Details

analyze4.0ms (0.1%)

Algorithm

1×

Search

True	Other	False	Iter
0%	100%	0%	0
0%	100%	0%	1
0%	100%	0%	2
25%	75%	0%	3
62.5%	37.5%	0%	4
68.7%	18.7%	12.5%	5
71.8%	9.4%	18.8%	6
73.4%	4.7%	21.9%	7
74.2%	2.3%	23.5%	8
74.6%	1.2%	24.3%	9
75%	0.6%	24.5%	10
75.1%	0.3%	24.6%	11
75.1%	0.1%	24.7%	12

Compiler

Compiled 8 to 6 computations (25% saved)

sample2.2s (50.4%)

Results

1.1s	2686×	body	1024	valid
594.0ms	3938×	body	256	valid
350.0ms	1341×	body	512	valid
109.0ms	291×	body	2048	valid
0.0ms	5×	body	256	invalid

preprocess172.0ms (3.9%)

Algorithm

2×	egg-herbie

Rules

95×	`fma-def_binary64`
80×	`fma-neg_binary64`
32×	`distribute-rgt-in_binary64`
28×	`cancel-sign-sub-inv_binary64`
26×	`distribute-lft-in_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	6	6
1	15	6
2	18	6
3	22	6
4	30	6
5	40	6
6	59	6
7	100	6
8	145	6
9	223	6
10	352	6
11	511	6
12	583	6
13	619	6
0	1	1

Stop Event

1×	saturated
1×	saturated

Calls

Call 1

Inputs
0

Outputs
0

Call 2

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

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

Compiler

Compiled 8 to 6 computations (25% saved)

simplify30.0ms (0.7%)

Algorithm

1×	egg-herbie

Rules

95×	`fma-def_binary64`
80×	`fma-neg_binary64`
32×	`distribute-rgt-in_binary64`
28×	`cancel-sign-sub-inv_binary64`
26×	`distribute-lft-in_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	6	6
1	15	6
2	18	6
3	22	6
4	30	6
5	40	6
6	59	6
7	100	6
8	145	6
9	223	6
10	352	6
11	511	6
12	583	6
13	619	6

Stop Event

1×

saturated

Counts

1 → 2

Calls

Call 1

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

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

eval1.0ms (0%)

Compiler: Compiled 11 to 7 computations (36.4% 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

0.0b

Counts

3 → 1

Alt Table

Click to see full alt table

Status	Error	Program
▶	0.0b	(/.f64 (expm1.f64 x) x)

Compiler

Compiled 5 to 3 computations (40% saved)

localize43.0ms (1%)

Local error

Found 1 expressions with local error:

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

Compiler

Compiled 8 to 3 computations (62.5% saved)

series4.0ms (0.1%)

Counts

1 → 12

Calls

3 calls:

Time	Variable		Point	Expression
2.0ms	x	@	-inf	(/.f64 (expm1.f64 x) x)
1.0ms	x	@	inf	(/.f64 (expm1.f64 x) x)
1.0ms	x	@	0	(/.f64 (expm1.f64 x) x)

rewrite52.0ms (1.2%)

Algorithm

1×	batch-egg-rewrite

Rules

449×	`pow1_binary64`
430×	`add-sqr-sqrt_binary64`
424×	`*-un-lft-identity_binary64`
417×	`add-log-exp_binary64`
417×	`log1p-expm1-u_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	4	6
1	83	6
2	1104	6

Stop Event

1×	node limit

Counts

1 → 31

Calls

Call 1

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

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

Outputs

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

simplify61.0ms (1.4%)

Algorithm

1×	egg-herbie

Rules

688×	`times-frac_binary64`
636×	`associate-/l/_binary64`
536×	`unswap-sqr_binary64`
495×	`associate-l_binary64`
448×	`fma-def_binary64`

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	22	87
1	60	85
2	120	85
3	325	79
4	816	76
5	2522	76
6	4510	76

Stop Event

1×	node limit

Counts

43 → 40

Calls

Call 1

Inputs
1
(+.f64 (*.f64 1/2 x) 1)
(+.f64 (.f64 1/2 x) (+.f64 (.f64 1/6 (pow.f64 x 2)) 1))
(+.f64 (.f64 1/2 x) (+.f64 (.f64 1/6 (pow.f64 x 2)) (+.f64 1 (*.f64 1/24 (pow.f64 x 3)))))
(/.f64 (-.f64 (exp.f64 x) 1) x)
(/.f64 (-.f64 (exp.f64 x) 1) x)
(/.f64 (-.f64 (exp.f64 x) 1) x)
(/.f64 (-.f64 (exp.f64 x) 1) x)
(/.f64 (-.f64 (exp.f64 x) 1) x)
(/.f64 (-.f64 (exp.f64 x) 1) x)
(/.f64 (-.f64 (exp.f64 x) 1) x)
(/.f64 (-.f64 (exp.f64 x) 1) x)

