Details

analyze124.0ms (2%)

Algorithm

1×

Search

Probability	Valid	Unknown	Precondition	Infinite	Domain	Can't	Iter
0%	0%	100%	0%	0%	0%	0%	0
0%	0%	100%	0%	0%	0%	0%	1
0%	0%	100%	0%	0%	0%	0%	2
25%	25%	75%	0%	0%	0%	0%	3
28.6%	25%	62.5%	0%	0%	0%	12.5%	4
30.8%	25%	56.2%	0%	0%	0%	18.7%	5
36%	28.1%	50%	0%	0%	0%	21.9%	6
38.8%	29.7%	46.9%	0%	0%	0%	23.4%	7
40.2%	30.5%	45.3%	0%	0%	0%	24.2%	8
40.7%	30.8%	44.9%	0%	0%	0%	24.2%	9
41.2%	31.2%	44.5%	0%	0%	0%	24.2%	10
41.4%	31.3%	44.4%	0%	0%	0%	24.2%	11
41.5%	31.4%	44.3%	0%	0%	0%	24.3%	12

Compiler

Compiled 9 to 6 computations (33.3% saved)

sample2.4s (39.3%)

Results

1.3s	2742×	body	1024	valid
639.0ms	3870×	body	256	valid
291.0ms	1365×	body	512	valid
101.0ms	279×	body	2048	valid
0.0ms	2×	body	256	unsamplable

Bogosity

preprocess15.0ms (0.3%)

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)

simplify7.0ms (0.1%)

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))

eval8.0ms (0.1%)

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

prune1.0ms (0%)

Pruning

1 alts after pruning (1 fresh and 0 done)

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

Error

0.5b

Counts

3 → 1

Alt Table

Click to see full alt table

Status	Error	Program
▶	0.5b	(/.f64 (exp.f64 x) (expm1.f64 x))

Compiler

Compiled 6 to 4 computations (33.3% saved)

localize6.0ms (0.1%)

Local error

Found 1 expressions with local error:

New	Error	Program
✓	0.5b	(/.f64 (exp.f64 x) (expm1.f64 x))

Compiler

Compiled 11 to 4 computations (63.6% saved)

series2.0ms (0%)

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))

rewrite44.0ms (0.7%)

Algorithm

1×	batch-egg-rewrite

Rules

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

Iterations

Useful iterations: 0 (0.0ms)

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

Stop Event

1×	node limit

Counts

1 → 30

Calls

Call 1

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

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

simplify181.0ms (3%)

Algorithm

1×	egg-herbie

Rules

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

Iterations

Useful iterations: 0 (0.0ms)

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

Stop Event

1×	node limit

Counts

42 → 39

Calls

Call 1

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

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

eval7.0ms (0.1%)

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

prune14.0ms (0.2%)

Pruning

7 alts after pruning (6 fresh and 1 done)

	Pruned	Kept	Total
New	33	6	39
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	33	7	40

Error

0.4b

Counts

40 → 7

Alt Table

Click to see full alt table

Status	Error	Program
▶	0.5b	(pow.f64 (/.f64 (expm1.f64 x) (exp.f64 x)) -1)
✓	0.5b	(/.f64 (exp.f64 x) (expm1.f64 x))
	24.4b	(+.f64 1/2 (+.f64 (.f64 -1/720 (pow.f64 x 3)) (+.f64 (.f64 1/12 x) (/.f64 1 x))))
▶	23.9b	(+.f64 (/.f64 1 x) (fma.f64 x 1/12 1/2))
▶	23.9b	(+.f64 1/2 (+.f64 (*.f64 1/12 x) (/.f64 1 x)))
▶	24.0b	(+.f64 (/.f64 1 x) 1/2)
▶	23.9b	(/.f64 1 x)

Compiler

Compiled 112 to 88 computations (21.4% saved)

localize8.0ms (0.1%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.0b	(pow.f64 (/.f64 (expm1.f64 x) (exp.f64 x)) -1)
✓	0.5b	(/.f64 (expm1.f64 x) (exp.f64 x))

Compiler

Compiled 19 to 7 computations (63.2% saved)

series4.0ms (0.1%)

Counts

2 → 24

Calls

6 calls:

Time	Variable		Point	Expression
1.0ms	x	@	inf	(/.f64 (expm1.f64 x) (exp.f64 x))
1.0ms	x	@	inf	(pow.f64 (/.f64 (expm1.f64 x) (exp.f64 x)) -1)
1.0ms	x	@	-inf	(pow.f64 (/.f64 (expm1.f64 x) (exp.f64 x)) -1)
1.0ms	x	@	-inf	(/.f64 (expm1.f64 x) (exp.f64 x))
1.0ms	x	@	0	(/.f64 (expm1.f64 x) (exp.f64 x))

rewrite72.0ms (1.2%)

Algorithm

1×	batch-egg-rewrite

Rules

672×	`pow1_binary64`
625×	`add-log-exp_binary64`
625×	`log1p-expm1-u_binary64`
625×	`expm1-log1p-u_binary64`
609×	`add-exp-log_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	7	19
1	141	16
2	1747	16

Stop Event

1×	node limit

Counts

2 → 72

Calls

Call 1

Inputs
(/.f64 (expm1.f64 x) (exp.f64 x))
(pow.f64 (/.f64 (expm1.f64 x) (exp.f64 x)) -1)

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

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

simplify79.0ms (1.3%)

Algorithm

1×	egg-herbie

Rules

803×	`unswap-sqr_binary64`
513×	`distribute-lft-out_binary64`
416×	`*-commutative_binary64`
384×	`fma-def_binary64`
246×	`distribute-rgt-out_binary64`

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	35	214
1	90	214
2	205	214
3	592	208
4	1654	200
5	2810	200
6	5087	200
7	6222	200

