Details

analyze438.0ms (10.6%)

Algorithm

1×

Search

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

Compiler

Compiled 9 to 6 computations (33.3% saved)

sample2.1s (50.6%)

Results

1.1s	2647×	body	1024	valid
479.0ms	4012×	body	256	valid
329.0ms	1310×	body	512	valid
118.0ms	287×	body	2048	valid
0.0ms	1×	body	2048	infinite
0.0ms	2×	body	256	unsamplable

Bogosity

preprocess19.0ms (0.5%)

Algorithm

2×	egg-herbie

Rules

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

Iterations

Useful iterations: 0 (0.0ms)

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

Stop Event

1×	saturated
1×	saturated

Calls

Call 1

Inputs
0

Outputs
0

Call 2

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

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

Compiler

Compiled 9 to 6 computations (33.3% saved)

simplify7.0ms (0.2%)

Algorithm

1×	egg-herbie

Rules

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

Iterations

Useful iterations: 0 (0.0ms)

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

Stop Event

1×

saturated

Counts

1 → 2

Calls

Call 1

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

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

eval1.0ms (0%)

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

prune1.0ms (0%)

Pruning

3 alts after pruning (3 fresh and 0 done)

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

Error

0.5b

Counts

3 → 2

Alt Table

Click to see full alt table

Status	Error	Program
▶	38.6b	(/.f64 (exp.f64 x) (-.f64 (exp.f64 x) 1))
▶	0.5b	(/.f64 (exp.f64 x) (expm1.f64 x))

Compiler

Compiled 14 to 9 computations (35.7% saved)

localize6.0ms (0.1%)

Local error

Found 1 expressions with local error:

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

Compiler

Compiled 11 to 4 computations (63.6% saved)

series2.0ms (0.1%)

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))

rewrite44.0ms (1.1%)

Algorithm

1×	batch-egg-rewrite

Rules

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

Iterations

Useful iterations: 0 (0.0ms)

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

Stop Event

1×	node limit

Counts

1 → 30

Calls

Call 1

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

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

Outputs

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

simplify180.0ms (4.4%)

Algorithm

1×	egg-herbie

Rules

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

Iterations

Useful iterations: 0 (0.0ms)

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

Stop Event

1×	node limit

Counts

42 → 39

Calls

Call 1

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

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

localize7.0ms (0.2%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.5b	(/.f64 (exp.f64 x) (-.f64 (exp.f64 x) 1))
✓	4.0b	(-.f64 (exp.f64 x) 1)

Compiler

Compiled 16 to 8 computations (50% saved)

series2.0ms (0.1%)

Counts

2 → 8

Calls

6 calls:

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

rewrite53.0ms (1.3%)

Algorithm

1×	batch-egg-rewrite

Rules

661×	`pow1_binary64`
617×	`add-log-exp_binary64`
616×	`log1p-expm1-u_binary64`
616×	`expm1-log1p-u_binary64`
604×	`add-exp-log_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	6	11
1	127	11
2	1676	11

Stop Event

1×	node limit

Counts

2 → 64

Calls

Call 1

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

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

Outputs

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

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

simplify113.0ms (2.8%)

Algorithm

1×	egg-herbie

Rules

803×	`unswap-sqr_binary64`
531×	`associate-/r*_binary64`
521×	`distribute-lft-out_binary64`
406×	`*-commutative_binary64`
382×	`fma-def_binary64`

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	30	86
1	78	86
2	184	86
3	550	80
4	1565	80
5	2643	80
6	4693	80
7	5026	80
8	5516	80
9	6431	80
10	6956	80
11	7563	80

Stop Event

1×	node limit

Counts

72 → 77

Calls

Call 1

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

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

eval21.0ms (0.5%)

Compiler: Compiled 1234 to 529 computations (57.1% saved)

prune23.0ms (0.6%)

Pruning

7 alts after pruning (5 fresh and 2 done)

	Pruned	Kept	Total
New	111	5	116
Fresh	0	0	0
Picked	0	1	1
Done	0	1	1
Total	111	7	118