Outputs
1
(+.f64 (*.f64 1/2 x) 1)
(fma.f64 1/2 x 1)
(+.f64 (.f64 1/2 x) (+.f64 (.f64 1/6 (pow.f64 x 2)) 1))
(fma.f64 1/2 x (fma.f64 1/6 (*.f64 x x) 1))
(fma.f64 1/2 x (fma.f64 x (*.f64 x 1/6) 1))
(fma.f64 x (fma.f64 x 1/6 1/2) 1)
(+.f64 (.f64 1/2 x) (+.f64 (.f64 1/6 (pow.f64 x 2)) (+.f64 1 (*.f64 1/24 (pow.f64 x 3)))))
(fma.f64 1/2 x (+.f64 (fma.f64 1/6 (.f64 x x) 1) (.f64 1/24 (pow.f64 x 3))))
(fma.f64 1/2 x (fma.f64 1/6 (*.f64 x x) (fma.f64 1/24 (pow.f64 x 3) 1)))
(fma.f64 1/2 x (fma.f64 x (*.f64 x 1/6) (fma.f64 1/24 (pow.f64 x 3) 1)))
(fma.f64 x (fma.f64 x 1/6 1/2) (fma.f64 1/24 (pow.f64 x 3) 1))
(fma.f64 x (fma.f64 x (fma.f64 x 1/24 1/6) 1/2) 1)
(/.f64 (-.f64 (exp.f64 x) 1) x)
(/.f64 (expm1.f64 x) x)
(/.f64 (-.f64 (exp.f64 x) 1) x)
(/.f64 (expm1.f64 x) x)
(/.f64 (-.f64 (exp.f64 x) 1) x)
(/.f64 (expm1.f64 x) x)
(/.f64 (-.f64 (exp.f64 x) 1) x)
(/.f64 (expm1.f64 x) x)
(/.f64 (-.f64 (exp.f64 x) 1) x)
(/.f64 (expm1.f64 x) x)
(/.f64 (-.f64 (exp.f64 x) 1) x)
(/.f64 (expm1.f64 x) x)
(/.f64 (-.f64 (exp.f64 x) 1) x)
(/.f64 (expm1.f64 x) x)
(/.f64 (-.f64 (exp.f64 x) 1) x)
(/.f64 (expm1.f64 x) x)

eval13.0ms (0.3%)

Compiler: Compiled 345 to 161 computations (53.3% saved)

prune12.0ms (0.3%)

Pruning

6 alts after pruning (5 fresh and 1 done)

	Pruned	Kept	Total
New	35	5	40
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	35	6	41

Error

Counts

41 → 6

Alt Table

Click to see full alt table

Status	Error	Program
▶	18.0b	(-.f64 (+.f64 1 (/.f64 (expm1.f64 x) x)) 1)
✓	0.0b	(/.f64 (expm1.f64 x) x)
▶	0.1b	(*.f64 (neg.f64 (expm1.f64 x)) (/.f64 1 (neg.f64 x)))
▶	20.4b	(+.f64 (*.f64 1/2 x) 1)
	20.0b	1
▶	0.5b	(pow.f64 (cbrt.f64 (/.f64 (expm1.f64 x) x)) 3)

Compiler

Compiled 39 to 30 computations (23.1% saved)

localize21.0ms (0.5%)

Local error

Found 1 expressions with local error:

New	Error	Program
✓	0.1b	(*.f64 (neg.f64 (expm1.f64 x)) (/.f64 1 (neg.f64 x)))

Compiler

Compiled 22 to 10 computations (54.5% saved)

series2.0ms (0%)

Counts

1 → 12

Calls

3 calls:

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

rewrite85.0ms (1.9%)

Algorithm

1×	batch-egg-rewrite

Rules

555×	`pow1_binary64`
514×	`add-log-exp_binary64`
514×	`log1p-expm1-u_binary64`
514×	`expm1-log1p-u_binary64`
503×	`add-exp-log_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	8	10
1	163	6
2	2149	6

Stop Event

1×	node limit

Counts

1 → 23

Calls

Call 1

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

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

Outputs

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

simplify48.0ms (1.1%)

Algorithm

1×	egg-herbie

Rules

688×	`times-frac_binary64`
636×	`associate-/l/_binary64`
536×	`unswap-sqr_binary64`
495×	`associate-l_binary64`
448×	`fma-def_binary64`

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	22	87
1	60	85
2	120	85
3	325	79
4	816	76
5	2522	76
6	4510	76

Stop Event

1×	node limit

Counts

35 → 31

Calls

Call 1

Inputs
1
(+.f64 (*.f64 1/2 x) 1)
(+.f64 (.f64 1/2 x) (+.f64 (.f64 1/6 (pow.f64 x 2)) 1))
(+.f64 (.f64 1/2 x) (+.f64 (.f64 1/6 (pow.f64 x 2)) (+.f64 1 (*.f64 1/24 (pow.f64 x 3)))))
(/.f64 (-.f64 (exp.f64 x) 1) x)
(/.f64 (-.f64 (exp.f64 x) 1) x)
(/.f64 (-.f64 (exp.f64 x) 1) x)
(/.f64 (-.f64 (exp.f64 x) 1) x)
(/.f64 (-.f64 (exp.f64 x) 1) x)
(/.f64 (-.f64 (exp.f64 x) 1) x)
(/.f64 (-.f64 (exp.f64 x) 1) x)
(/.f64 (-.f64 (exp.f64 x) 1) x)