Stop Event

1×	node limit

Counts

96 → 89

Calls

Call 1

Inputs
x
(+.f64 (*.f64 -1/2 (pow.f64 x 2)) x)
(+.f64 (.f64 1/6 (pow.f64 x 3)) (+.f64 (.f64 -1/2 (pow.f64 x 2)) x))
(+.f64 (.f64 1/6 (pow.f64 x 3)) (+.f64 (.f64 -1/2 (pow.f64 x 2)) (+.f64 (*.f64 -1/24 (pow.f64 x 4)) x)))
(/.f64 (-.f64 (exp.f64 x) 1) (exp.f64 x))
(/.f64 (-.f64 (exp.f64 x) 1) (exp.f64 x))
(/.f64 (-.f64 (exp.f64 x) 1) (exp.f64 x))
(/.f64 (-.f64 (exp.f64 x) 1) (exp.f64 x))
(/.f64 (-.f64 (exp.f64 x) 1) (exp.f64 x))
(/.f64 (-.f64 (exp.f64 x) 1) (exp.f64 x))
(/.f64 (-.f64 (exp.f64 x) 1) (exp.f64 x))
(/.f64 (-.f64 (exp.f64 x) 1) (exp.f64 x))
(/.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
x
(+.f64 (*.f64 -1/2 (pow.f64 x 2)) x)
(fma.f64 -1/2 (*.f64 x x) x)
(fma.f64 x (*.f64 x -1/2) x)
(*.f64 x (fma.f64 x -1/2 1))
(+.f64 (.f64 1/6 (pow.f64 x 3)) (+.f64 (.f64 -1/2 (pow.f64 x 2)) x))
(fma.f64 1/6 (pow.f64 x 3) (fma.f64 -1/2 (*.f64 x x) x))
(fma.f64 x (*.f64 x -1/2) (fma.f64 1/6 (pow.f64 x 3) x))
(fma.f64 x (*.f64 x (fma.f64 x 1/6 -1/2)) x)
(fma.f64 (*.f64 x x) (fma.f64 x 1/6 -1/2) x)
(+.f64 (.f64 1/6 (pow.f64 x 3)) (+.f64 (.f64 -1/2 (pow.f64 x 2)) (+.f64 (*.f64 -1/24 (pow.f64 x 4)) x)))
(fma.f64 1/6 (pow.f64 x 3) (fma.f64 -1/2 (*.f64 x x) (fma.f64 -1/24 (pow.f64 x 4) x)))
(fma.f64 x (*.f64 x -1/2) (fma.f64 1/6 (pow.f64 x 3) (fma.f64 -1/24 (pow.f64 x 4) x)))
(fma.f64 x (*.f64 x (fma.f64 x 1/6 -1/2)) (fma.f64 -1/24 (pow.f64 x 4) x))
(fma.f64 (*.f64 x x) (fma.f64 x 1/6 -1/2) (fma.f64 -1/24 (pow.f64 x 4) x))
(/.f64 (-.f64 (exp.f64 x) 1) (exp.f64 x))
(/.f64 (expm1.f64 x) (exp.f64 x))
(-.f64 1 (exp.f64 (neg.f64 x)))
(neg.f64 (expm1.f64 (neg.f64 x)))
(/.f64 (-.f64 (exp.f64 x) 1) (exp.f64 x))
(/.f64 (expm1.f64 x) (exp.f64 x))
(-.f64 1 (exp.f64 (neg.f64 x)))
(neg.f64 (expm1.f64 (neg.f64 x)))
(/.f64 (-.f64 (exp.f64 x) 1) (exp.f64 x))
(/.f64 (expm1.f64 x) (exp.f64 x))
(-.f64 1 (exp.f64 (neg.f64 x)))
(neg.f64 (expm1.f64 (neg.f64 x)))
(/.f64 (-.f64 (exp.f64 x) 1) (exp.f64 x))
(/.f64 (expm1.f64 x) (exp.f64 x))
(-.f64 1 (exp.f64 (neg.f64 x)))
(neg.f64 (expm1.f64 (neg.f64 x)))
(/.f64 (-.f64 (exp.f64 x) 1) (exp.f64 x))
(/.f64 (expm1.f64 x) (exp.f64 x))
(-.f64 1 (exp.f64 (neg.f64 x)))
(neg.f64 (expm1.f64 (neg.f64 x)))
(/.f64 (-.f64 (exp.f64 x) 1) (exp.f64 x))
(/.f64 (expm1.f64 x) (exp.f64 x))
(-.f64 1 (exp.f64 (neg.f64 x)))
(neg.f64 (expm1.f64 (neg.f64 x)))
(/.f64 (-.f64 (exp.f64 x) 1) (exp.f64 x))
(/.f64 (expm1.f64 x) (exp.f64 x))
(-.f64 1 (exp.f64 (neg.f64 x)))
(neg.f64 (expm1.f64 (neg.f64 x)))
(/.f64 (-.f64 (exp.f64 x) 1) (exp.f64 x))
(/.f64 (expm1.f64 x) (exp.f64 x))
(-.f64 1 (exp.f64 (neg.f64 x)))
(neg.f64 (expm1.f64 (neg.f64 x)))
(/.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 (pow.f64 x 3) -1/720 (fma.f64 x 1/12 (/.f64 1 x))))
(+.f64 (fma.f64 x 1/12 1/2) (fma.f64 (pow.f64 x 3) -1/720 (/.f64 1 x)))
(+.f64 (/.f64 1 x) (fma.f64 x 1/12 (fma.f64 (pow.f64 x 3) -1/720 1/2)))
(+.f64 (fma.f64 x 1/12 (/.f64 1 x)) (fma.f64 (pow.f64 x 3) -1/720 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))

localize3.0ms (0%)

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

localize5.0ms (0.1%)

Local error

Found 1 expressions with local error:

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

Compiler

Compiled 12 to 9 computations (25% saved)

series1.0ms (0%)

Counts

1 → 12

Calls

3 calls:

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

rewrite46.0ms (0.8%)

Algorithm

1×	batch-egg-rewrite

Rules

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

Iterations

Useful iterations: 0 (0.0ms)

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

Stop Event

1×	node limit

Counts

1 → 30

Calls

Call 1

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

Outputs

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

simplify7.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

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

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	6	69
1	9	69

Stop Event

1×

saturated

Counts

42 → 34

Calls

Call 1

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

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

localize11.0ms (0.2%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	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)

Compiler

Compiled 27 to 20 computations (25.9% saved)

series4.0ms (0.1%)

Counts

3 → 19

Calls

9 calls:

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

rewrite74.0ms (1.2%)

Algorithm

1×	batch-egg-rewrite

Rules

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

Iterations

Useful iterations: 0 (0.0ms)

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

Stop Event

1×	node limit

Counts

3 → 154

Calls

Call 1

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

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

simplify11.0ms (0.2%)

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))

localize9.0ms (0.2%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.0b	(+.f64 (/.f64 1 x) (fma.f64 x 1/12 1/2))
✓	0.1b	(fma.f64 x 1/12 1/2)

Compiler

Compiled 20 to 15 computations (25% saved)

series2.0ms (0%)

Counts

2 → 24

Calls

6 calls:

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

rewrite57.0ms (0.9%)

Algorithm

1×	batch-egg-rewrite

Rules

842×	`pow1_binary64`
790×	`add-log-exp_binary64`
790×	`log1p-expm1-u_binary64`
790×	`expm1-log1p-u_binary64`
776×	`add-exp-log_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	8	16
1	172	16
2	2131	16

Stop Event

1×	node limit

Counts

2 → 54

Calls

Call 1

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

Outputs

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

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

simplify10.0ms (0.2%)

Algorithm

1×	egg-herbie

Rules

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

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	13	171
1	23	149
2	28	149
3	30	149