Error

0.4b

Counts

118 → 7

Alt Table

Click to see full alt table

Status	Error	Program
✓	38.6b	(/.f64 (exp.f64 x) (-.f64 (exp.f64 x) 1))
▶	24.4b	(+.f64 1/2 (+.f64 (.f64 -1/720 (pow.f64 x 3)) (+.f64 (.f64 1/12 x) (/.f64 1 x))))
✓	0.5b	(/.f64 (exp.f64 x) (expm1.f64 x))
▶	1.8b	(/.f64 (exp.f64 x) x)
▶	24.1b	(+.f64 (/.f64 1 x) 1/2)
▶	24.0b	(+.f64 1/2 (+.f64 (*.f64 1/12 x) (/.f64 1 x)))
▶	24.0b	(/.f64 1 x)

Compiler

Compiled 96 to 73 computations (24% saved)

localize4.0ms (0.1%)

Local error

Found 1 expressions with local error:

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

Compiler

Compiled 8 to 3 computations (62.5% saved)

series2.0ms (0%)

Counts

1 → 4

Calls

3 calls:

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

rewrite44.0ms (1.1%)

Algorithm

1×	batch-egg-rewrite

Rules

440×	`pow1_binary64`
421×	`add-sqr-sqrt_binary64`
415×	`*-un-lft-identity_binary64`
408×	`add-log-exp_binary64`
408×	`log1p-expm1-u_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	4	6
1	81	6
2	1090	6

Stop Event

1×	node limit

Counts

1 → 33

Calls

Call 1

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

Outputs

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

simplify120.0ms (2.9%)

Algorithm

1×	egg-herbie

Rules

815×	`fma-def_binary64`
602×	`sqr-pow_binary64`
544×	`associate-/l/_binary64`
540×	`associate-l_binary64`
434×	`unswap-sqr_binary64`

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	15	40
1	36	40
2	72	40
3	161	37
4	324	37
5	706	37
6	2108	37
7	3814	37
8	4781	37
9	4996	37
10	5221	37
11	5544	37
12	5971	37
13	6572	37
14	7141	37
15	7829	37

Stop Event

1×	node limit

Counts

37 → 39

Calls

Call 1

Inputs
(/.f64 1 x)
(+.f64 1 (/.f64 1 x))
(+.f64 1 (+.f64 (*.f64 1/2 x) (/.f64 1 x)))
(+.f64 1 (+.f64 (.f64 1/6 (pow.f64 x 2)) (+.f64 (.f64 1/2 x) (/.f64 1 x))))

Outputs
(/.f64 1 x)
(+.f64 1 (/.f64 1 x))
(+.f64 1 (+.f64 (*.f64 1/2 x) (/.f64 1 x)))
(+.f64 1 (fma.f64 1/2 x (/.f64 1 x)))
(+.f64 1 (fma.f64 x 1/2 (/.f64 1 x)))
(+.f64 (/.f64 1 x) (fma.f64 x 1/2 1))
(+.f64 1 (+.f64 (.f64 1/6 (pow.f64 x 2)) (+.f64 (.f64 1/2 x) (/.f64 1 x))))
(+.f64 1 (fma.f64 1/6 (*.f64 x x) (fma.f64 1/2 x (/.f64 1 x))))
(+.f64 1 (fma.f64 1/6 (*.f64 x x) (fma.f64 x 1/2 (/.f64 1 x))))
(+.f64 1 (fma.f64 x (*.f64 x 1/6) (fma.f64 x 1/2 (/.f64 1 x))))
(fma.f64 x (fma.f64 x 1/6 1/2) (+.f64 1 (/.f64 1 x)))
(+.f64 (/.f64 1 x) (fma.f64 x (fma.f64 x 1/6 1/2) 1))
(+.f64 1 (fma.f64 x (fma.f64 x 1/6 1/2) (/.f64 1 x)))

localize3.0ms (0.1%)

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

localize5.0ms (0.1%)

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

localize11.0ms (0.3%)

Local error

Found 2 expressions with local error:

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

Compiler

Compiled 27 to 20 computations (25.9% saved)

series3.0ms (0.1%)

Counts

2 → 9

Calls

6 calls:

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

rewrite56.0ms (1.4%)