Outputs
1
(+.f64 (*.f64 1/2 x) 1)
(fma.f64 1/2 x 1)
(+.f64 (.f64 1/2 x) (+.f64 (.f64 1/6 (pow.f64 x 2)) 1))
(fma.f64 1/2 x (fma.f64 1/6 (*.f64 x x) 1))
(fma.f64 1/2 x (fma.f64 x (*.f64 x 1/6) 1))
(fma.f64 x (fma.f64 x 1/6 1/2) 1)
(+.f64 (.f64 1/2 x) (+.f64 (.f64 1/6 (pow.f64 x 2)) (+.f64 1 (*.f64 1/24 (pow.f64 x 3)))))
(fma.f64 1/2 x (+.f64 (fma.f64 1/6 (.f64 x x) 1) (.f64 1/24 (pow.f64 x 3))))
(fma.f64 1/2 x (fma.f64 1/6 (*.f64 x x) (fma.f64 1/24 (pow.f64 x 3) 1)))
(fma.f64 1/2 x (fma.f64 x (*.f64 x 1/6) (fma.f64 1/24 (pow.f64 x 3) 1)))
(fma.f64 x (fma.f64 x 1/6 1/2) (fma.f64 1/24 (pow.f64 x 3) 1))
(fma.f64 x (fma.f64 x (fma.f64 x 1/24 1/6) 1/2) 1)
(/.f64 (-.f64 (exp.f64 x) 1) x)
(/.f64 (expm1.f64 x) x)
(/.f64 (-.f64 (exp.f64 x) 1) x)
(/.f64 (expm1.f64 x) x)
(/.f64 (-.f64 (exp.f64 x) 1) x)
(/.f64 (expm1.f64 x) x)
(/.f64 (-.f64 (exp.f64 x) 1) x)
(/.f64 (expm1.f64 x) x)
(/.f64 (-.f64 (exp.f64 x) 1) x)
(/.f64 (expm1.f64 x) x)
(/.f64 (-.f64 (exp.f64 x) 1) x)
(/.f64 (expm1.f64 x) x)
(/.f64 (-.f64 (exp.f64 x) 1) x)
(/.f64 (expm1.f64 x) x)
(/.f64 (-.f64 (exp.f64 x) 1) x)
(/.f64 (expm1.f64 x) x)

localize5.0ms (0.1%)

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

localize12.0ms (0.3%)

Local error

Found 2 expressions with local error:

New	Error	Program
	0.0b	(/.f64 (expm1.f64 x) x)
✓	1.2b	(-.f64 (+.f64 1 (/.f64 (expm1.f64 x) x)) 1)

Compiler

Compiled 23 to 10 computations (56.5% saved)

series1.0ms (0%)

Counts

1 → 12

Calls

3 calls:

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

rewrite102.0ms (2.3%)

Algorithm

1×	batch-egg-rewrite

Rules

831×	`pow1_binary64`
779×	`add-log-exp_binary64`
779×	`log1p-expm1-u_binary64`
779×	`expm1-log1p-u_binary64`
765×	`add-exp-log_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	7	12
1	159	6
2	2334	6

Stop Event

1×	node limit

Counts

1 → 62

Calls

Call 1

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

Outputs

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

simplify56.0ms (1.3%)

Algorithm

1×	egg-herbie

Rules

688×	`times-frac_binary64`
636×	`associate-/l/_binary64`
536×	`unswap-sqr_binary64`
495×	`associate-l_binary64`
448×	`fma-def_binary64`

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	22	87
1	60	85
2	120	85
3	325	79
4	816	76
5	2522	76
6	4510	76

Stop Event

1×	node limit

Counts

74 → 70

Calls

Call 1

Inputs
1
(+.f64 (*.f64 1/2 x) 1)
(+.f64 (.f64 1/2 x) (+.f64 (.f64 1/6 (pow.f64 x 2)) 1))
(+.f64 (.f64 1/2 x) (+.f64 (.f64 1/6 (pow.f64 x 2)) (+.f64 1 (*.f64 1/24 (pow.f64 x 3)))))
(/.f64 (-.f64 (exp.f64 x) 1) x)
(/.f64 (-.f64 (exp.f64 x) 1) x)
(/.f64 (-.f64 (exp.f64 x) 1) x)
(/.f64 (-.f64 (exp.f64 x) 1) x)
(/.f64 (-.f64 (exp.f64 x) 1) x)
(/.f64 (-.f64 (exp.f64 x) 1) x)
(/.f64 (-.f64 (exp.f64 x) 1) x)
(/.f64 (-.f64 (exp.f64 x) 1) x)