Stop Event

1×

saturated

Counts

78 → 63

Calls

Call 1

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

eval133.0ms (2.2%)

Compiler: Compiled 4737 to 3398 computations (28.3% saved)

prune56.0ms (0.9%)

Pruning

10 alts after pruning (7 fresh and 3 done)

	Pruned	Kept	Total
New	344	6	350
Fresh	0	1	1
Picked	1	0	1
Done	2	3	5
Total	347	10	357

Error

Counts

357 → 10

Alt Table

Click to see full alt table

Status	Error	Program
✓	0.5b	(/.f64 (exp.f64 x) (expm1.f64 x))
▶	61.7b	(+.f64 1/2 (*.f64 x 1/12))
▶	24.0b	(-.f64 (+.f64 1 (+.f64 (/.f64 1 x) 1/2)) 1)
	61.6b	1/2
▶	23.9b	(+.f64 (/.f64 1 x) (+.f64 (*.f64 x 1/12) 1/2))
▶	0.0b	(pow.f64 (neg.f64 (expm1.f64 (neg.f64 x))) -1)
	24.4b	(+.f64 1/2 (+.f64 (.f64 -1/720 (pow.f64 x 3)) (+.f64 (.f64 1/12 x) (/.f64 1 x))))
✓	24.0b	(+.f64 (/.f64 1 x) 1/2)
▶	24.6b	(+.f64 (/.f64 1 x) (*.f64 1/12 x))
✓	23.9b	(/.f64 1 x)

Compiler

Compiled 132 to 108 computations (18.2% saved)

localize13.0ms (0.2%)

Local error

Found 1 expressions with local error:

New	Error	Program
✓	0.0b	(pow.f64 (neg.f64 (expm1.f64 (neg.f64 x))) -1)

Compiler

Compiled 18 to 7 computations (61.1% saved)

series2.0ms (0%)

Counts

1 → 12

Calls

3 calls:

Time	Variable		Point	Expression
1.0ms	x	@	inf	(pow.f64 (neg.f64 (expm1.f64 (neg.f64 x))) -1)
1.0ms	x	@	-inf	(pow.f64 (neg.f64 (expm1.f64 (neg.f64 x))) -1)
1.0ms	x	@	0	(pow.f64 (neg.f64 (expm1.f64 (neg.f64 x))) -1)

rewrite40.0ms (0.7%)

Algorithm

1×	batch-egg-rewrite

Rules

457×	`pow1_binary64`
447×	`add-sqr-sqrt_binary64`
436×	`*-un-lft-identity_binary64`
428×	`add-log-exp_binary64`
426×	`log1p-expm1-u_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	7	10
1	142	6
2	1693	6

Stop Event

1×	node limit

Counts

1 → 20

Calls

Call 1

Inputs
(pow.f64 (neg.f64 (expm1.f64 (neg.f64 x))) -1)

Outputs

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

simplify66.0ms (1.1%)

Algorithm

1×	egg-herbie

Rules

756×	`fma-def_binary64`
592×	`associate-l_binary64`
429×	`unswap-sqr_binary64`
326×	`*-commutative_binary64`
318×	`distribute-rgt-in_binary64`

Iterations

Useful iterations: 5 (0.0ms)

Iter	Nodes	Cost
0	25	128
1	60	128
2	115	128
3	262	120
4	451	120
5	931	104
6	2316	104
7	4631	104
8	7665	104

Stop Event

1×	node limit

Counts

32 → 30

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 1 (-.f64 1 (exp.f64 (neg.f64 x))))
(/.f64 1 (-.f64 1 (exp.f64 (neg.f64 x))))
(/.f64 1 (-.f64 1 (exp.f64 (neg.f64 x))))
(/.f64 1 (-.f64 1 (exp.f64 (neg.f64 x))))
(/.f64 1 (-.f64 1 (exp.f64 (*.f64 -1 x))))
(/.f64 1 (-.f64 1 (exp.f64 (*.f64 -1 x))))
(/.f64 1 (-.f64 1 (exp.f64 (*.f64 -1 x))))
(/.f64 1 (-.f64 1 (exp.f64 (*.f64 -1 x))))

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

localize5.0ms (0.1%)

Local error

Found 2 expressions with local error:

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

Compiler

Compiled 12 to 9 computations (25% saved)

series2.0ms (0%)

Counts

2 → 24

Calls

6 calls:

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

rewrite62.0ms (1%)

Algorithm

1×	batch-egg-rewrite

Rules

653×	`pow1_binary64`
616×	`add-log-exp_binary64`
616×	`log1p-expm1-u_binary64`
616×	`expm1-log1p-u_binary64`
607×	`add-exp-log_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	6	11
1	132	9
2	1604	9

Stop Event

1×	node limit

Counts

2 → 43

Calls

Call 1

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

Outputs

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

((#(struct:change #<rule egg-rr> (2) ((x -.f64 (+.f64 1 (fma.f64 x 1/12 1/2)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (/.f64 1/4 (+.f64 1/2 (*.f64 -1/12 x))) (/.f64 (pow.f64 (*.f64 x 1/12) 2) (+.f64 1/2 (*.f64 -1/12 x))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (fma.f64 x 1/12 1/2) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 1 (fma.f64 x 1/12 1/2))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 (fma.f64 x 1/12 1/2)) (pow.f64 (cbrt.f64 (fma.f64 x 1/12 1/2)) 2))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (cbrt.f64 (fma.f64 x 1/12 1/2)) 2) (cbrt.f64 (fma.f64 x 1/12 1/2)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (sqrt.f64 (fma.f64 x 1/12 1/2)) (sqrt.f64 (fma.f64 x 1/12 1/2)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (+.f64 1/8 (*.f64 1/1728 (pow.f64 x 3))) (/.f64 1 (+.f64 1/4 (-.f64 (pow.f64 (*.f64 x 1/12) 2) (*.f64 1/24 x)))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (-.f64 1/4 (pow.f64 (*.f64 x 1/12) 2)) (/.f64 1 (+.f64 1/2 (*.f64 -1/12 x))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 1 (/.f64 (+.f64 1/4 (-.f64 (pow.f64 (*.f64 x 1/12) 2) (*.f64 1/24 x))) (+.f64 1/8 (*.f64 1/1728 (pow.f64 x 3)))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 1 (/.f64 (+.f64 1/2 (*.f64 -1/12 x)) (-.f64 1/4 (pow.f64 (*.f64 x 1/12) 2))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (+.f64 1/8 (*.f64 1/1728 (pow.f64 x 3))) (+.f64 1/4 (-.f64 (pow.f64 (*.f64 x 1/12) 2) (*.f64 1/24 x))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (+.f64 1/8 (*.f64 1/1728 (pow.f64 x 3))) (+.f64 (pow.f64 (*.f64 x 1/12) 2) (-.f64 1/4 (*.f64 1/24 x))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (-.f64 1/4 (pow.f64 (*.f64 x 1/12) 2)) (+.f64 1/2 (*.f64 -1/12 x)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (neg.f64 (+.f64 1/8 (*.f64 1/1728 (pow.f64 x 3)))) (neg.f64 (+.f64 1/4 (-.f64 (pow.f64 (*.f64 x 1/12) 2) (*.f64 1/24 x)))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (neg.f64 (-.f64 1/4 (pow.f64 (*.f64 x 1/12) 2))) (neg.f64 (+.f64 1/2 (*.f64 -1/12 x))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (-.f64 (pow.f64 (*.f64 x 1/12) 2) 1/4) (-.f64 (*.f64 x 1/12) 1/2))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (fma.f64 x 1/12 1/2) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (fma.f64 x 1/12 1/2) 3) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (cbrt.f64 (fma.f64 x 1/12 1/2)) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (sqrt.f64 (fma.f64 x 1/12 1/2)) 2)))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f64 (pow.f64 (fma.f64 x 1/12 1/2) 2))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (exp.f64 (fma.f64 x 1/12 1/2)))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (pow.f64 (fma.f64 x 1/12 1/2) 3))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (fma.f64 x 1/12 1/2)))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (fma.f64 x 1/12 1/2)))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (log.f64 (fma.f64 x 1/12 1/2)))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 x 1/12 1/2)))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 1/12 x 1/2)))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 1 (*.f64 x 1/12) 1/2)))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (pow.f64 (cbrt.f64 (*.f64 x 1/12)) 2) (cbrt.f64 (*.f64 x 1/12)) 1/2)))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (sqrt.f64 (*.f64 x 1/12)) (sqrt.f64 (*.f64 x 1/12)) 1/2)))))

