2 (/.f64 1 (pow.f64 x 2))) (/.f64 1 x))))
(-.f64 (.f64 -1/2 x) (+.f64 1/2 (+.f64 (.f64 2 (/.f64 1 (pow.f64 x 2))) (/.f64 1 x))))
1/2
(+.f64 1/2 (/.f64 1 x))
(+.f64 1/2 (+.f64 (/.f64 1 x) (*.f64 2 (/.f64 1 (pow.f64 x 2)))))
(+.f64 1/2 (+.f64 (.f64 8 (/.f64 1 (pow.f64 x 3))) (+.f64 (/.f64 1 x) (.f64 2 (/.f64 1 (pow.f64 x 2))))))
1/2
(+.f64 1/2 (/.f64 1 x))
(+.f64 1/2 (+.f64 (/.f64 1 x) (*.f64 2 (/.f64 1 (pow.f64 x 2)))))
(+.f64 1/2 (+.f64 (.f64 8 (/.f64 1 (pow.f64 x 3))) (+.f64 (/.f64 1 x) (.f64 2 (/.f64 1 (pow.f64 x 2))))))
(*.f64 -2 x)
(+.f64 (.f64 -2 x) (.f64 -1 (pow.f64 x 2)))
(+.f64 (.f64 -1/2 (pow.f64 x 3)) (+.f64 (.f64 -2 x) (*.f64 -1 (pow.f64 x 2))))
(+.f64 (.f64 -1/2 (pow.f64 x 3)) (+.f64 (.f64 -2 x) (+.f64 (.f64 -1 (pow.f64 x 2)) (.f64 -1/4 (pow.f64 x 4)))))
4
(+.f64 4 (*.f64 8 (/.f64 1 x)))
(+.f64 4 (+.f64 (.f64 8 (/.f64 1 x)) (.f64 16 (/.f64 1 (pow.f64 x 2)))))
(+.f64 4 (+.f64 (.f64 8 (/.f64 1 x)) (+.f64 (.f64 32 (/.f64 1 (pow.f64 x 3))) (*.f64 16 (/.f64 1 (pow.f64 x 2))))))
4
(+.f64 4 (*.f64 8 (/.f64 1 x)))
(+.f64 4 (+.f64 (.f64 8 (/.f64 1 x)) (.f64 16 (/.f64 1 (pow.f64 x 2)))))
(+.f64 4 (+.f64 (.f64 8 (/.f64 1 x)) (+.f64 (.f64 32 (/.f64 1 (pow.f64 x 3))) (*.f64 16 (/.f64 1 (pow.f64 x 2))))))
(/.f64 -1/2 x)
(-.f64 1/4 (*.f64 1/2 (/.f64 1 x)))
(-.f64 1/4 (*.f64 1/2 (/.f64 1 x)))
(-.f64 1/4 (*.f64 1/2 (/.f64 1 x)))
1/4
(-.f64 1/4 (*.f64 1/2 (/.f64 1 x)))
(-.f64 1/4 (*.f64 1/2 (/.f64 1 x)))
(-.f64 1/4 (*.f64 1/2 (/.f64 1 x)))
1/4
(-.f64 1/4 (*.f64 1/2 (/.f64 1 x)))
(-.f64 1/4 (*.f64 1/2 (/.f64 1 x)))
(-.f64 1/4 (*.f64 1/2 (/.f64 1 x)))