Outputs
1
(+.f64 (*.f64 1/2 x) 1)
(fma.f64 1/2 x 1)
(+.f64 (.f64 1/2 x) (+.f64 (.f64 1/6 (pow.f64 x 2)) 1))
(fma.f64 1/2 x (fma.f64 1/6 (*.f64 x x) 1))
(fma.f64 1/2 x (fma.f64 x (*.f64 x 1/6) 1))
(fma.f64 x (fma.f64 x 1/6 1/2) 1)
(+.f64 (.f64 1/2 x) (+.f64 (.f64 1/6 (pow.f64 x 2)) (+.f64 1 (*.f64 1/24 (pow.f64 x 3)))))
(fma.f64 1/2 x (+.f64 (fma.f64 1/6 (.f64 x x) 1) (.f64 1/24 (pow.f64 x 3))))
(fma.f64 1/2 x (fma.f64 1/6 (*.f64 x x) (fma.f64 1/24 (pow.f64 x 3) 1)))
(fma.f64 1/2 x (fma.f64 x (*.f64 x 1/6) (fma.f64 1/24 (pow.f64 x 3) 1)))
(fma.f64 x (fma.f64 x 1/6 1/2) (fma.f64 1/24 (pow.f64 x 3) 1))
(fma.f64 x (fma.f64 x (fma.f64 x 1/24 1/6) 1/2) 1)
(/.f64 (-.f64 (exp.f64 x) 1) x)
(/.f64 (expm1.f64 x) x)
(/.f64 (-.f64 (exp.f64 x) 1) x)
(/.f64 (expm1.f64 x) x)
(/.f64 (-.f64 (exp.f64 x) 1) x)
(/.f64 (expm1.f64 x) x)
(/.f64 (-.f64 (exp.f64 x) 1) x)
(/.f64 (expm1.f64 x) x)
(/.f64 (-.f64 (exp.f64 x) 1) x)
(/.f64 (expm1.f64 x) x)
(/.f64 (-.f64 (exp.f64 x) 1) x)
(/.f64 (expm1.f64 x) x)
(/.f64 (-.f64 (exp.f64 x) 1) x)
(/.f64 (expm1.f64 x) x)
(/.f64 (-.f64 (exp.f64 x) 1) x)
(/.f64 (expm1.f64 x) x)

localize9.0ms (0.2%)

Local error

Found 3 expressions with local error:

New	Error	Program
	0.0b	(/.f64 (expm1.f64 x) x)
✓	0.2b	(cbrt.f64 (/.f64 (expm1.f64 x) x))
✓	0.2b	(pow.f64 (cbrt.f64 (/.f64 (expm1.f64 x) x)) 3)

Compiler

Compiled 21 to 7 computations (66.7% saved)

series8.0ms (0.2%)

Counts

2 → 8

Calls

6 calls:

Time	Variable		Point	Expression
4.0ms	x	@	-inf	(pow.f64 (cbrt.f64 (/.f64 (expm1.f64 x) x)) 3)
1.0ms	x	@	inf	(pow.f64 (cbrt.f64 (/.f64 (expm1.f64 x) x)) 3)
1.0ms	x	@	0	(pow.f64 (cbrt.f64 (/.f64 (expm1.f64 x) x)) 3)
1.0ms	x	@	-inf	(cbrt.f64 (/.f64 (expm1.f64 x) x))
1.0ms	x	@	inf	(cbrt.f64 (/.f64 (expm1.f64 x) x))

rewrite61.0ms (1.4%)

Algorithm

1×	batch-egg-rewrite

Rules

624×	`pow1_binary64`
590×	`add-log-exp_binary64`
590×	`log1p-expm1-u_binary64`
590×	`expm1-log1p-u_binary64`
575×	`add-exp-log_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	7	14
1	152	14
2	1626	14

Stop Event

1×	node limit

Counts

2 → 72

Calls

Call 1

Inputs
(pow.f64 (cbrt.f64 (/.f64 (expm1.f64 x) x)) 3)
(cbrt.f64 (/.f64 (expm1.f64 x) x))

Outputs

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

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

simplify170.0ms (3.9%)

Algorithm

1×	egg-herbie

Rules

1218×	`fma-def_binary64`
750×	`sqr-pow_binary64`
605×	`cube-prod_binary64`
477×	`fabs-mul_binary64`
370×	`pow-sqr_binary64`

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	30	82
1	77	78
2	182	75
3	519	62
4	1386	56
5	2414	56
6	2936	56
7	3069	56
8	3223	56
9	3413	56
10	3666	56
11	4316	56
12	4723	56
13	5252	56
14	5914	56
15	6738	56
16	7139	56
17	7507	56
18	7845	56

Stop Event

1×	node limit

Counts

80 → 85

Calls

Call 1

Inputs
1
(+.f64 (*.f64 1/2 x) 1)
(+.f64 (.f64 1/2 x) (+.f64 (.f64 1/6 (pow.f64 x 2)) 1))
(+.f64 (.f64 1/2 x) (+.f64 (.f64 1/6 (pow.f64 x 2)) (+.f64 1 (*.f64 1/24 (pow.f64 x 3)))))
1
(+.f64 1 (*.f64 1/6 x))
(+.f64 1 (+.f64 (.f64 1/6 x) (.f64 1/36 (pow.f64 x 2))))
(+.f64 1 (+.f64 (.f64 1/6 x) (+.f64 (.f64 1/324 (pow.f64 x 3)) (*.f64 1/36 (pow.f64 x 2)))))