simplify9.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

2×	`fma-def_binary64`
1×	`+-commutative_binary64`
1×	`*-commutative_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	6	120
1	8	102
2	10	102

Stop Event

1×

saturated

Counts

67 → 46

Calls

Call 1

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

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

localize8.0ms (0.1%)

Local error

Found 2 expressions with local error:

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

Compiler

Compiled 17 to 12 computations (29.4% saved)

series1.0ms (0%)

Counts

1 → 6

Calls

3 calls:

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

rewrite206.0ms (3.4%)

Algorithm

1×	batch-egg-rewrite

Rules

752×	`pow1_binary64`
706×	`add-log-exp_binary64`
706×	`log1p-expm1-u_binary64`
706×	`expm1-log1p-u_binary64`
692×	`add-exp-log_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	7	10
1	150	8
2	1948	8

Stop Event

1×	node limit

Counts

1 → 35

Calls

Call 1

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

Outputs

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

simplify7.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

2×	`fma-def_binary64`
1×	`+-commutative_binary64`
1×	`*-commutative_binary64`
1×	`1-exp_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	7	36
1	12	36
2	13	36

Stop Event

1×

saturated

Counts

41 → 39

Calls

Call 1

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

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

localize11.0ms (0.2%)

Local error

Found 3 expressions with local error:

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

Compiler

Compiled 25 to 19 computations (24% saved)

series2.0ms (0%)

Counts

2 → 24

Calls

6 calls:

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

rewrite288.0ms (4.7%)

Algorithm

1×	batch-egg-rewrite

Rules

875×	`prod-diff_binary64`
620×	`unpow-prod-down_binary64`
408×	`log-prod_binary64`
342×	`fma-def_binary64`
252×	`pow2_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	9	16
1	204	16
2	2775	16

Stop Event

1×	node limit

Counts

2 → 136

Calls

Call 1

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

Outputs

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((#(struct:change #<rule egg-rr> (2) ((x -.f64 (exp.f64 (log1p.f64 (fma.f64 x 1/12 1/2))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (/.f64 (*.f64 1/144 (*.f64 x x)) (fma.f64 x 1/12 -1/2)) (/.f64 1/4 (fma.f64 x 1/12 -1/2)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 1 (fma.f64 x 1/12 1/2))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (fma.f64 x 1/12 1/2) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 (fma.f64 x 1/12 1/2)) (pow.f64 (cbrt.f64 (fma.f64 x 1/12 1/2)) 2))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (cbrt.f64 (fma.f64 x 1/12 1/2)) 2) (cbrt.f64 (fma.f64 x 1/12 1/2)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (sqrt.f64 (fma.f64 x 1/12 1/2)) (sqrt.f64 (fma.f64 x 1/12 1/2)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (fma.f64 1/1728 (pow.f64 x 3) 1/8) (/.f64 1 (-.f64 (fma.f64 1/144 (*.f64 x x) 1/4) (*.f64 x 1/24))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (fma.f64 1/1728 (pow.f64 x 3) 1/8) (pow.f64 (/.f64 1 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3/2) 1/3))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (*.f64 (pow.f64 (fma.f64 x 1/12 1/2) 2) (pow.f64 (cbrt.f64 (fma.f64 x 1/12 1/2)) 2)) 1/3) (cbrt.f64 (cbrt.f64 (fma.f64 x 1/12 1/2))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (*.f64 (pow.f64 (fma.f64 x 1/12 1/2) 2) (sqrt.f64 (fma.f64 x 1/12 1/2))) 1/3) (cbrt.f64 (sqrt.f64 (fma.f64 x 1/12 1/2))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 1 (/.f64 (-.f64 (fma.f64 1/144 (*.f64 x x) 1/4) (*.f64 x 1/24)) (fma.f64 1/1728 (pow.f64 x 3) 1/8)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 1 (/.f64 (fma.f64 x 1/12 -1/2) (fma.f64 1/144 (*.f64 x x) -1/4)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (fma.f64 1/1728 (pow.f64 x 3) 1/8) (-.f64 (fma.f64 1/144 (*.f64 x x) 1/4) (*.f64 x 1/24)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (fma.f64 1/1728 (pow.f64 x 3) 1/8) (+.f64 1/4 (-.f64 (*.f64 1/144 (*.f64 x x)) (*.f64 x 1/24))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (fma.f64 1/144 (*.f64 x x) -1/4) (fma.f64 x 1/12 -1/2))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (neg.f64 (fma.f64 1/1728 (pow.f64 x 3) 1/8)) (neg.f64 (-.f64 (fma.f64 1/144 (*.f64 x x) 1/4) (*.f64 x 1/24))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (neg.f64 (fma.f64 1/144 (*.f64 x x) -1/4)) (neg.f64 (fma.f64 x 1/12 -1/2)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (-.f64 1/4 (*.f64 1/144 (*.f64 x x))) (-.f64 1/2 (*.f64 x 1/12)))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (fma.f64 x 1/12 1/2) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (fma.f64 x 1/12 1/2) 2) 1/2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (cbrt.f64 (fma.f64 x 1/12 1/2)) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (sqrt.f64 (fma.f64 x 1/12 1/2)) 2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (fma.f64 x 1/12 1/2) 3) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (/.f64 (-.f64 (fma.f64 1/144 (*.f64 x x) 1/4) (*.f64 x 1/24)) (fma.f64 1/1728 (pow.f64 x 3) 1/8)) -1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (/.f64 (fma.f64 x 1/12 -1/2) (fma.f64 1/144 (*.f64 x x) -1/4)) -1)))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f64 (pow.f64 (fma.f64 x 1/12 1/2) 2))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (exp.f64 (fma.f64 x 1/12 1/2)))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (+.f64 1 (expm1.f64 (fma.f64 x 1/12 1/2))))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (pow.f64 (fma.f64 x 1/12 1/2) 3))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (fma.f64 x 1/12 1/2)))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (fma.f64 x 1/12 1/2)))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (log.f64 (fma.f64 x 1/12 1/2)))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (log.f64 (fma.f64 x 1/12 1/2)) 1))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 1 (*.f64 x 1/12) 1/2)))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 x 1/12 1/2)))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 1/12 x 1/2)))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (*.f64 x 1/12) 1 1/2)))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (cbrt.f64 (*.f64 x 1/12)) (cbrt.f64 (*.f64 1/144 (*.f64 x x))) 1/2)))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (cbrt.f64 (*.f64 1/144 (*.f64 x x))) (cbrt.f64 (*.f64 x 1/12)) 1/2)))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (pow.f64 (cbrt.f64 x) 2) (*.f64 (cbrt.f64 x) 1/12) 1/2)))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (sqrt.f64 (*.f64 x 1/12)) (sqrt.f64 (*.f64 x 1/12)) 1/2)))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (sqrt.f64 x) (*.f64 (sqrt.f64 x) 1/12) 1/2)))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (*.f64 1/12 (pow.f64 (cbrt.f64 x) 2)) (cbrt.f64 x) 1/2)))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (*.f64 1/12 (sqrt.f64 x)) (sqrt.f64 x) 1/2)))))

