Details

analyze479.0ms (18%)

Algorithm

1×

Search

True	Other	False	Iter
0%	100%	0%	0
0%	100%	0%	1
0%	100%	0%	2
25%	75%	0%	3
25%	62.5%	12.5%	4
25%	56.2%	18.8%	5
28.1%	50%	21.9%	6
29.7%	46.9%	23.5%	7
30.5%	45.3%	24.3%	8
30.8%	44.9%	24.3%	9
31.2%	44.5%	24.3%	10
31.3%	44.4%	24.3%	11
31.4%	44.3%	24.3%	12
31.4%	44.2%	24.3%	13
31.5%	44.2%	24.3%	14

Compiler

Compiled 9 to 6 computations (33.3% saved)

sample1.6s (58.8%)

Results

825.0ms	2692×	body	1024	valid
266.0ms	1316×	body	512	valid
248.0ms	3279×	body	128	valid
118.0ms	297×	body	2048	valid
96.0ms	672×	body	256	valid
1.0ms	3×	body	2048	invalid

Compiler

Compiled 18 to 12 computations (33.3% saved)

preprocess19.0ms (0.7%)

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 8 to 5 computations (37.5% saved)

simplify6.0ms (0.2%)

Algorithm

1×	egg-herbie

Rules

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

Iterations

Useful iterations: 0 (0.0ms)

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

Stop Event

1×

saturated

Counts

1 → 2

Calls

Call 1

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

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

prune3.0ms (0.1%)

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

0.3b

Counts

3 → 1

Alt Table

Status	Error	Program
▶	0.3b	(/.f64 (exp.f64 x) (expm1.f64 x))

Compiler

Compiled 25 to 15 computations (40% saved)

localize3.0ms (0.1%)

Local error

Found 1 expressions with local error:

New	Error	Program
✓	0.3b	(/.f64 (exp.f64 x) (expm1.f64 x))

series2.0ms (0.1%)

Counts

1 → 12

Calls

3 calls:

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

rewrite32.0ms (1.2%)

Algorithm

1×	batch-egg-rewrite

Rules

516×	`pow1_binary64`
477×	`add-log-exp_binary64`
477×	`log1p-expm1-u_binary64`
477×	`expm1-log1p-u_binary64`
465×	`add-exp-log_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 → 31

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

Outputs

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

simplify32.0ms (1.2%)

Algorithm

1×	egg-herbie

Rules

1089×	`fma-neg_binary64`
754×	`fma-def_binary64`
260×	`cancel-sign-sub-inv_binary64`
211×	`associate-l_binary64`
208×	`unswap-sqr_binary64`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	18	110
1	46	106
2	101	104
3	306	104
4	830	104
5	1782	104
6	3144	104
7	4892	104

Stop Event

1×	node limit

Counts

43 → 40

Calls

Call 1

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

prune23.0ms (0.8%)

Pruning

3 alts after pruning (2 fresh and 1 done)

	Pruned	Kept	Total
New	38	2	40
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	38	3	41

Error

0.2b

Counts

41 → 3

Alt Table

Status	Error	Program
	22.6b	(-.f64 (fma.f64 x 1/12 (/.f64 1 x)) (fma.f64 1/720 (pow.f64 x 3) -1/2))
✓	0.3b	(/.f64 (exp.f64 x) (expm1.f64 x))
▶	22.4b	(+.f64 1/2 (/.f64 1 x))

Compiler

Compiled 435 to 202 computations (53.6% saved)

localize3.0ms (0.1%)

Local error

Found 1 expressions with local error:

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

series1.0ms (0%)

Counts

1 → 3

Calls

3 calls:

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

rewrite31.0ms (1.2%)

Algorithm

1×	batch-egg-rewrite

Rules

628×	`pow1_binary64`
588×	`add-log-exp_binary64`
588×	`log1p-expm1-u_binary64`
588×	`expm1-log1p-u_binary64`
64×	`add-sqr-sqrt_binary64`

Iterations

Useful iterations: 0 (0.0ms)

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

Stop Event

1×	node limit

Counts

1 → 31

Calls

Call 1

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

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

Outputs

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

simplify6.0ms (0.2%)

Algorithm

1×	egg-herbie

Rules

1×	`1-exp_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	5	6
1	7	6

Stop Event

1×

saturated

Counts

34 → 33

Calls

Call 1

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

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

prune16.0ms (0.6%)

Pruning

3 alts after pruning (2 fresh and 1 done)

	Pruned	Kept	Total
New	32	1	33
Fresh	0	1	1
Picked	1	0	1
Done	0	1	1
Total	33	3	36

Error

0.2b

Counts

36 → 3

Alt Table

Status	Error	Program
	43.8b	(pow.f64 (sqrt.f64 (+.f64 1/2 (/.f64 1 x))) 2)
▶	22.6b	(-.f64 (fma.f64 x 1/12 (/.f64 1 x)) (fma.f64 1/720 (pow.f64 x 3) -1/2))
✓	0.3b	(/.f64 (exp.f64 x) (expm1.f64 x))

Compiler

Compiled 391 to 327 computations (16.4% saved)

localize11.0ms (0.4%)

Local error

Found 3 expressions with local error:

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

series5.0ms (0.2%)

Counts

3 → 36

Calls

9 calls:

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

rewrite61.0ms (2.3%)

Algorithm

1×	batch-egg-rewrite

Rules

509×	`prod-diff_binary64`
243×	`fma-def_binary64`
209×	`expm1-udef_binary64`
209×	`log1p-udef_binary64`
136×	`fma-neg_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	12	34
1	263	34
2	3003	34