Outputs
1
(+.f64 (*.f64 1/2 x) 1)
(fma.f64 1/2 x 1)
(+.f64 (.f64 1/2 x) (+.f64 (.f64 1/6 (pow.f64 x 2)) 1))
(fma.f64 1/2 x (fma.f64 1/6 (*.f64 x x) 1))
(fma.f64 x (*.f64 x 1/6) (fma.f64 1/2 x 1))
(fma.f64 x (fma.f64 x 1/6 1/2) 1)
(+.f64 (.f64 1/2 x) (+.f64 (.f64 1/6 (pow.f64 x 2)) (+.f64 1 (*.f64 1/24 (pow.f64 x 3)))))
(fma.f64 1/2 x (+.f64 (fma.f64 1/6 (.f64 x x) 1) (.f64 1/24 (pow.f64 x 3))))
(fma.f64 1/2 x (fma.f64 1/6 (*.f64 x x) (fma.f64 1/24 (pow.f64 x 3) 1)))
(fma.f64 1/2 x (fma.f64 x (*.f64 x 1/6) (fma.f64 1/24 (pow.f64 x 3) 1)))
(fma.f64 1/2 x (fma.f64 (*.f64 x x) (fma.f64 x 1/24 1/6) 1))
(fma.f64 x (fma.f64 x (fma.f64 x 1/24 1/6) 1/2) 1)
1
(+.f64 1 (*.f64 1/6 x))
(+.f64 1 (*.f64 x 1/6))
(fma.f64 x 1/6 1)
(+.f64 1 (+.f64 (.f64 1/6 x) (.f64 1/36 (pow.f64 x 2))))
(+.f64 1 (fma.f64 1/6 x (.f64 (.f64 x x) 1/36)))
(+.f64 1 (fma.f64 x 1/6 (.f64 x (.f64 x 1/36))))
(fma.f64 x (*.f64 x 1/36) (fma.f64 x 1/6 1))
(fma.f64 x (fma.f64 x 1/36 1/6) 1)
(+.f64 1 (+.f64 (.f64 1/6 x) (+.f64 (.f64 1/324 (pow.f64 x 3)) (*.f64 1/36 (pow.f64 x 2)))))
(+.f64 1 (fma.f64 1/6 x (fma.f64 1/324 (pow.f64 x 3) (.f64 (.f64 x x) 1/36))))
(+.f64 1 (fma.f64 x 1/6 (fma.f64 (.f64 x x) 1/36 (.f64 (pow.f64 x 3) 1/324))))
(+.f64 (fma.f64 x 1/6 1) (.f64 (.f64 x x) (+.f64 1/36 (*.f64 x 1/324))))
(fma.f64 (pow.f64 x 3) 1/324 (fma.f64 x (fma.f64 x 1/36 1/6) 1))
(fma.f64 x (fma.f64 x (fma.f64 x 1/324 1/36) 1/6) 1)

eval61.0ms (1.4%)

Compiler: Compiled 2896 to 1404 computations (51.5% saved)

prune54.0ms (1.2%)

Pruning

7 alts after pruning (3 fresh and 4 done)

	Pruned	Kept	Total
New	263	3	266
Fresh	1	0	1
Picked	0	1	1
Done	1	3	4
Total	265	7	272

Error

Counts

272 → 7

Alt Table

Click to see full alt table

Status	Error	Program
✓	18.0b	(-.f64 (+.f64 1 (/.f64 (expm1.f64 x) x)) 1)
	20.0b	1
▶	20.4b	(-.f64 (+.f64 1 (+.f64 (*.f64 1/2 x) 1)) 1)
✓	0.0b	(/.f64 (expm1.f64 x) x)
✓	0.5b	(pow.f64 (cbrt.f64 (/.f64 (expm1.f64 x) x)) 3)
▶	0.0b	(/.f64 1 (/.f64 x (expm1.f64 x)))
✓	20.4b	(+.f64 (*.f64 1/2 x) 1)

Compiler

Compiled 47 to 37 computations (21.3% saved)

localize12.0ms (0.3%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.0b	(+.f64 1 (+.f64 (*.f64 1/2 x) 1))
✓	0.0b	(-.f64 (+.f64 1 (+.f64 (*.f64 1/2 x) 1)) 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	@	inf	(-.f64 (+.f64 1 (+.f64 (*.f64 1/2 x) 1)) 1)
0.0ms	x	@	0	(-.f64 (+.f64 1 (+.f64 (*.f64 1/2 x) 1)) 1)
0.0ms	x	@	-inf	(-.f64 (+.f64 1 (+.f64 (*.f64 1/2 x) 1)) 1)
0.0ms	x	@	inf	(+.f64 1 (+.f64 (*.f64 1/2 x) 1))
0.0ms	x	@	0	(+.f64 1 (+.f64 (*.f64 1/2 x) 1))

rewrite80.0ms (1.8%)

Algorithm

1×	batch-egg-rewrite

Rules

895×	`pow1_binary64`
838×	`add-log-exp_binary64`
838×	`log1p-expm1-u_binary64`
838×	`expm1-log1p-u_binary64`
825×	`add-exp-log_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	8	19
1	187	12
2	2615	12

Stop Event

1×	node limit

Counts

2 → 83

Calls

Call 1

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

Outputs

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

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

simplify22.0ms (0.5%)

Algorithm

1×	egg-herbie

Rules

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

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	10	108
1	15	108
2	17	108

Stop Event

1×

saturated

Counts

107 → 89

Calls

Call 1

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

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

localize11.0ms (0.2%)

Local error

Found 2 expressions with local error:

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

Compiler

Compiled 15 to 6 computations (60% saved)

series48.0ms (1.1%)

Counts

2 → 24

Calls

6 calls:

Time	Variable		Point	Expression
44.0ms	x	@	0	(/.f64 1 (/.f64 x (expm1.f64 x)))
1.0ms	x	@	inf	(/.f64 x (expm1.f64 x))
1.0ms	x	@	-inf	(/.f64 x (expm1.f64 x))
1.0ms	x	@	0	(/.f64 x (expm1.f64 x))
0.0ms	x	@	inf	(/.f64 1 (/.f64 x (expm1.f64 x)))

rewrite75.0ms (1.7%)

Algorithm

1×	batch-egg-rewrite

Rules

606×	`pow1_binary64`
562×	`add-log-exp_binary64`
562×	`log1p-expm1-u_binary64`
562×	`expm1-log1p-u_binary64`
548×	`add-exp-log_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	6	15
1	124	12
2	1584	12

Stop Event

1×	node limit

Counts

2 → 66

Calls

Call 1

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

Outputs

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

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

simplify51.0ms (1.1%)

Algorithm

1×	egg-herbie

Rules

933×	`fma-def_binary64`
803×	`unswap-sqr_binary64`
585×	`associate-/l/_binary64`
562×	`times-frac_binary64`
385×	`associate-/r*_binary64`

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	35	176
1	88	170
2	187	170
3	521	158
4	1475	155
5	3045	155
6	5017	155

Stop Event

1×	node limit

Counts

90 → 83

Calls

Call 1

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

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

eval77.0ms (1.7%)

Compiler: Compiled 1978 to 1398 computations (29.3% saved)

prune32.0ms (0.7%)

Pruning

9 alts after pruning (4 fresh and 5 done)

	Pruned	Kept	Total
New	169	3	172
Fresh	0	1	1
Picked	0	1	1
Done	1	4	5
Total	170	9	179

Error

Counts

179 → 9

Alt Table

Click to see full alt table

Status	Error	Program
✓	18.0b	(-.f64 (+.f64 1 (/.f64 (expm1.f64 x) x)) 1)
	20.0b	1
▶	20.5b	(/.f64 (-.f64 1 (.f64 1/4 (.f64 x x))) (-.f64 1 (*.f64 1/2 x)))
✓	0.0b	(/.f64 (expm1.f64 x) x)
✓	0.5b	(pow.f64 (cbrt.f64 (/.f64 (expm1.f64 x) x)) 3)
✓	0.0b	(/.f64 1 (/.f64 x (expm1.f64 x)))
▶	17.0b	(/.f64 1 (+.f64 (*.f64 -1/2 x) 1))
▶	61.9b	(*.f64 1/2 x)
✓	20.4b	(+.f64 (*.f64 1/2 x) 1)

Compiler

Compiled 63 to 49 computations (22.2% saved)

localize3.0ms (0.1%)

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

localize9.0ms (0.2%)

Local error

Found 1 expressions with local error:

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

rewrite54.0ms (1.2%)

Algorithm

1×	batch-egg-rewrite

Rules

688×	`pow1_binary64`
641×	`log1p-expm1-u_binary64`
641×	`expm1-log1p-u_binary64`
640×	`add-log-exp_binary64`
628×	`add-exp-log_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	7	8
1	151	8
2	1827	8

Stop Event

1×	node limit

Counts

1 → 22

Calls

Call 1

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

Outputs

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

simplify58.0ms (1.3%)

Algorithm

1×	egg-herbie

Rules

724×	`fma-neg_binary64`
686×	`times-frac_binary64`
450×	`fma-def_binary64`
417×	`cancel-sign-sub-inv_binary64`
398×	`associate-*l/_binary64`

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	41	193
1	112	179
2	306	177
3	985	171
4	3002	171

Stop Event

1×	node limit

Counts

34 → 36

Calls

Call 1

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

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

localize78.0ms (1.8%)

Local error

Found 1 expressions with local error:

New	Error	Program
✓	8.2b	(/.f64 (-.f64 1 (.f64 1/4 (.f64 x x))) (-.f64 1 (*.f64 1/2 x)))

Compiler

Compiled 41 to 26 computations (36.6% saved)

series6.0ms (0.1%)

Counts

1 → 12

Calls

3 calls:

Time	Variable		Point	Expression
3.0ms	x	@	inf	(/.f64 (-.f64 1 (.f64 1/4 (.f64 x x))) (-.f64 1 (*.f64 1/2 x)))
1.0ms	x	@	0	(/.f64 (-.f64 1 (.f64 1/4 (.f64 x x))) (-.f64 1 (*.f64 1/2 x)))
1.0ms	x	@	-inf	(/.f64 (-.f64 1 (.f64 1/4 (.f64 x x))) (-.f64 1 (*.f64 1/2 x)))

rewrite78.0ms (1.8%)

Algorithm

1×	batch-egg-rewrite

Rules

566×	`log-prod_binary64`
319×	`pow-prod-down_binary64`
291×	`pow2_binary64`
282×	`fma-def_binary64`
199×	`pow1/3_binary64`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	11	19
1	250	7
2	3420	5

Stop Event

1×	node limit

Counts

1 → 66

Calls

Call 1

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

Outputs

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

simplify51.0ms (1.2%)

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	54
1	11	54
2	12	54

Stop Event

1×

saturated

Counts

78 → 70

Calls

Call 1

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

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

eval68.0ms (1.5%)

Compiler: Compiled 1263 to 1002 computations (20.7% saved)

prune33.0ms (0.8%)

Pruning

11 alts after pruning (3 fresh and 8 done)