Outputs
(/.f64 -2 (pow.f64 x 2))
(/.f64 -2 (*.f64 x x))
(neg.f64 (+.f64 (*.f64 2 (/.f64 1 (pow.f64 x 2))) (/.f64 1 x)))
(neg.f64 (+.f64 (/.f64 2 (*.f64 x x)) (/.f64 1 x)))
(-.f64 (/.f64 -2 (*.f64 x x)) (/.f64 1 x))
(-.f64 (/.f64 -1 x) (/.f64 2 (*.f64 x x)))
(+.f64 (/.f64 -2 (*.f64 x x)) (/.f64 -1 x))
(neg.f64 (+.f64 1/2 (+.f64 (*.f64 2 (/.f64 1 (pow.f64 x 2))) (/.f64 1 x))))
(neg.f64 (+.f64 1/2 (+.f64 (/.f64 2 (*.f64 x x)) (/.f64 1 x))))
(+.f64 -1/2 (-.f64 (/.f64 -2 (*.f64 x x)) (/.f64 1 x)))
(+.f64 -1/2 (-.f64 (/.f64 -1 x) (/.f64 2 (*.f64 x x))))
(+.f64 (/.f64 -1 x) (+.f64 -1/2 (/.f64 -2 (*.f64 x x))))
(+.f64 -1/2 (+.f64 (/.f64 -2 (*.f64 x x)) (/.f64 -1 x)))
(-.f64 (.f64 -1/2 x) (+.f64 1/2 (+.f64 (.f64 2 (/.f64 1 (pow.f64 x 2))) (/.f64 1 x))))
(-.f64 (.f64 x -1/2) (+.f64 1/2 (+.f64 (/.f64 2 (.f64 x x)) (/.f64 1 x))))
(+.f64 (fma.f64 x -1/2 -1/2) (-.f64 (/.f64 -2 (*.f64 x x)) (/.f64 1 x)))
(+.f64 (-.f64 (/.f64 -1 x) (/.f64 2 (*.f64 x x))) (fma.f64 x -1/2 -1/2))
(+.f64 -1/2 (+.f64 (/.f64 -1 x) (fma.f64 x -1/2 (/.f64 -2 (*.f64 x x)))))
1/2
(+.f64 1/2 (/.f64 1 x))
(+.f64 (/.f64 1 x) 1/2)
(-.f64 1/2 (/.f64 -1 x))
(+.f64 1/2 (+.f64 (/.f64 1 x) (*.f64 2 (/.f64 1 (pow.f64 x 2)))))
(+.f64 1/2 (+.f64 (/.f64 2 (*.f64 x x)) (/.f64 1 x)))
(+.f64 (/.f64 2 (*.f64 x x)) (+.f64 (/.f64 1 x) 1/2))
(+.f64 (/.f64 1 x) (+.f64 (/.f64 2 (*.f64 x x)) 1/2))
(+.f64 1/2 (-.f64 (/.f64 2 (*.f64 x x)) (/.f64 -1 x)))
(+.f64 1/2 (+.f64 (.f64 8 (/.f64 1 (pow.f64 x 3))) (+.f64 (/.f64 1 x) (.f64 2 (/.f64 1 (pow.f64 x 2))))))
(+.f64 1/2 (+.f64 (+.f64 (/.f64 2 (*.f64 x x)) (/.f64 1 x)) (/.f64 8 (pow.f64 x 3))))
(+.f64 (+.f64 (/.f64 2 (*.f64 x x)) (/.f64 1 x)) (+.f64 1/2 (/.f64 8 (pow.f64 x 3))))
(+.f64 (+.f64 (/.f64 1 x) (/.f64 8 (pow.f64 x 3))) (+.f64 (/.f64 2 (*.f64 x x)) 1/2))
(+.f64 (/.f64 2 (*.f64 x x)) (+.f64 (/.f64 1 x) (+.f64 1/2 (/.f64 8 (pow.f64 x 3)))))
(+.f64 (/.f64 2 (*.f64 x x)) (+.f64 (-.f64 1/2 (/.f64 -1 x)) (/.f64 8 (pow.f64 x 3))))
1/2
(+.f64 1/2 (/.f64 1 x))
(+.f64 (/.f64 1 x) 1/2)
(-.f64 1/2 (/.f64 -1 x))
(+.f64 1/2 (+.f64 (/.f64 1 x) (*.f64 2 (/.f64 1 (pow.f64 x 2)))))
(+.f64 1/2 (+.f64 (/.f64 2 (*.f64 x x)) (/.f64 1 x)))
(+.f64 (/.f64 2 (*.f64 x x)) (+.f64 (/.f64 1 x) 1/2))
(+.f64 (/.f64 1 x) (+.f64 (/.f64 2 (*.f64 x x)) 1/2))
(+.f64 1/2 (-.f64 (/.f64 2 (*.f64 x x)) (/.f64 -1 x)))
(+.f64 1/2 (+.f64 (.f64 8 (/.f64 1 (pow.f64 x 3))) (+.f64 (/.f64 1 x) (.f64 2 (/.f64 1 (pow.f64 x 2))))))
(+.f64 1/2 (+.f64 (+.f64 (/.f64 2 (*.f64 x x)) (/.f64 1 x)) (/.f64 8 (pow.f64 x 3))))
(+.f64 (+.f64 (/.f64 2 (*.f64 x x)) (/.f64 1 x)) (+.f64 1/2 (/.f64 8 (pow.f64 x 3))))
(+.f64 (+.f64 (/.f64 1 x) (/.f64 8 (pow.f64 x 3))) (+.f64 (/.f64 2 (*.f64 x x)) 1/2))
(+.f64 (/.f64 2 (*.f64 x x)) (+.f64 (/.f64 1 x) (+.f64 1/2 (/.f64 8 (pow.f64 x 3)))))
(+.f64 (/.f64 2 (*.f64 x x)) (+.f64 (-.f64 1/2 (/.f64 -1 x)) (/.f64 8 (pow.f64 x 3))))
(*.f64 -2 x)
(+.f64 (.f64 -2 x) (.f64 -1 (pow.f64 x 2)))
(fma.f64 -2 x (neg.f64 (*.f64 x x)))
(*.f64 x (-.f64 -2 x))
(+.f64 (.f64 -1/2 (pow.f64 x 3)) (+.f64 (.f64 -2 x) (*.f64 -1 (pow.f64 x 2))))
(fma.f64 -1/2 (pow.f64 x 3) (fma.f64 -2 x (neg.f64 (*.f64 x x))))