simplify14.0ms (0.2%)

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	13	171
1	22	149
2	27	149
3	29	149

Stop Event

1×

saturated

Counts

160 → 146

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

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

localize15.0ms (0.3%)

Local error

Found 3 expressions with local error:

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

Compiler

Compiled 28 to 23 computations (17.9% saved)

series2.0ms (0%)

Counts

2 → 24

Calls

6 calls:

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

rewrite61.0ms (1%)

Algorithm

1×	batch-egg-rewrite

Rules

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

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	8	23
1	192	14
2	2779	14

Stop Event

1×	node limit

Counts

2 → 91

Calls

Call 1

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

Outputs

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

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

simplify10.0ms (0.2%)

Algorithm

1×	egg-herbie

Rules

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

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	8	138
1	12	138

Stop Event

1×

saturated

Counts

115 → 96

Calls

Call 1

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

Outputs
(/.f64 1 x)
(+.f64 1/2 (/.f64 1 x))
(+.f64 (/.f64 1 x) 1/2)
(+.f64 1/2 (/.f64 1 x))
(+.f64 (/.f64 1 x) 1/2)
(+.f64 1/2 (/.f64 1 x))
(+.f64 (/.f64 1 x) 1/2)
1/2
(+.f64 1/2 (/.f64 1 x))
(+.f64 (/.f64 1 x) 1/2)
(+.f64 1/2 (/.f64 1 x))
(+.f64 (/.f64 1 x) 1/2)
(+.f64 1/2 (/.f64 1 x))
(+.f64 (/.f64 1 x) 1/2)
1/2
(+.f64 1/2 (/.f64 1 x))
(+.f64 (/.f64 1 x) 1/2)
(+.f64 1/2 (/.f64 1 x))
(+.f64 (/.f64 1 x) 1/2)
(+.f64 1/2 (/.f64 1 x))
(+.f64 (/.f64 1 x) 1/2)
(/.f64 1 x)
(+.f64 3/2 (/.f64 1 x))
(+.f64 (/.f64 1 x) 3/2)
(+.f64 3/2 (/.f64 1 x))
(+.f64 (/.f64 1 x) 3/2)
(+.f64 3/2 (/.f64 1 x))
(+.f64 (/.f64 1 x) 3/2)
3/2
(+.f64 3/2 (/.f64 1 x))
(+.f64 (/.f64 1 x) 3/2)
(+.f64 3/2 (/.f64 1 x))
(+.f64 (/.f64 1 x) 3/2)
(+.f64 3/2 (/.f64 1 x))
(+.f64 (/.f64 1 x) 3/2)
3/2
(+.f64 3/2 (/.f64 1 x))
(+.f64 (/.f64 1 x) 3/2)
(+.f64 3/2 (/.f64 1 x))
(+.f64 (/.f64 1 x) 3/2)
(+.f64 3/2 (/.f64 1 x))
(+.f64 (/.f64 1 x) 3/2)

eval140.0ms (2.3%)

Compiler: Compiled 5632 to 4517 computations (19.8% saved)

prune69.0ms (1.1%)

Pruning

12 alts after pruning (6 fresh and 6 done)

	Pruned	Kept	Total
New	415	5	420
Fresh	1	1	2
Picked	1	0	1
Done	1	6	7
Total	418	12	430

Error

Counts

430 → 12

Alt Table

Click to see full alt table

Status	Error	Program
✓	0.5b	(/.f64 (exp.f64 x) (expm1.f64 x))
✓	61.7b	(+.f64 1/2 (*.f64 x 1/12))
✓	23.9b	(+.f64 (/.f64 1 x) (+.f64 (*.f64 x 1/12) 1/2))
▶	41.5b	(-.f64 (/.f64 (-.f64 (*.f64 (+.f64 1 (/.f64 1 x)) (+.f64 1 (/.f64 1 x))) 1/4) (-.f64 (+.f64 1 (/.f64 1 x)) 1/2)) 1)
✓	24.6b	(+.f64 (/.f64 1 x) (*.f64 1/12 x))
▶	61.5b	(*.f64 x 1/12)
▶	0.0b	(/.f64 -1 (expm1.f64 (neg.f64 x)))
▶	24.0b	(-.f64 (+.f64 (/.f64 1 x) 3/2) 1)
	61.6b	1/2
▶	3.4b	(-.f64 (+.f64 1 (/.f64 1 x)) 1)
✓	24.0b	(+.f64 (/.f64 1 x) 1/2)
✓	23.9b	(/.f64 1 x)

Compiler

Compiled 142 to 119 computations (16.2% saved)

localize6.0ms (0.1%)

Local error

Found 1 expressions with local error:

New	Error	Program
✓	0.0b	(/.f64 -1 (expm1.f64 (neg.f64 x)))

Compiler

Compiled 13 to 6 computations (53.8% saved)

series7.0ms (0.1%)