	Pruned	Kept	Total
New	104	2	106
Fresh	0	1	1
Picked	0	1	1
Done	0	7	7
Total	104	11	115

Error

Counts

115 → 11

Alt Table

Click to see full alt table

Status	Error	Program
✓	18.0b	(-.f64 (+.f64 1 (/.f64 (expm1.f64 x) x)) 1)
	20.0b	1
✓	20.5b	(/.f64 (-.f64 1 (.f64 1/4 (.f64 x x))) (-.f64 1 (*.f64 1/2 x)))
✓	0.0b	(/.f64 (expm1.f64 x) x)
✓	0.5b	(pow.f64 (cbrt.f64 (/.f64 (expm1.f64 x) x)) 3)
✓	0.0b	(/.f64 1 (/.f64 x (expm1.f64 x)))
✓	17.0b	(/.f64 1 (+.f64 (*.f64 -1/2 x) 1))
✓	61.9b	(*.f64 1/2 x)
	60.0b	(-.f64 (/.f64 (/.f64 -4 x) x) (/.f64 2 x))
	58.9b	(/.f64 -2 x)
✓	20.4b	(+.f64 (*.f64 1/2 x) 1)

Compiler

Compiled 77 to 59 computations (23.4% saved)

regimes48.0ms (1.1%)

Counts

15 → 1

Calls

Call 1

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

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

Calls

3 calls:

18.0ms	x
16.0ms	(/.f64 (-.f64 (exp.f64 x) 1) x)
6.0ms	(/.f64 (-.f64 (exp.f64 x) 1) x)

Results

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

Compiler

Compiled 107 to 73 computations (31.8% saved)

regimes10.0ms (0.2%)

Counts

10 → 1

Calls

Call 1

Inputs
1
1
(/.f64 -2 x)
(*.f64 1/2 x)
(+.f64 (*.f64 1/2 x) 1)
(/.f64 1 (+.f64 (*.f64 -1/2 x) 1))
(-.f64 (/.f64 (/.f64 -4 x) x) (/.f64 2 x))
(-.f64 (+.f64 1 (+.f64 (*.f64 1/2 x) 1)) 1)
(/.f64 (-.f64 1 (.f64 1/4 (.f64 x x))) (-.f64 1 (*.f64 1/2 x)))
(/.f64 (expm1.f64 x) x)

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

Calls

1 calls:

8.0ms

Results

Error	Segments	Branch
0.0b	1	`x`

Compiler

Compiled 58 to 44 computations (24.1% saved)

regimes10.0ms (0.2%)

Counts

9 → 1

Calls

Call 1

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

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

Calls

1 calls:

7.0ms

Results

Error	Segments	Branch
17.0b	1	`x`

Compiler

Compiled 54 to 42 computations (22.2% saved)

regimes10.0ms (0.2%)

Counts

5 → 2

Calls

Call 1

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

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

Calls

1 calls:

9.0ms

Results

Error	Segments	Branch
17.0b	2	`x`

Compiler

Compiled 16 to 12 computations (25% saved)

bsearch49.0ms (1.1%)

Algorithm

1×	binary-search

Steps

Time	Left	Right
48.0ms	-1.629159470582278	-0.602516291185853

Compiler

Compiled 11 to 8 computations (27.3% saved)

regimes12.0ms (0.3%)

Counts

4 → 2

Calls

Call 1

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

Outputs
(/.f64 -2 x)
1

Calls

1 calls:

11.0ms

Results

Error	Segments	Branch
17.4b	2	`x`

Compiler

Compiled 11 to 8 computations (27.3% saved)

bsearch18.0ms (0.4%)

Algorithm

1×	binary-search

Steps

Time	Left	Right
17.0ms	-104.35134519839956	-1.629159470582278

Compiler

Compiled 11 to 8 computations (27.3% saved)

regimes20.0ms (0.4%)

Accuracy

Total -0.0b remaining (-0%)

Threshold costs -0.0b (-0%)

Counts

2 → 1

Calls

Call 1

Inputs
1
1

Outputs
1

Calls

1 calls:

3.0ms

Results

Error	Segments	Branch
20.0b	1	`x`

Compiler

Compiled 5 to 4 computations (20% saved)

simplify5.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

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

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	23	54
1	29	54

Stop Event

1×	fuel
1×	saturated

Calls

Call 1

Inputs
(/.f64 1 (/.f64 x (expm1.f64 x)))
(/.f64 (expm1.f64 x) x)
(/.f64 1 (+.f64 (*.f64 -1/2 x) 1))
(if (<=.f64 x -3668540992320731/2251799813685248) (/.f64 -2 x) (+.f64 (*.f64 1/2 x) 1))
(if (<=.f64 x -7343073114861285/70368744177664) (/.f64 -2 x) 1)
1

Outputs
(/.f64 1 (/.f64 x (expm1.f64 x)))
(/.f64 (expm1.f64 x) x)
(/.f64 1 (+.f64 (*.f64 -1/2 x) 1))
(/.f64 1 (+.f64 1 (*.f64 x -1/2)))
(if (<=.f64 x -3668540992320731/2251799813685248) (/.f64 -2 x) (+.f64 (*.f64 1/2 x) 1))
(if (<=.f64 x -3668540992320731/2251799813685248) (/.f64 -2 x) (+.f64 1 (*.f64 x 1/2)))
(if (<=.f64 x -7343073114861285/70368744177664) (/.f64 -2 x) 1)
1