(-.f64 (fma.f64 -1/2 (pow.f64 x 3) (.f64 -2 x)) (.f64 x x))
(fma.f64 -1/2 (pow.f64 x 3) (*.f64 x (-.f64 -2 x)))
(.f64 x (-.f64 (fma.f64 x (.f64 x -1/2) -2) x))
(+.f64 (.f64 -1/2 (pow.f64 x 3)) (+.f64 (.f64 -2 x) (+.f64 (.f64 -1 (pow.f64 x 2)) (.f64 -1/4 (pow.f64 x 4)))))
(fma.f64 -1/2 (pow.f64 x 3) (fma.f64 -2 x (fma.f64 -1 (.f64 x x) (.f64 -1/4 (pow.f64 x 4)))))
(fma.f64 -1/2 (pow.f64 x 3) (fma.f64 -2 x (fma.f64 -1/4 (pow.f64 x 4) (neg.f64 (*.f64 x x)))))
(fma.f64 -1/2 (pow.f64 x 3) (fma.f64 -1/4 (pow.f64 x 4) (*.f64 x (-.f64 -2 x))))
(fma.f64 x (-.f64 -2 x) (.f64 (pow.f64 x 3) (+.f64 -1/2 (.f64 x -1/4))))
(fma.f64 (pow.f64 x 3) (+.f64 -1/2 (.f64 x -1/4)) (.f64 x (-.f64 -2 x)))
4
(+.f64 4 (*.f64 8 (/.f64 1 x)))
(+.f64 4 (/.f64 8 x))
(+.f64 4 (+.f64 (.f64 8 (/.f64 1 x)) (.f64 16 (/.f64 1 (pow.f64 x 2)))))
(+.f64 4 (+.f64 (/.f64 8 x) (/.f64 16 (*.f64 x x))))
(+.f64 (+.f64 4 (/.f64 8 x)) (/.f64 16 (*.f64 x x)))
(+.f64 4 (+.f64 (.f64 8 (/.f64 1 x)) (+.f64 (.f64 32 (/.f64 1 (pow.f64 x 3))) (*.f64 16 (/.f64 1 (pow.f64 x 2))))))
(+.f64 (+.f64 4 (/.f64 8 x)) (+.f64 (/.f64 16 (*.f64 x x)) (/.f64 32 (pow.f64 x 3))))
(+.f64 4 (+.f64 (/.f64 16 (*.f64 x x)) (+.f64 (/.f64 8 x) (/.f64 32 (pow.f64 x 3)))))
(+.f64 (/.f64 16 (*.f64 x x)) (+.f64 4 (+.f64 (/.f64 8 x) (/.f64 32 (pow.f64 x 3)))))
(+.f64 4 (+.f64 (/.f64 8 x) (+.f64 (/.f64 16 (*.f64 x x)) (/.f64 32 (pow.f64 x 3)))))
(+.f64 4 (+.f64 (+.f64 (/.f64 8 x) (/.f64 16 (*.f64 x x))) (/.f64 32 (pow.f64 x 3))))
4
(+.f64 4 (*.f64 8 (/.f64 1 x)))
(+.f64 4 (/.f64 8 x))
(+.f64 4 (+.f64 (.f64 8 (/.f64 1 x)) (.f64 16 (/.f64 1 (pow.f64 x 2)))))
(+.f64 4 (+.f64 (/.f64 8 x) (/.f64 16 (*.f64 x x))))
(+.f64 (+.f64 4 (/.f64 8 x)) (/.f64 16 (*.f64 x x)))
(+.f64 4 (+.f64 (.f64 8 (/.f64 1 x)) (+.f64 (.f64 32 (/.f64 1 (pow.f64 x 3))) (*.f64 16 (/.f64 1 (pow.f64 x 2))))))
(+.f64 (+.f64 4 (/.f64 8 x)) (+.f64 (/.f64 16 (*.f64 x x)) (/.f64 32 (pow.f64 x 3))))
(+.f64 4 (+.f64 (/.f64 16 (*.f64 x x)) (+.f64 (/.f64 8 x) (/.f64 32 (pow.f64 x 3)))))
(+.f64 (/.f64 16 (*.f64 x x)) (+.f64 4 (+.f64 (/.f64 8 x) (/.f64 32 (pow.f64 x 3)))))
(+.f64 4 (+.f64 (/.f64 8 x) (+.f64 (/.f64 16 (*.f64 x x)) (/.f64 32 (pow.f64 x 3)))))
(+.f64 4 (+.f64 (+.f64 (/.f64 8 x) (/.f64 16 (*.f64 x x))) (/.f64 32 (pow.f64 x 3))))
(/.f64 -1/2 x)
(-.f64 1/4 (*.f64 1/2 (/.f64 1 x)))
(-.f64 1/4 (/.f64 1/2 x))
(+.f64 1/4 (/.f64 -1/2 x))
(-.f64 1/4 (*.f64 1/2 (/.f64 1 x)))
(-.f64 1/4 (/.f64 1/2 x))
(+.f64 1/4 (/.f64 -1/2 x))
(-.f64 1/4 (*.f64 1/2 (/.f64 1 x)))
(-.f64 1/4 (/.f64 1/2 x))
(+.f64 1/4 (/.f64 -1/2 x))
1/4
(-.f64 1/4 (*.f64 1/2 (/.f64 1 x)))
(-.f64 1/4 (/.f64 1/2 x))
(+.f64 1/4 (/.f64 -1/2 x))
(-.f64 1/4 (*.f64 1/2 (/.f64 1 x)))
(-.f64 1/4 (/.f64 1/2 x))
(+.f64 1/4 (/.f64 -1/2 x))
(-.f64 1/4 (*.f64 1/2 (/.f64 1 x)))
(-.f64 1/4 (/.f64 1/2 x))
(+.f64 1/4 (/.f64 -1/2 x))
1/4
(-.f64 1/4 (*.f64 1/2 (/.f64 1 x)))
(-.f64 1/4 (/.f64 1/2 x))
(+.f64 1/4 (/.f64 -1/2 x))
(-.f64 1/4 (*.f64 1/2 (/.f64 1 x)))
(-.f64 1/4 (/.f64 1/2 x))
(+.f64 1/4 (/.f64 -1/2 x))
(-.f64 1/4 (*.f64 1/2 (/.f64 1 x)))
(-.f64 1/4 (/.f64 1/2 x))
(+.f64 1/4 (/.f64 -1/2 x))