Algorithm

1×	batch-egg-rewrite

Rules

748×	`pow1_binary64`
701×	`add-log-exp_binary64`
701×	`log1p-expm1-u_binary64`
701×	`expm1-log1p-u_binary64`
687×	`add-exp-log_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	7	12
1	151	12
2	1947	12

Stop Event

1×	node limit

Counts

2 → 46

Calls

Call 1

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

Outputs

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

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

simplify9.0ms (0.2%)

Algorithm

1×	egg-herbie

Rules

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

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	7	72
1	11	60
2	13	60

Stop Event

1×

saturated

Counts

55 → 50

Calls

Call 1

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

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

localize25.0ms (0.6%)

Local error

Found 4 expressions with local error:

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

Compiler

Compiled 56 to 43 computations (23.2% saved)

series3.0ms (0.1%)

Counts

2 → 12

Calls

6 calls:

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

rewrite74.0ms (1.8%)

Algorithm

1×	batch-egg-rewrite

Rules

552×	`fma-def_binary64`
549×	`log-prod_binary64`
320×	`pow2_binary64`
303×	`fma-neg_binary64`
220×	`expm1-udef_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	12	22
1	273	22
2	3506	22

Stop Event

1×	node limit

Counts

2 → 106

Calls

Call 1

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

Outputs

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1/12) (+.f64 (/.f64 1 x) (*.f64 -1/720 (pow.f64 x 3))))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (/.f64 1 (cbrt.f64 x)) (cbrt.f64 (pow.f64 x -2)) (fma.f64 -1/720 (pow.f64 x 3) (*.f64 x 1/12)))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (cbrt.f64 (pow.f64 x -2)) (/.f64 1 (cbrt.f64 x)) (fma.f64 -1/720 (pow.f64 x 3) (*.f64 x 1/12)))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (sqrt.f64 (fma.f64 x 1/12 (/.f64 1 x))) (sqrt.f64 (fma.f64 x 1/12 (/.f64 1 x))) (*.f64 -1/720 (pow.f64 x 3)))))) (#(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) (*.f64 -1/720 (pow.f64 x 3))))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (*.f64 (sqrt.f64 -1/720) (pow.f64 x 3/2)) (*.f64 (sqrt.f64 -1/720) (pow.f64 x 3/2)) (fma.f64 x 1/12 (/.f64 1 x)))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (sqrt.f64 x) (*.f64 (sqrt.f64 x) 1/12) (+.f64 (/.f64 1 x) (*.f64 -1/720 (pow.f64 x 3))))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (pow.f64 x -1/2) (pow.f64 x -1/2) (fma.f64 -1/720 (pow.f64 x 3) (*.f64 x 1/12)))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 -1 (/.f64 1 (neg.f64 x)) (fma.f64 -1/720 (pow.f64 x 3) (*.f64 x 1/12)))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (fma.f64 (pow.f64 x 3) 1/1728 (pow.f64 x -3)) (/.f64 1 (-.f64 (fma.f64 (*.f64 x x) 1/144 (pow.f64 x -2)) (/.f64 (*.f64 x 1/12) x))) (*.f64 -1/720 (pow.f64 x 3)))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (-.f64 (*.f64 (*.f64 x x) 1/144) (pow.f64 x -2)) (/.f64 1 (-.f64 (*.f64 x 1/12) (/.f64 1 x))) (*.f64 -1/720 (pow.f64 x 3)))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (pow.f64 x 3/2) (*.f64 (pow.f64 x 3/2) -1/720) (fma.f64 x 1/12 (/.f64 1 x)))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (fma.f64 -1/720 (pow.f64 x 3) (*.f64 x 1/12)) 1 (/.f64 1 x))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (pow.f64 (cbrt.f64 (fma.f64 -1/720 (pow.f64 x 3) (*.f64 x 1/12))) 2) (cbrt.f64 (fma.f64 -1/720 (pow.f64 x 3) (*.f64 x 1/12))) (/.f64 1 x))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (sqrt.f64 (fma.f64 -1/720 (pow.f64 x 3) (*.f64 x 1/12))) (sqrt.f64 (fma.f64 -1/720 (pow.f64 x 3) (*.f64 x 1/12))) (/.f64 1 x))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (pow.f64 (cbrt.f64 x) -2) (/.f64 1 (cbrt.f64 x)) (fma.f64 -1/720 (pow.f64 x 3) (*.f64 x 1/12)))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (*.f64 1/12 (pow.f64 (cbrt.f64 x) 2)) (cbrt.f64 x) (+.f64 (/.f64 1 x) (*.f64 -1/720 (pow.f64 x 3))))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (*.f64 1/12 (sqrt.f64 x)) (sqrt.f64 x) (+.f64 (/.f64 1 x) (*.f64 -1/720 (pow.f64 x 3))))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (*.f64 -1/720 x) (*.f64 x x) (fma.f64 x 1/12 (/.f64 1 x)))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (*.f64 -1/720 (*.f64 x x)) x (fma.f64 x 1/12 (/.f64 1 x)))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (*.f64 -1/720 (pow.f64 x 3/2)) (pow.f64 x 3/2) (fma.f64 x 1/12 (/.f64 1 x)))))))