Compiler

Compiled 44 to 34 computations (22.7% saved)

soundness28.0ms (0.6%)

Algorithm

1×	egg-herbie

Rules

95×	`fma-def_binary64`
80×	`fma-neg_binary64`
32×	`distribute-rgt-in_binary64`
28×	`cancel-sign-sub-inv_binary64`
26×	`distribute-lft-in_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	6	6
1	15	6
2	18	6
3	22	6
4	30	6
5	40	6
6	59	6
7	100	6
8	145	6
9	223	6
10	352	6
11	511	6
12	583	6
13	619	6

Stop Event

1×

saturated

Compiler

Compiled 12 to 8 computations (33.3% saved)

end40.0ms (0.9%)

Compiler: Compiled 39 to 28 computations (28.2% saved)

Iter	Nodes	Cost
0	6	6
1	15	6
2	18	6
3	22	6
4	30	6
5	40	6
6	59	6
7	100	6
8	145	6
9	223	6
10	352	6
11	511	6
12	583	6
13	619	6
0	1	1

Iter	Nodes	Cost
0	6	6
1	15	6
2	18	6
3	22	6
4	30	6
5	40	6
6	59	6
7	100	6
8	145	6
9	223	6
10	352	6
11	511	6
12	583	6
13	619	6

Iter	Nodes	Cost
0	6	6
1	15	6
2	18	6
3	22	6
4	30	6
5	40	6
6	59	6
7	100	6
8	145	6
9	223	6
10	352	6
11	511	6
12	583	6
13	619	6

Iter	Nodes	Cost
0	6	6
1	15	6
2	18	6
3	22	6
4	30	6
5	40	6
6	59	6
7	100	6
8	145	6
9	223	6
10	352	6
11	511	6
12	583	6
13	619	6
0	1	1

Iter	Nodes	Cost
0	6	6
1	15	6
2	18	6
3	22	6
4	30	6
5	40	6
6	59	6
7	100	6
8	145	6
9	223	6
10	352	6
11	511	6
12	583	6
13	619	6

Iter	Nodes	Cost
0	6	6
1	15	6
2	18	6
3	22	6
4	30	6
5	40	6
6	59	6
7	100	6
8	145	6
9	223	6
10	352	6
11	511	6
12	583	6
13	619	6

Details

analyze4.0ms (0.1%)

sample2.2s (50.4%)

preprocess172.0ms (3.9%)

simplify30.0ms (0.7%)

eval1.0ms (0%)

prune1.0ms (0%)

localize43.0ms (1%)

series4.0ms (0.1%)

rewrite52.0ms (1.2%)

simplify61.0ms (1.4%)

eval13.0ms (0.3%)

prune12.0ms (0.3%)

localize21.0ms (0.5%)

series2.0ms (0%)

rewrite85.0ms (1.9%)

simplify48.0ms (1.1%)

localize5.0ms (0.1%)

localize12.0ms (0.3%)

series1.0ms (0%)

rewrite102.0ms (2.3%)

simplify56.0ms (1.3%)

localize9.0ms (0.2%)

series8.0ms (0.2%)

rewrite61.0ms (1.4%)

simplify170.0ms (3.9%)

eval61.0ms (1.4%)

prune54.0ms (1.2%)

localize12.0ms (0.3%)

series2.0ms (0%)

rewrite80.0ms (1.8%)

simplify22.0ms (0.5%)

localize11.0ms (0.2%)

series48.0ms (1.1%)

rewrite75.0ms (1.7%)

simplify51.0ms (1.1%)

eval77.0ms (1.7%)

prune32.0ms (0.7%)

localize3.0ms (0.1%)

localize9.0ms (0.2%)

series1.0ms (0%)

rewrite54.0ms (1.2%)

simplify58.0ms (1.3%)

localize78.0ms (1.8%)

series6.0ms (0.1%)

rewrite78.0ms (1.8%)

simplify51.0ms (1.2%)

eval68.0ms (1.5%)

prune33.0ms (0.8%)

regimes48.0ms (1.1%)

regimes10.0ms (0.2%)

regimes10.0ms (0.2%)

regimes10.0ms (0.2%)

bsearch49.0ms (1.1%)

regimes12.0ms (0.3%)

bsearch18.0ms (0.4%)

regimes20.0ms (0.4%)

simplify5.0ms (0.1%)

soundness28.0ms (0.6%)

end40.0ms (0.9%)

Profiling

Iter	Nodes	Cost
0	6	6
1	15	6
2	18	6
3	22	6
4	30	6
5	40	6
6	59	6
7	100	6
8	145	6
9	223	6
10	352	6
11	511	6
12	583	6
13	619	6
0	1	1

Iter	Nodes	Cost
0	6	6
1	15	6
2	18	6
3	22	6
4	30	6
5	40	6
6	59	6
7	100	6
8	145	6
9	223	6
10	352	6
11	511	6
12	583	6
13	619	6

Iter	Nodes	Cost
0	6	6
1	15	6
2	18	6
3	22	6
4	30	6
5	40	6
6	59	6
7	100	6
8	145	6
9	223	6
10	352	6
11	511	6
12	583	6
13	619	6