localize6.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.1b	(*.f64 (+.f64 1/8 (pow.f64 x -3)) (+.f64 4 (/.f64 8 x)))
	0.0b	(+.f64 4 (/.f64 8 x))
✓	0.0b	(+.f64 4 (/.f64 8 x))
✓	0.1b	(*.f64 (+.f64 1/8 (pow.f64 x -3)) (+.f64 4 (/.f64 8 x)))

series3.0ms (0.1%)

Counts

2 → 24

Calls

6 calls:

Time	Variable		Point	Expression
2.0ms	x	@	0	(*.f64 (+.f64 1/8 (pow.f64 x -3)) (+.f64 4 (/.f64 8 x)))
0.0ms	x	@	inf	(*.f64 (+.f64 1/8 (pow.f64 x -3)) (+.f64 4 (/.f64 8 x)))
0.0ms	x	@	-inf	(*.f64 (+.f64 1/8 (pow.f64 x -3)) (+.f64 4 (/.f64 8 x)))
0.0ms	x	@	0	(+.f64 4 (/.f64 8 x))
0.0ms	x	@	-inf	(+.f64 4 (/.f64 8 x))

rewrite62.0ms (1.6%)

Algorithm

1×	batch-egg-rewrite

Rules

511×	`log-prod_binary64`
371×	`pow-prod-down_binary64`
318×	`pow2_binary64`
299×	`prod-diff_binary64`
219×	`pow1/3_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	11	23
1	262	23
2	3474	23

Stop Event

1×	node limit

Counts

2 → 112

Calls

Call 1

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

Outputs

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

((#(struct:change #<rule egg-rr> (2) ((x -.f64 (exp.f64 (log1p.f64 (+.f64 4 (/.f64 8 x)))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (/.f64 16 (-.f64 4 (/.f64 8 x))) (/.f64 (/.f64 64 (*.f64 x x)) (-.f64 4 (/.f64 8 x))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (+.f64 4 (/.f64 8 x)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 1 (+.f64 4 (/.f64 8 x)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 (+.f64 4 (/.f64 8 x))) (pow.f64 (cbrt.f64 (+.f64 4 (/.f64 8 x))) 2))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (cbrt.f64 (+.f64 4 (/.f64 8 x))) 2) (cbrt.f64 (+.f64 4 (/.f64 8 x))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (sqrt.f64 (+.f64 4 (/.f64 8 x))) (sqrt.f64 (+.f64 4 (/.f64 8 x))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (fma.f64 512 (pow.f64 x -3) 64) (/.f64 1 (fma.f64 (/.f64 8 x) (-.f64 (/.f64 8 x) 4) 16)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (-.f64 16 (/.f64 64 (*.f64 x x))) (/.f64 1 (-.f64 4 (/.f64 8 x))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 1 (/.f64 (fma.f64 (/.f64 8 x) (-.f64 (/.f64 8 x) 4) 16) (fma.f64 512 (pow.f64 x -3) 64)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 1 (/.f64 (-.f64 4 (/.f64 8 x)) (-.f64 16 (/.f64 64 (*.f64 x x)))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (fma.f64 512 (pow.f64 x -3) 64) (fma.f64 (/.f64 8 x) (-.f64 (/.f64 8 x) 4) 16))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (fma.f64 512 (pow.f64 x -3) 64) (+.f64 (/.f64 64 (*.f64 x x)) (-.f64 16 (/.f64 32 x))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (-.f64 16 (/.f64 64 (*.f64 x x))) (-.f64 4 (/.f64 8 x)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (neg.f64 (fma.f64 512 (pow.f64 x -3) 64)) (neg.f64 (fma.f64 (/.f64 8 x) (-.f64 (/.f64 8 x) 4) 16)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (neg.f64 (-.f64 16 (/.f64 64 (*.f64 x x)))) (neg.f64 (-.f64 4 (/.f64 8 x))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (-.f64 (/.f64 64 (*.f64 x x)) 16) (-.f64 (/.f64 8 x) 4))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (+.f64 4 (/.f64 8 x)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (+.f64 4 (/.f64 8 x)) 2) 1/2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (+.f64 4 (/.f64 8 x)) 3) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (cbrt.f64 (+.f64 4 (/.f64 8 x))) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (sqrt.f64 (+.f64 4 (/.f64 8 x))) 2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (/.f64 (fma.f64 (/.f64 8 x) (-.f64 (/.f64 8 x) 4) 16) (fma.f64 512 (pow.f64 x -3) 64)) -1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (/.f64 (-.f64 4 (/.f64 8 x)) (-.f64 16 (/.f64 64 (*.f64 x x)))) -1)))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f64 (pow.f64 (+.f64 4 (/.f64 8 x)) 2))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (exp.f64 (+.f64 4 (/.f64 8 x))))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (+.f64 1 (expm1.f64 (+.f64 4 (/.f64 8 x)))))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (pow.f64 (+.f64 4 (/.f64 8 x)) 3))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (+.f64 4 (/.f64 8 x))))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (+.f64 4 (/.f64 8 x))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (log.f64 (+.f64 4 (/.f64 8 x))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (log.f64 (+.f64 4 (/.f64 8 x))) 1))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 8 (/.f64 1 x) 4)))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (/.f64 8 x) 1 4)))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 1 (/.f64 8 x) 4)))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (/.f64 2 (cbrt.f64 x)) (pow.f64 (/.f64 2 (cbrt.f64 x)) 2) 4)))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (pow.f64 (/.f64 2 (cbrt.f64 x)) 2) (/.f64 2 (cbrt.f64 x)) 4)))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (sqrt.f64 (/.f64 8 x)) (sqrt.f64 (/.f64 8 x)) 4)))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 -8 (/.f64 1 (neg.f64 x)) 4)))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (/.f64 1 x) 8 4)))))