Counts

1 → 12

Calls

3 calls:

Time	Variable		Point	Expression
6.0ms	x	@	-inf	(/.f64 -1 (expm1.f64 (neg.f64 x)))
1.0ms	x	@	inf	(/.f64 -1 (expm1.f64 (neg.f64 x)))
0.0ms	x	@	0	(/.f64 -1 (expm1.f64 (neg.f64 x)))

rewrite38.0ms (0.6%)

Algorithm

1×	batch-egg-rewrite

Rules

461×	`pow1_binary64`
446×	`add-sqr-sqrt_binary64`
440×	`*-un-lft-identity_binary64`
425×	`add-log-exp_binary64`
423×	`log1p-expm1-u_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	6	8
1	120	6
2	1411	6

Stop Event

1×	node limit

Counts

1 → 21

Calls

Call 1

Inputs
(/.f64 -1 (expm1.f64 (neg.f64 x)))

Outputs

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

simplify53.0ms (0.9%)

Algorithm

1×	egg-herbie

Rules

628×	`fma-def_binary64`
566×	`distribute-rgt-in_binary64`
532×	`associate-l_binary64`
491×	`distribute-lft-in_binary64`
446×	`unswap-sqr_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	25	104
1	61	104
2	112	104
3	249	104
4	411	104
5	804	104
6	2225	104
7	4468	104

Stop Event

1×	node limit

Counts

33 → 31

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 -1 (-.f64 (exp.f64 (neg.f64 x)) 1))
(/.f64 -1 (-.f64 (exp.f64 (neg.f64 x)) 1))
(/.f64 -1 (-.f64 (exp.f64 (neg.f64 x)) 1))
(/.f64 -1 (-.f64 (exp.f64 (neg.f64 x)) 1))
(/.f64 -1 (-.f64 (exp.f64 (*.f64 -1 x)) 1))
(/.f64 -1 (-.f64 (exp.f64 (*.f64 -1 x)) 1))
(/.f64 -1 (-.f64 (exp.f64 (*.f64 -1 x)) 1))
(/.f64 -1 (-.f64 (exp.f64 (*.f64 -1 x)) 1))

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

localize3.0ms (0%)

Local error

Found 1 expressions with local error:

New	Error	Program
	0.3b	(*.f64 x 1/12)

Compiler

Compiled 6 to 4 computations (33.3% saved)

localize8.0ms (0.1%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.0b	(+.f64 1 (/.f64 1 x))
✓	1.5b	(-.f64 (+.f64 1 (/.f64 1 x)) 1)

Compiler

Compiled 18 to 14 computations (22.2% saved)

series3.0ms (0.1%)

Counts

2 → 15

Calls

6 calls:

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

rewrite56.0ms (0.9%)

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	2008	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 (cbrt.f64 (/.f64 1 x)) (cbrt.f64 (pow.f64 x -2)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 (pow.f64 x -2)) (cbrt.f64 (/.f64 1 x)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 x -1/2) (pow.f64 x -1/2))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 -1 (/.f64 1 (neg.f64 x)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (+.f64 (pow.f64 (+.f64 1 (/.f64 1 x)) 3) -1) (/.f64 1 (+.f64 (pow.f64 (+.f64 1 (/.f64 1 x)) 2) (+.f64 (/.f64 1 x) 2))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (*.f64 (+.f64 (/.f64 1 x) 2) (/.f64 1 x)) (/.f64 1 (+.f64 (/.f64 1 x) 2)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (pow.f64 (cbrt.f64 x) 2) -1) (pow.f64 (cbrt.f64 x) -1))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (sqrt.f64 x) -1) (pow.f64 (sqrt.f64 x) -1))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (+.f64 (hypot.f64 1 (pow.f64 x -1/2)) 1) (-.f64 (hypot.f64 1 (pow.f64 x -1/2)) 1))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 1 x)))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 1 (neg.f64 (neg.f64 x)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 1 (/.f64 (+.f64 (pow.f64 (+.f64 1 (/.f64 1 x)) 2) (+.f64 (/.f64 1 x) 2)) (+.f64 (pow.f64 (+.f64 1 (/.f64 1 x)) 3) -1)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 1 (/.f64 (+.f64 (/.f64 1 x) 2) (*.f64 (+.f64 (/.f64 1 x) 2) (/.f64 1 x))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (pow.f64 x -1/2) (sqrt.f64 x))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 -1 (neg.f64 x))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (+.f64 (pow.f64 (+.f64 1 (/.f64 1 x)) 3) -1) (+.f64 (pow.f64 (+.f64 1 (/.f64 1 x)) 2) (+.f64 (/.f64 1 x) 2)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (+.f64 (pow.f64 (+.f64 1 (/.f64 1 x)) 3) -1) (+.f64 (pow.f64 (+.f64 1 (/.f64 1 x)) 2) (-.f64 1 (*.f64 (+.f64 1 (/.f64 1 x)) -1))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (*.f64 (+.f64 (/.f64 1 x) 2) (/.f64 1 x)) (+.f64 (/.f64 1 x) 2))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (*.f64 (+.f64 (/.f64 1 x) 2) (/.f64 1 x)) (-.f64 (+.f64 1 (/.f64 1 x)) -1))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (neg.f64 (+.f64 (pow.f64 (+.f64 1 (/.f64 1 x)) 3) -1)) (neg.f64 (+.f64 (pow.f64 (+.f64 1 (/.f64 1 x)) 2) (+.f64 (/.f64 1 x) 2))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (neg.f64 (*.f64 (+.f64 (/.f64 1 x) 2) (/.f64 1 x))) (neg.f64 (+.f64 (/.f64 1 x) 2)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (+.f64 1 (pow.f64 (+.f64 (/.f64 1 x) -1) 3)) (+.f64 1 (-.f64 (*.f64 (+.f64 (/.f64 1 x) -1) (+.f64 (/.f64 1 x) -1)) (+.f64 (/.f64 1 x) -1))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (-.f64 1 (*.f64 (+.f64 (/.f64 1 x) -1) (+.f64 (/.f64 1 x) -1))) (-.f64 1 (+.f64 (/.f64 1 x) -1)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (/.f64 1 (pow.f64 (cbrt.f64 x) 2)) (cbrt.f64 x))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 x -1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (/.f64 1 x) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (cbrt.f64 (/.f64 1 x)) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 x -1/2) 2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 x -3) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f64 (pow.f64 x -2))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (exp.f64 (/.f64 1 x)))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (pow.f64 x -3))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (/.f64 1 x)))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.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 expm1.f64 (log.f64 (+.f64 (/.f64 1 x) 2)))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (+.f64 1 (/.f64 1 x))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (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)) (cbrt.f64 (/.f64 1 x)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (pow.f64 x -1/2) (pow.f64 x -1/2) 1)))))

simplify7.0ms (0.1%)