simplify170.0ms (4.1%)

Algorithm

1×	egg-herbie

Rules

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

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	16	138
1	39	138
2	64	138
3	126	138
4	199	138
5	424	138
6	1345	138
7	2090	138
8	2177	138
9	2310	138
10	2468	138
11	2713	138
12	3035	138
13	3458	138
14	3959	138
15	4558	138
16	5278	138
17	5599	138
18	5885	138
19	6109	138
20	6289	138
21	6371	138
22	7311	138

Stop Event

1×	node limit

Counts

118 → 115

Calls

Call 1

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

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

eval102.0ms (2.5%)

Compiler: Compiled 4394 to 3318 computations (24.5% saved)

prune34.0ms (0.8%)

Pruning

10 alts after pruning (3 fresh and 7 done)

	Pruned	Kept	Total
New	251	3	254
Fresh	0	0	0
Picked	0	1	1
Done	0	6	6
Total	251	10	261

Error

0.2b

Counts

261 → 10

Alt Table

Click to see full alt table

Status	Error	Program
✓	38.6b	(/.f64 (exp.f64 x) (-.f64 (exp.f64 x) 1))
✓	24.4b	(+.f64 1/2 (+.f64 (.f64 -1/720 (pow.f64 x 3)) (+.f64 (.f64 1/12 x) (/.f64 1 x))))
▶	44.0b	(+.f64 1/2 (/.f64 1 (/.f64 (-.f64 (.f64 1/12 x) (/.f64 1 x)) (-.f64 (.f64 (*.f64 x x) 1/144) (pow.f64 x -2)))))
▶	24.3b	(+.f64 1 (/.f64 1 x))
✓	0.5b	(/.f64 (exp.f64 x) (expm1.f64 x))
✓	1.8b	(/.f64 (exp.f64 x) x)
✓	24.1b	(+.f64 (/.f64 1 x) 1/2)
▶	62.0b	(+.f64 1/2 (*.f64 x 1/12))
✓	24.0b	(+.f64 1/2 (+.f64 (*.f64 1/12 x) (/.f64 1 x)))
✓	24.0b	(/.f64 1 x)

Compiler

Compiled 89 to 68 computations (23.6% saved)

localize5.0ms (0.1%)

Local error

Found 1 expressions with local error:

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

Compiler

Compiled 12 to 9 computations (25% saved)

series1.0ms (0%)

Counts

1 → 12

Calls

3 calls:

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

rewrite43.0ms (1%)

Algorithm

1×	batch-egg-rewrite

Rules

345×	`pow1_binary64`
338×	`add-sqr-sqrt_binary64`
329×	`*-un-lft-identity_binary64`
321×	`add-log-exp_binary64`
321×	`log1p-expm1-u_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	4	4
1	80	4
2	873	4

Stop Event

1×	node limit

Counts

1 → 25

Calls

Call 1

Inputs
(*.f64 x 1/12)