simplify104.0ms (2.7%)

Algorithm

1×	egg-herbie

Rules

935×	`fma-def_binary64`
641×	`sqr-pow_binary64`
522×	`*-commutative_binary64`
512×	`associate-*l/_binary64`
492×	`associate-/l*_binary64`

Iterations

Useful iterations: 6 (0.0ms)

Iter	Nodes	Cost
0	24	237
1	59	237
2	118	237
3	204	237
4	389	237
5	1392	229
6	4471	222
7	4757	222
8	5078	222
9	5336	222
10	5791	222
11	6451	222
12	7066	222
13	7593	222

Stop Event

1×	node limit

Counts

136 → 128

Calls

Call 1

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

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

localize4.0ms (0.1%)

Local error

Found 2 expressions with local error:

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

series1.0ms (0%)

Counts

1 → 12

Calls

3 calls:

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

rewrite46.0ms (1.2%)

Algorithm

1×	batch-egg-rewrite

Rules

918×	`pow1_binary64`
863×	`add-log-exp_binary64`
862×	`log1p-expm1-u_binary64`
862×	`expm1-log1p-u_binary64`
850×	`add-exp-log_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	8	10
1	176	7
2	2244	7

Stop Event

1×	node limit

Counts

1 → 33

Calls

Call 1

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

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 1 (-.f64 -5/2 (/.f64 1 x))) (/.f64 (pow.f64 (+.f64 (/.f64 1 x) 3/2) 2) (-.f64 -5/2 (/.f64 1 x))))))) (#(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 1 (+.f64 (pow.f64 (+.f64 (/.f64 1 x) 3/2) 2) (+.f64 (/.f64 1 x) 3/2)))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (-.f64 1 (pow.f64 (+.f64 (/.f64 1 x) 3/2) 2)) (/.f64 1 (-.f64 -5/2 (/.f64 1 x))))))) (#(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 1 (+.f64 (pow.f64 (+.f64 (/.f64 1 x) 3/2) 2) (+.f64 (/.f64 1 x) 3/2))) (+.f64 -1 (pow.f64 (+.f64 (/.f64 1 x) 3/2) 3))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 1 (/.f64 (-.f64 -5/2 (/.f64 1 x)) (-.f64 1 (pow.f64 (+.f64 (/.f64 1 x) 3/2) 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 (/.f64 1 x) 3/2))))))) (#(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 (neg.f64 (+.f64 (/.f64 1 x) 3/2)))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (-.f64 1 (pow.f64 (+.f64 (/.f64 1 x) 3/2) 2)) (-.f64 -5/2 (/.f64 1 x)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (neg.f64 (+.f64 -1 (pow.f64 (+.f64 (/.f64 1 x) 3/2) 3))) (neg.f64 (+.f64 1 (+.f64 (pow.f64 (+.f64 (/.f64 1 x) 3/2) 2) (+.f64 (/.f64 1 x) 3/2)))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (neg.f64 (-.f64 1 (pow.f64 (+.f64 (/.f64 1 x) 3/2) 2))) (neg.f64 (-.f64 -5/2 (/.f64 1 x))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (+.f64 (pow.f64 (+.f64 -1 (/.f64 1 x)) 3) 27/8) (+.f64 (*.f64 (+.f64 -1 (/.f64 1 x)) (+.f64 -1 (/.f64 1 x))) (-.f64 9/4 (*.f64 (+.f64 -1 (/.f64 1 x)) 3/2))))))) (#(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 (*.f64 (+.f64 -1 (/.f64 1 x)) (+.f64 -1 (/.f64 1 x))) 9/4) (-.f64 (+.f64 -1 (/.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 log1p.f64 (expm1.f64 (+.f64 (/.f64 1 x) 1/2)))))) (#(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 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 (sqrt.f64 (+.f64 (/.f64 1 x) 3/2)) (sqrt.f64 (+.f64 (/.f64 1 x) 3/2)) -1)))))

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

45 → 37

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%)