Stop Event

1×	node limit

Counts

3 → 132

Calls

Call 1

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

Outputs

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

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

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

simplify42.0ms (1.6%)

Algorithm

1×	egg-herbie

Rules

1114×	`fma-neg_binary64`
449×	`fma-def_binary64`
329×	`cancel-sign-sub-inv_binary64`
235×	`associate-l_binary64`
208×	`unswap-sqr_binary64`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	22	351
1	55	317
2	123	307
3	378	307
4	948	307
5	2015	307
6	3228	307
7	4915	307

Stop Event

1×	node limit

Counts

168 → 153

Calls

Call 1

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

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

prune116.0ms (4.4%)

Pruning

3 alts after pruning (1 fresh and 2 done)

	Pruned	Kept	Total
New	153	0	153
Fresh	0	1	1
Picked	0	1	1
Done	0	1	1
Total	153	3	156

Error

0.2b

Counts

156 → 3

Alt Table

Status	Error	Program
▶	43.8b	(pow.f64 (sqrt.f64 (+.f64 1/2 (/.f64 1 x))) 2)
✓	22.6b	(-.f64 (fma.f64 x 1/12 (/.f64 1 x)) (fma.f64 1/720 (pow.f64 x 3) -1/2))
✓	0.3b	(/.f64 (exp.f64 x) (expm1.f64 x))

Compiler

Compiled 3680 to 2988 computations (18.8% saved)

localize5.0ms (0.2%)

Local error

Found 3 expressions with local error:

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

series13.0ms (0.5%)

Counts

2 → 16

Calls

6 calls:

Time	Variable		Point	Expression
5.0ms	x	@	inf	(pow.f64 (sqrt.f64 (+.f64 1/2 (/.f64 1 x))) 2)
4.0ms	x	@	-inf	(pow.f64 (sqrt.f64 (+.f64 1/2 (/.f64 1 x))) 2)
2.0ms	x	@	0	(pow.f64 (sqrt.f64 (+.f64 1/2 (/.f64 1 x))) 2)
1.0ms	x	@	0	(sqrt.f64 (+.f64 1/2 (/.f64 1 x)))
1.0ms	x	@	inf	(sqrt.f64 (+.f64 1/2 (/.f64 1 x)))

rewrite37.0ms (1.4%)

Algorithm

1×	batch-egg-rewrite

Rules

758×	`pow1_binary64`
709×	`log1p-expm1-u_binary64`
709×	`expm1-log1p-u_binary64`
82×	`add-sqr-sqrt_binary64`
78×	`add-log-exp_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	9	16
1	194	16
2	2000	16

Stop Event

1×	node limit

Counts

2 → 59

Calls

Call 1

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

Outputs

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

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

simplify30.0ms (1.1%)

Algorithm

1×	egg-herbie

Rules

759×	`associate-/r*_binary64`
675×	`fma-def_binary64`
377×	`associate-l_binary64`
308×	`associate-r_binary64`
294×	`fma-neg_binary64`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	31	276
1	93	236
2	250	224
3	886	224
4	4301	224

Stop Event

1×	node limit

Counts

75 → 69

Calls

Call 1

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

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

prune45.0ms (1.7%)

Pruning

3 alts after pruning (1 fresh and 2 done)

	Pruned	Kept	Total
New	101	1	102
Fresh	0	0	0
Picked	1	0	1
Done	0	2	2
Total	102	3	105

Error

0.2b

Counts

105 → 3

Alt Table

Status	Error	Program
✓	22.6b	(-.f64 (fma.f64 x 1/12 (/.f64 1 x)) (fma.f64 1/720 (pow.f64 x 3) -1/2))
✓	0.3b	(/.f64 (exp.f64 x) (expm1.f64 x))
	62.5b	(pow.f64 (+.f64 (sqrt.f64 1/2) (/.f64 (/.f64 1/2 (sqrt.f64 1/2)) x)) 2)

Compiler

Compiled 1347 to 1173 computations (12.9% saved)

regimes23.0ms (0.9%)

Accuracy

Total 0.1b remaining (20.1%)

Threshold costs 0.1b (20.1%)

Counts

19 → 1

Compiler

Compiled 182 to 127 computations (30.2% saved)

simplify2.0ms (0.1%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	5	8

Stop Event

1×

saturated

Calls

Call 1

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

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

end51.0ms (1.9%)

Stop Event

1×

fuel

Compiler

Compiled 44 to 34 computations (22.7% saved)

Details

analyze479.0ms (18%)

sample1.6s (58.8%)

preprocess19.0ms (0.7%)

simplify6.0ms (0.2%)

prune3.0ms (0.1%)

localize3.0ms (0.1%)

series2.0ms (0.1%)

rewrite32.0ms (1.2%)

simplify32.0ms (1.2%)

prune23.0ms (0.8%)

localize3.0ms (0.1%)

series1.0ms (0%)

rewrite31.0ms (1.2%)

simplify6.0ms (0.2%)

prune16.0ms (0.6%)

localize11.0ms (0.4%)

series5.0ms (0.2%)

rewrite61.0ms (2.3%)

simplify42.0ms (1.6%)

prune116.0ms (4.4%)

localize5.0ms (0.2%)

series13.0ms (0.5%)

rewrite37.0ms (1.4%)

simplify30.0ms (1.1%)

prune45.0ms (1.7%)

regimes23.0ms (0.9%)

simplify2.0ms (0.1%)

end51.0ms (1.9%)

Profiling