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

localize8.0ms (0.1%)

Local error

Found 1 expressions with local error:

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

Compiler

Compiled 19 to 15 computations (21.1% saved)

series1.0ms (0%)

Counts

1 → 12

Calls

3 calls:

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

rewrite49.0ms (0.8%)

Algorithm

1×	batch-egg-rewrite

Rules

835×	`pow1_binary64`
788×	`add-log-exp_binary64`
787×	`log1p-expm1-u_binary64`
787×	`expm1-log1p-u_binary64`
775×	`add-exp-log_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	7	7
1	163	7
2	2152	7

Stop Event

1×	node limit

Counts

1 → 40

Calls

Call 1

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

Outputs

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

simplify7.0ms (0.1%)

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

52 → 42

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)

localize34.0ms (0.6%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(-.f64 (+.f64 1 (/.f64 1 x)) 1/2)
✓	0.0b	(-.f64 (/.f64 (-.f64 (*.f64 (+.f64 1 (/.f64 1 x)) (+.f64 1 (/.f64 1 x))) 1/4) (-.f64 (+.f64 1 (/.f64 1 x)) 1/2)) 1)
✓	0.2b	(*.f64 (+.f64 1 (/.f64 1 x)) (+.f64 1 (/.f64 1 x)))
✓	16.4b	(/.f64 (-.f64 (*.f64 (+.f64 1 (/.f64 1 x)) (+.f64 1 (/.f64 1 x))) 1/4) (-.f64 (+.f64 1 (/.f64 1 x)) 1/2))

Compiler

Compiled 88 to 74 computations (15.9% saved)

series6.0ms (0.1%)

Counts

4 → 48

Calls

12 calls:

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

rewrite147.0ms (2.4%)

Algorithm

1×	batch-egg-rewrite

Rules

721×	`prod-diff_binary64`
610×	`fma-def_binary64`
417×	`fma-neg_binary64`
227×	`expm1-udef_binary64`
226×	`log1p-udef_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	12	91
1	297	31
2	4443	31

Stop Event

1×	node limit

Counts

4 → 442

Calls

Call 1

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

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

simplify118.0ms (1.9%)

Algorithm

1×	egg-herbie

Rules

785×	`associate-/r/_binary64`
586×	`sqr-pow_binary64`
565×	`fma-def_binary64`
503×	`associate-/l/_binary64`
434×	`unswap-sqr_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	15	339
1	31	339
2	45	339
3	64	339
4	111	339
5	292	339
6	1055	339
7	3103	339
8	3500	339
9	3862	339
10	4158	339
11	4544	339
12	5056	339
13	6556	339
14	7787	339

Stop Event

1×	node limit

Counts

490 → 348

Calls

Call 1

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

eval386.0ms (6.3%)

Compiler: Compiled 13875 to 12081 computations (12.9% saved)

prune137.0ms (2.2%)

Pruning

14 alts after pruning (4 fresh and 10 done)

	Pruned	Kept	Total
New	511	3	514
Fresh	0	1	1
Picked	0	1	1
Done	1	9	10
Total	512	14	526

Error

Counts

526 → 14

Alt Table

Click to see full alt table

Status	Error	Program
✓	0.5b	(/.f64 (exp.f64 x) (expm1.f64 x))
✓	61.7b	(+.f64 1/2 (*.f64 x 1/12))
✓	23.9b	(+.f64 (/.f64 1 x) (+.f64 (*.f64 x 1/12) 1/2))
✓	41.5b	(-.f64 (/.f64 (-.f64 (*.f64 (+.f64 1 (/.f64 1 x)) (+.f64 1 (/.f64 1 x))) 1/4) (-.f64 (+.f64 1 (/.f64 1 x)) 1/2)) 1)
✓	24.6b	(+.f64 (/.f64 1 x) (*.f64 1/12 x))
✓	61.5b	(*.f64 x 1/12)
	41.0b	(-.f64 1 1)
✓	23.9b	(/.f64 1 x)
✓	0.0b	(/.f64 -1 (expm1.f64 (neg.f64 x)))
✓	24.0b	(-.f64 (+.f64 (/.f64 1 x) 3/2) 1)
	61.6b	1/2
	3.4b	(+.f64 (+.f64 (/.f64 1 x) -1) 1)
	41.4b	(/.f64 1 (/.f64 (+.f64 (/.f64 1 x) 2) (*.f64 (+.f64 (/.f64 1 x) 2) (/.f64 1 x))))
✓	24.0b	(+.f64 (/.f64 1 x) 1/2)

Compiler

Compiled 114 to 95 computations (16.7% saved)

regimes57.0ms (0.9%)

Counts

22 → 1

Calls

Call 1

Inputs
1/2
(-.f64 1 1)
(*.f64 x 1/12)
(/.f64 1 x)
(+.f64 1/2 (*.f64 x 1/12))
(+.f64 (/.f64 1 x) 1/2)
(+.f64 (+.f64 (/.f64 1 x) -1) 1)
(-.f64 (+.f64 (/.f64 1 x) 3/2) 1)
(-.f64 (+.f64 1 (/.f64 1 x)) 1)
(+.f64 (/.f64 1 x) (*.f64 1/12 x))
(-.f64 (+.f64 1 (+.f64 (/.f64 1 x) 1/2)) 1)
(+.f64 (/.f64 1 x) (+.f64 (*.f64 x 1/12) 1/2))
(+.f64 1/2 (+.f64 (*.f64 1/12 x) (/.f64 1 x)))
(/.f64 1 (/.f64 (+.f64 (/.f64 1 x) 2) (*.f64 (+.f64 (/.f64 1 x) 2) (/.f64 1 x))))
(-.f64 (/.f64 (-.f64 (*.f64 (+.f64 1 (/.f64 1 x)) (+.f64 1 (/.f64 1 x))) 1/4) (-.f64 (+.f64 1 (/.f64 1 x)) 1/2)) 1)
(/.f64 -1 (expm1.f64 (neg.f64 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 (exp.f64 x) (expm1.f64 x))
(pow.f64 (neg.f64 (expm1.f64 (neg.f64 x))) -1)
(/.f64 (exp.f64 x) (-.f64 (exp.f64 x) 1))
(pow.f64 (/.f64 (expm1.f64 x) (exp.f64 x)) -1)

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

Calls

5 calls:

19.0ms	x
9.0ms	(/.f64 (exp.f64 x) (-.f64 (exp.f64 x) 1))
7.0ms	(/.f64 (exp.f64 x) (-.f64 (exp.f64 x) 1))
6.0ms	(exp.f64 x)
6.0ms	(exp.f64 x)