Local error

Found 4 expressions with local error:

New	Error	Program
	1.4b	(-.f64 (+.f64 1 (/.f64 1 x)) 1)
	0.0b	(+.f64 1 (/.f64 1 x))
✓	0.0b	(+.f64 1 (/.f64 1 x))
✓	1.4b	(-.f64 (+.f64 1 (/.f64 1 x)) 1)

series2.0ms (0%)

Counts

2 → 15

Calls

6 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	@	0	(+.f64 1 (/.f64 1 x))
0.0ms	x	@	inf	(+.f64 1 (/.f64 1 x))
0.0ms	x	@	inf	(-.f64 (+.f64 1 (/.f64 1 x)) 1)

rewrite47.0ms (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	17
1	139	11
2	1920	11

Stop Event

1×	node limit

Counts

2 → 80

Calls

Call 1

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

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

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

simplify7.0ms (0.2%)

Algorithm

1×	egg-herbie

Rules

1×	`1-exp_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	4	54
1	6	54

Stop Event

1×

saturated

Counts

95 → 81

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)
(/.f64 1 x)
1
1

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)
(/.f64 1 x)
1
1

eval168.0ms (4.4%)

Compiler: Compiled 6700 to 5622 computations (16.1% saved)

prune57.0ms (1.5%)

Pruning

17 alts after pruning (11 fresh and 6 done)

	Pruned	Kept	Total
New	403	11	414
Fresh	1	0	1
Picked	1	0	1
Done	2	6	8
Total	407	17	424

Error

0.8b

Counts

424 → 17

Alt Table

Click to see full alt table

Status	Error	Program
	61.7b	1/2
✓	21.1b	(+.f64 -1 (+.f64 (/.f64 1 x) 3/2))
	62.1b	(+.f64 (/.f64 2 (*.f64 x x)) (+.f64 (-.f64 1/2 (/.f64 -1 x)) (/.f64 8 (pow.f64 x 3))))
	43.0b	(-.f64 1 1)
	50.5b	(/.f64 (+.f64 4 (/.f64 8 x)) (pow.f64 x 3))
	62.4b	(*.f64 (+.f64 1/8 (pow.f64 x -3)) (pow.f64 (/.f64 1 (cbrt.f64 (+.f64 1/4 (/.f64 -1/2 x)))) 3))
	62.4b	(*.f64 (+.f64 1/8 (pow.f64 x -3)) (pow.f64 (cbrt.f64 (+.f64 1/4 (/.f64 -1/2 x))) -3))
	63.1b	(log.f64 (exp.f64 (/.f64 (+.f64 1/8 (pow.f64 x -3)) (+.f64 1/4 (/.f64 -1/2 x)))))
	62.4b	(/.f64 (+.f64 1/8 (pow.f64 x -3)) (+.f64 1/4 (/.f64 -1/2 x)))
	53.7b	(/.f64 -2 (*.f64 x x))
✓	21.1b	(+.f64 1/2 (/.f64 1 x))
	62.2b	(+.f64 1/2 (-.f64 (/.f64 2 (*.f64 x x)) (/.f64 -1 x)))
✓	1.0b	(/.f64 (exp.f64 x) (expm1.f64 x))
	63.1b	(+.f64 (log.f64 (pow.f64 (cbrt.f64 (exp.f64 (/.f64 (+.f64 1/8 (pow.f64 x -3)) (+.f64 1/4 (/.f64 -1/2 x))))) 2)) (log.f64 (cbrt.f64 (exp.f64 (/.f64 (+.f64 1/8 (pow.f64 x -3)) (+.f64 1/4 (/.f64 -1/2 x)))))))
✓	21.4b	(+.f64 1/2 (+.f64 (.f64 -1/720 (pow.f64 x 3)) (+.f64 (.f64 1/12 x) (/.f64 1 x))))
✓	21.0b	(+.f64 1/2 (+.f64 (*.f64 1/12 x) (/.f64 1 x)))
✓	21.2b	(/.f64 1 x)

Compiler

Compiled 192 to 159 computations (17.2% saved)

regimes40.0ms (1.1%)