Outputs

((#(struct:change #<rule egg-rr> (2) ((x +.f64 (+.f64 1 (*.f64 x 1/12)) -1)))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 0 (*.f64 x 1/12))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (log.f64 (pow.f64 (exp.f64 x) 1/24)) (log.f64 (pow.f64 (exp.f64 x) 1/24)))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (log.f64 (cbrt.f64 (pow.f64 (exp.f64 1/6) x))) (log.f64 (cbrt.f64 (pow.f64 (exp.f64 1/12) x))))))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (+.f64 1 (*.f64 x 1/12)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (-.f64 (pow.f64 (+.f64 1 (*.f64 x 1/12)) 3) 1) (+.f64 (*.f64 (+.f64 1 (*.f64 x 1/12)) (+.f64 1 (*.f64 x 1/12))) (+.f64 1 (*.f64 (+.f64 1 (*.f64 x 1/12)) 1))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (-.f64 (*.f64 (+.f64 1 (*.f64 x 1/12)) (+.f64 1 (*.f64 x 1/12))) 1) (+.f64 (+.f64 1 (*.f64 x 1/12)) 1))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (*.f64 x 1/12) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (*.f64 x 1/12) 2) 1/2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (*.f64 1/1728 (pow.f64 x 3)) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (cbrt.f64 (*.f64 x 1/12)) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (sqrt.f64 (*.f64 x 1/12)) 2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (E.f64) (log.f64 (*.f64 x 1/12)))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (exp.f64 (sqrt.f64 (log.f64 (*.f64 x 1/12)))) (sqrt.f64 (log.f64 (*.f64 x 1/12))))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (exp.f64 (pow.f64 (cbrt.f64 (log.f64 (*.f64 x 1/12))) 2)) (cbrt.f64 (log.f64 (*.f64 x 1/12))))))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f64 (pow.f64 (*.f64 x 1/12) 2))))) (#(struct:change #<rule egg-rr> (2) ((x fabs.f64 (*.f64 x 1/12))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (pow.f64 (exp.f64 1/12) x))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (*.f64 1/1728 (pow.f64 x 3)))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (*.f64 x 1/12)))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (log.f64 (*.f64 x 1/12)))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (*.f64 3 (log.f64 (*.f64 x 1/12))) 1/3))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (log.f64 (cbrt.f64 (*.f64 x 1/12))) 3))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (log.f64 (sqrt.f64 (*.f64 x 1/12))) 2))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (*.f64 x 1/12)))))))

simplify8.0ms (0.2%)

Algorithm

1×	egg-herbie

Rules

1×	`*-commutative_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	4	48
1	5	48

Stop Event

1×

saturated

Counts

37 → 26

Calls

Call 1

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

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

localize36.0ms (0.9%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.1b	(/.f64 1 (/.f64 (-.f64 (.f64 1/12 x) (/.f64 1 x)) (-.f64 (.f64 (*.f64 x x) 1/144) (pow.f64 x -2))))
✓	0.2b	(.f64 (.f64 x x) 1/144)
	0.3b	(*.f64 1/12 x)
✓	28.0b	(/.f64 (-.f64 (.f64 1/12 x) (/.f64 1 x)) (-.f64 (.f64 (*.f64 x x) 1/144) (pow.f64 x -2)))

Compiler

Compiled 97 to 64 computations (34% saved)

series6.0ms (0.2%)

Counts

3 → 36

Calls

9 calls:

Time	Variable		Point	Expression
2.0ms	x	@	-inf	(/.f64 1 (/.f64 (-.f64 (.f64 1/12 x) (/.f64 1 x)) (-.f64 (.f64 (*.f64 x x) 1/144) (pow.f64 x -2))))
1.0ms	x	@	0	(/.f64 (-.f64 (.f64 1/12 x) (/.f64 1 x)) (-.f64 (.f64 (*.f64 x x) 1/144) (pow.f64 x -2)))
1.0ms	x	@	inf	(/.f64 (-.f64 (.f64 1/12 x) (/.f64 1 x)) (-.f64 (.f64 (*.f64 x x) 1/144) (pow.f64 x -2)))
1.0ms	x	@	inf	(/.f64 1 (/.f64 (-.f64 (.f64 1/12 x) (/.f64 1 x)) (-.f64 (.f64 (*.f64 x x) 1/144) (pow.f64 x -2))))
1.0ms	x	@	-inf	(/.f64 (-.f64 (.f64 1/12 x) (/.f64 1 x)) (-.f64 (.f64 (*.f64 x x) 1/144) (pow.f64 x -2)))

rewrite98.0ms (2.4%)