Results

Error	Segments	Branch
0.0b	1	`x`
0.0b	1	`(/.f64 (exp.f64 x) (-.f64 (exp.f64 x) 1))`
0.0b	1	`(/.f64 (exp.f64 x) (-.f64 (exp.f64 x) 1))`
0.0b	1	`(exp.f64 x)`
0.0b	1	`(exp.f64 x)`

Compiler

Compiled 193 to 145 computations (24.9% saved)

regimes20.0ms (0.3%)

Counts

15 → 2

Calls

Call 1

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

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

Calls

1 calls:

15.0ms

Results

Error	Segments	Branch
2.4b	2	`x`

Compiler

Compiled 118 to 97 computations (17.8% saved)

bsearch19.0ms (0.3%)

Algorithm

1×	binary-search

Steps

Time	Left	Right
18.0ms	-2059700.993233555	-168.9727928461201

Compiler

Compiled 12 to 8 computations (33.3% saved)

regimes9.0ms (0.2%)

Counts

11 → 1

Calls

Call 1

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

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

Calls

1 calls:

7.0ms

Results

Error	Segments	Branch
3.4b	1	`x`

Compiler

Compiled 60 to 49 computations (18.3% saved)

regimes8.0ms (0.1%)

Counts

8 → 1

Calls

Call 1

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

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

Calls

1 calls:

5.0ms

Results

Error	Segments	Branch
3.4b	1	`x`

Compiler

Compiled 37 to 30 computations (18.9% saved)

regimes12.0ms (0.2%)

Counts

6 → 2

Calls

Call 1

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

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

Calls

1 calls:

11.0ms

Results

Error	Segments	Branch
2.6b	2	`x`

Compiler

Compiled 23 to 18 computations (21.7% saved)

bsearch17.0ms (0.3%)

Algorithm

1×	binary-search

Steps

Time	Left	Right
17.0ms	-10.621655339931833	-5.697095499802206e-6

Compiler

Compiled 12 to 8 computations (33.3% saved)

regimes11.0ms (0.2%)

Counts

5 → 2

Calls

Call 1

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

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

Calls

1 calls:

9.0ms

Results

Error	Segments	Branch
3.2b	2	`x`

Compiler

Compiled 18 to 14 computations (22.2% saved)

bsearch18.0ms (0.3%)

Algorithm

1×	binary-search

Steps

Time	Left	Right
18.0ms	-2059700.993233555	-168.9727928461201

Compiler

Compiled 12 to 8 computations (33.3% saved)

regimes8.0ms (0.1%)

Counts

3 → 2

Calls

Call 1

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

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

Calls

1 calls:

7.0ms

Results

Error	Segments	Branch
40.0b	2	`x`

Compiler

Compiled 10 to 8 computations (20% saved)

bsearch18.0ms (0.3%)

Algorithm

1×	binary-search

Steps

Time	Left	Right
18.0ms	-2059700.993233555	-168.9727928461201

Compiler

Compiled 12 to 8 computations (33.3% saved)

regimes4.0ms (0.1%)

Accuracy

Total -21.6b remaining (-52.6%)

Threshold costs -21.6b (-52.6%)

Counts

2 → 1

Calls

Call 1

Inputs
1/2
(-.f64 1 1)

Outputs
(-.f64 1 1)

Calls

1 calls:

3.0ms

Results

Error	Segments	Branch
41.0b	1	`x`

Compiler

Compiled 7 to 6 computations (14.3% saved)

simplify7.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

8×	`+-commutative_binary64`
2×	`*-commutative_binary64`
2×	`sub-neg_binary64`
1×	`neg-sub0_binary64`
1×	`neg-mul-1_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	29	86
1	41	86
2	44	86
3	45	86

Stop Event

1×	fuel
1×	saturated

Calls

Call 1

Inputs
(/.f64 -1 (expm1.f64 (neg.f64 x)))
(if (<=.f64 x -2211587101369209/1073741824) (-.f64 1 1) (+.f64 (/.f64 1 x) (+.f64 (*.f64 x 1/12) 1/2)))
(-.f64 (+.f64 1 (/.f64 1 x)) 1)
(+.f64 (+.f64 (/.f64 1 x) -1) 1)
(if (<=.f64 x -5979460378871855/562949953421312) (-.f64 1 1) (+.f64 (/.f64 1 x) 1/2))
(if (<=.f64 x -2211587101369209/1073741824) (-.f64 1 1) (/.f64 1 x))
(if (<=.f64 x -2211587101369209/1073741824) (-.f64 1 1) (*.f64 x 1/12))
(-.f64 1 1)
1/2

Outputs
(/.f64 -1 (expm1.f64 (neg.f64 x)))
(if (<=.f64 x -2211587101369209/1073741824) (-.f64 1 1) (+.f64 (/.f64 1 x) (+.f64 (*.f64 x 1/12) 1/2)))
(if (<=.f64 x -2211587101369209/1073741824) 0 (+.f64 (/.f64 1 x) (+.f64 (*.f64 x 1/12) 1/2)))
(-.f64 (+.f64 1 (/.f64 1 x)) 1)
(+.f64 (+.f64 1 (/.f64 1 x)) -1)
(+.f64 -1 (+.f64 1 (/.f64 1 x)))
(+.f64 (+.f64 (/.f64 1 x) -1) 1)
(+.f64 1 (+.f64 -1 (/.f64 1 x)))
(if (<=.f64 x -5979460378871855/562949953421312) (-.f64 1 1) (+.f64 (/.f64 1 x) 1/2))
(if (<=.f64 x -5979460378871855/562949953421312) 0 (+.f64 (/.f64 1 x) 1/2))
(if (<=.f64 x -2211587101369209/1073741824) (-.f64 1 1) (/.f64 1 x))
(if (<=.f64 x -2211587101369209/1073741824) 0 (/.f64 1 x))
(if (<=.f64 x -2211587101369209/1073741824) (-.f64 1 1) (*.f64 x 1/12))
(if (<=.f64 x -2211587101369209/1073741824) 0 (*.f64 x 1/12))
(-.f64 1 1)
0
1/2

Compiler

Compiled 70 to 58 computations (17.1% saved)

soundness268.0ms (4.4%)

Algorithm

3×	egg-herbie

Rules

803×	`unswap-sqr_binary64`
756×	`fma-def_binary64`
592×	`associate-l_binary64`
513×	`distribute-lft-out_binary64`
429×	`unswap-sqr_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	6	8
1	12	8
2	13	8
0	35	214
1	90	214
2	205	214
3	592	208
4	1654	200
5	2810	200
6	5087	200
7	6222	200
0	25	128
1	60	128
2	115	128
3	262	120
4	451	120
5	931	104
6	2316	104
7	4631	104
8	7665	104

Stop Event

1×	node limit
1×	node limit
1×	saturated

Compiler

Compiled 183 to 152 computations (16.9% saved)

end114.0ms (1.9%)

Compiler: Compiled 62 to 50 computations (19.4% saved)