Counts

25 → 1

Calls

Call 1

Inputs
1/2
1/2
1/2
(-.f64 1 1)
(/.f64 1 x)
(/.f64 -2 (*.f64 x x))
(+.f64 1/2 (/.f64 1 x))
(-.f64 (+.f64 1 (/.f64 1 x)) 1)
(+.f64 -1 (+.f64 (/.f64 1 x) 3/2))
(-.f64 (+.f64 1 (+.f64 1/2 (/.f64 1 x))) 1)
(+.f64 1/2 (+.f64 (*.f64 1/12 x) (/.f64 1 x)))
(+.f64 1/2 (-.f64 (/.f64 2 (*.f64 x x)) (/.f64 -1 x)))
(/.f64 (+.f64 4 (/.f64 8 x)) (pow.f64 x 3))
(/.f64 (+.f64 1/8 (pow.f64 x -3)) (+.f64 1/4 (/.f64 -1/2 x)))
(*.f64 (+.f64 1/8 (pow.f64 x -3)) (+.f64 4 (/.f64 8 x)))
(*.f64 (+.f64 1/8 (pow.f64 x -3)) (/.f64 1 (+.f64 1/4 (/.f64 -1/2 x))))
(+.f64 1/2 (+.f64 (.f64 -1/720 (pow.f64 x 3)) (+.f64 (.f64 1/12 x) (/.f64 1 x))))
(+.f64 (/.f64 2 (*.f64 x x)) (+.f64 (-.f64 1/2 (/.f64 -1 x)) (/.f64 8 (pow.f64 x 3))))
(/.f64 (exp.f64 x) (expm1.f64 x))
(/.f64 (exp.f64 x) (-.f64 (exp.f64 x) 1))
(*.f64 (+.f64 1/8 (pow.f64 x -3)) (/.f64 1 (+.f64 1/4 (-.f64 (pow.f64 x -2) (/.f64 1/2 x)))))
(log.f64 (exp.f64 (/.f64 (+.f64 1/8 (pow.f64 x -3)) (+.f64 1/4 (/.f64 -1/2 x)))))
(*.f64 (+.f64 1/8 (pow.f64 x -3)) (pow.f64 (cbrt.f64 (+.f64 1/4 (/.f64 -1/2 x))) -3))
(*.f64 (+.f64 1/8 (pow.f64 x -3)) (pow.f64 (/.f64 1 (cbrt.f64 (+.f64 1/4 (/.f64 -1/2 x)))) 3))
(+.f64 (log.f64 (pow.f64 (cbrt.f64 (exp.f64 (/.f64 (+.f64 1/8 (pow.f64 x -3)) (+.f64 1/4 (/.f64 -1/2 x))))) 2)) (log.f64 (cbrt.f64 (exp.f64 (/.f64 (+.f64 1/8 (pow.f64 x -3)) (+.f64 1/4 (/.f64 -1/2 x)))))))

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

Calls

5 calls:

12.0ms	x
6.0ms	(exp.f64 x)
4.0ms	(/.f64 (exp.f64 x) (-.f64 (exp.f64 x) 1))
4.0ms	(/.f64 (exp.f64 x) (-.f64 (exp.f64 x) 1))
4.0ms	(exp.f64 x)

Results

Error	Segments	Branch
1.0b	1	`x`
1.0b	1	`(/.f64 (exp.f64 x) (-.f64 (exp.f64 x) 1))`
1.0b	1	`(/.f64 (exp.f64 x) (-.f64 (exp.f64 x) 1))`
1.0b	1	`(exp.f64 x)`
1.0b	1	`(exp.f64 x)`

Compiler

Compiled 266 to 209 computations (21.4% saved)

regimes22.0ms (0.6%)

Counts

18 → 2

Calls

Call 1

Inputs
1/2
1/2
1/2
(-.f64 1 1)
(/.f64 1 x)
(/.f64 -2 (*.f64 x x))
(+.f64 1/2 (/.f64 1 x))
(-.f64 (+.f64 1 (/.f64 1 x)) 1)
(+.f64 -1 (+.f64 (/.f64 1 x) 3/2))
(-.f64 (+.f64 1 (+.f64 1/2 (/.f64 1 x))) 1)
(+.f64 1/2 (+.f64 (*.f64 1/12 x) (/.f64 1 x)))
(+.f64 1/2 (-.f64 (/.f64 2 (*.f64 x x)) (/.f64 -1 x)))
(/.f64 (+.f64 4 (/.f64 8 x)) (pow.f64 x 3))
(/.f64 (+.f64 1/8 (pow.f64 x -3)) (+.f64 1/4 (/.f64 -1/2 x)))
(*.f64 (+.f64 1/8 (pow.f64 x -3)) (+.f64 4 (/.f64 8 x)))
(*.f64 (+.f64 1/8 (pow.f64 x -3)) (/.f64 1 (+.f64 1/4 (/.f64 -1/2 x))))
(+.f64 1/2 (+.f64 (.f64 -1/720 (pow.f64 x 3)) (+.f64 (.f64 1/12 x) (/.f64 1 x))))
(+.f64 (/.f64 2 (*.f64 x x)) (+.f64 (-.f64 1/2 (/.f64 -1 x)) (/.f64 8 (pow.f64 x 3))))

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

Calls

1 calls:

17.0ms

Results

Error	Segments	Branch
1.5b	2	`x`

Compiler

Compiled 141 to 111 computations (21.3% saved)

bsearch19.0ms (0.5%)

Algorithm

1×	binary-search

Steps

Time	Left	Right
18.0ms	-86089954.93386506	-3.65788890388525

Compiler

Compiled 12 to 8 computations (33.3% saved)

regimes16.0ms (0.4%)

Counts

10 → 2

Calls

Call 1

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

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

Calls

1 calls:

12.0ms

Results

Error	Segments	Branch
1.8b	2	`x`

Compiler

Compiled 45 to 37 computations (17.8% saved)

bsearch18.0ms (0.5%)

Algorithm

1×	binary-search

Steps

Time	Left	Right
18.0ms	-3.65788890388525	-1.1047065211262845

Compiler

Compiled 12 to 8 computations (33.3% saved)

regimes10.0ms (0.3%)

Counts

6 → 2

Calls

Call 1

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

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

Calls

1 calls:

9.0ms

Results

Error	Segments	Branch
2.3b	2	`x`

Compiler

Compiled 17 to 13 computations (23.5% saved)

bsearch19.0ms (0.5%)

Algorithm

1×	binary-search

Steps

Time	Left	Right
19.0ms	-86089954.93386506	-3.65788890388525

Compiler

Compiled 12 to 8 computations (33.3% saved)

regimes5.0ms (0.1%)

Counts

4 → 1

Calls

Call 1

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

Outputs
(-.f64 1 1)

Calls

1 calls:

4.0ms

Results

Error	Segments	Branch
43.0b	1	`x`

Compiler

Compiled 9 to 8 computations (11.1% saved)

regimes5.0ms (0.1%)

Accuracy

Total 0.0b remaining (0%)

Threshold costs 0.0b (0%)

Counts

3 → 1

Calls

Call 1

Inputs
1/2
1/2
1/2

Outputs
1/2

Calls

1 calls:

4.0ms

Results

Error	Segments	Branch
61.7b	1	`x`

Compiler

Compiled 6 to 5 computations (16.7% saved)

simplify3.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

3×	`+-commutative_binary64`
1×	`*-commutative_binary64`
1×	`1-exp_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	23	55
1	28	55

Stop Event

1×

saturated

Calls

Call 1

Inputs
(/.f64 (exp.f64 x) (expm1.f64 x))
(if (<=.f64 x -369753540955064256/4294967296) (-.f64 1 1) (+.f64 1/2 (+.f64 (*.f64 1/12 x) (/.f64 1 x))))
(if (<=.f64 x -4118416776125071/1125899906842624) (-.f64 1 1) (+.f64 1/2 (/.f64 1 x)))
(if (<=.f64 x -369753540955064256/4294967296) (-.f64 1 1) (/.f64 1 x))
(-.f64 1 1)
1/2

Outputs
(/.f64 (exp.f64 x) (expm1.f64 x))
(if (<=.f64 x -369753540955064256/4294967296) (-.f64 1 1) (+.f64 1/2 (+.f64 (*.f64 1/12 x) (/.f64 1 x))))
(if (<=.f64 x -5777399077422879/67108864) 0 (+.f64 1/2 (+.f64 (*.f64 x 1/12) (/.f64 1 x))))
(if (<=.f64 x -4118416776125071/1125899906842624) (-.f64 1 1) (+.f64 1/2 (/.f64 1 x)))
(if (<=.f64 x -4118416776125071/1125899906842624) 0 (+.f64 1/2 (/.f64 1 x)))
(if (<=.f64 x -369753540955064256/4294967296) (-.f64 1 1) (/.f64 1 x))
(if (<=.f64 x -5777399077422879/67108864) 0 (/.f64 1 x))
(-.f64 1 1)
0
1/2

end42.0ms (1.1%)

Stop Event

1×

fuel

Compiler

Compiled 85 to 67 computations (21.2% saved)

Details

analyze122.0ms (3.2%)

sample1.6s (43.5%)

preprocess18.0ms (0.5%)

simplify6.0ms (0.2%)

eval1.0ms (0%)

prune1.0ms (0%)

localize3.0ms (0.1%)

series2.0ms (0.1%)

rewrite37.0ms (1%)

simplify136.0ms (3.6%)

eval7.0ms (0.2%)

prune7.0ms (0.2%)

localize2.0ms (0%)

localize4.0ms (0.1%)

series1.0ms (0%)

rewrite43.0ms (1.1%)

simplify6.0ms (0.2%)

localize6.0ms (0.2%)

series3.0ms (0.1%)

rewrite64.0ms (1.7%)

simplify13.0ms (0.3%)

localize8.0ms (0.2%)

series4.0ms (0.1%)

rewrite68.0ms (1.8%)

simplify142.0ms (3.8%)

eval176.0ms (4.6%)

prune50.0ms (1.3%)

localize5.0ms (0.1%)

series1.0ms (0%)

rewrite51.0ms (1.3%)

simplify8.0ms (0.2%)

localize9.0ms (0.2%)

series7.0ms (0.2%)

rewrite81.0ms (2.1%)

simplify37.0ms (1%)

eval142.0ms (3.7%)

prune37.0ms (1%)

localize9.0ms (0.2%)

series3.0ms (0.1%)

rewrite66.0ms (1.7%)

simplify41.0ms (1.1%)

localize6.0ms (0.2%)

series3.0ms (0.1%)

rewrite62.0ms (1.6%)

simplify104.0ms (2.7%)

localize4.0ms (0.1%)

series1.0ms (0%)

rewrite46.0ms (1.2%)

simplify7.0ms (0.2%)

localize4.0ms (0.1%)

series2.0ms (0%)

rewrite47.0ms (1.2%)

simplify7.0ms (0.2%)

eval168.0ms (4.4%)

prune57.0ms (1.5%)

regimes40.0ms (1.1%)

regimes22.0ms (0.6%)

bsearch19.0ms (0.5%)

regimes16.0ms (0.4%)

bsearch18.0ms (0.5%)

regimes10.0ms (0.3%)

bsearch19.0ms (0.5%)

regimes5.0ms (0.1%)

regimes5.0ms (0.1%)

simplify3.0ms (0.1%)

end42.0ms (1.1%)

Profiling