Algorithm

1×	batch-egg-rewrite

Rules

781×	`log-prod_binary64`
603×	`fma-def_binary64`
341×	`fma-neg_binary64`
271×	`expm1-udef_binary64`
271×	`log1p-udef_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	15	60
1	346	26
2	4836	26

Stop Event

1×	node limit

Counts

3 → 158

Calls

Call 1

Inputs

(/.f64 (-.f64 (*.f64 1/12 x) (/.f64 1 x)) (-.f64 (*.f64 (*.f64 x x) 1/144) (pow.f64 x -2)))

(*.f64 (*.f64 x x) 1/144)

(/.f64 1 (/.f64 (-.f64 (*.f64 1/12 x) (/.f64 1 x)) (-.f64 (*.f64 (*.f64 x x) 1/144) (pow.f64 x -2))))

Outputs

((#(struct:change #<rule egg-rr> (2) ((x +.f64 0 (/.f64 1 (fma.f64 1/12 x (/.f64 1 x))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (/.f64 1/12 (/.f64 (-.f64 (*.f64 (*.f64 x x) 1/144) (pow.f64 x -2)) x)) (neg.f64 (/.f64 1 (*.f64 (-.f64 (*.f64 (*.f64 x x) 1/144) (pow.f64 x -2)) x))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (log.f64 (*.f64 (cbrt.f64 (exp.f64 (/.f64 1 (fma.f64 1/12 x (/.f64 1 x))))) (cbrt.f64 (exp.f64 (/.f64 1 (fma.f64 1/12 x (/.f64 1 x))))))) (log.f64 (cbrt.f64 (exp.f64 (/.f64 1 (fma.f64 1/12 x (/.f64 1 x)))))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (log.f64 (sqrt.f64 (exp.f64 (/.f64 1 (fma.f64 1/12 x (/.f64 1 x)))))) (log.f64 (sqrt.f64 (exp.f64 (/.f64 1 (fma.f64 1/12 x (/.f64 1 x)))))))))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (/.f64 1/12 (/.f64 (-.f64 (*.f64 (*.f64 x x) 1/144) (pow.f64 x -2)) x)) (/.f64 1 (*.f64 (-.f64 (*.f64 (*.f64 x x) 1/144) (pow.f64 x -2)) x)))))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (exp.f64 (log1p.f64 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1/12 x (/.f64 1 x))))))))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (exp.f64 (log1p.f64 (fma.f64 1/12 x (/.f64 1 x)))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (/.f64 (*.f64 (*.f64 x x) 1/144) (fma.f64 1/12 x (/.f64 -1 x))) (/.f64 (pow.f64 x -2) (fma.f64 1/12 x (/.f64 -1 x))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 1 (fma.f64 1/12 x (/.f64 1 x)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (-.f64 (*.f64 (*.f64 x x) 1/144) (pow.f64 x -2)) (/.f64 1 (fma.f64 1/12 x (/.f64 -1 x))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (fma.f64 1/12 x (/.f64 1 x)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 (fma.f64 1/12 x (/.f64 1 x))) (pow.f64 (cbrt.f64 (fma.f64 1/12 x (/.f64 1 x))) 2))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (cbrt.f64 (fma.f64 1/12 x (/.f64 1 x))) 2) (cbrt.f64 (fma.f64 1/12 x (/.f64 1 x))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (sqrt.f64 (fma.f64 1/12 x (/.f64 1 x))) (sqrt.f64 (fma.f64 1/12 x (/.f64 1 x))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 -1 (/.f64 1 (/.f64 -1 (fma.f64 1/12 x (/.f64 1 x)))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 1 (fma.f64 1/12 x (/.f64 -1 x))) (-.f64 (*.f64 (*.f64 x x) 1/144) (pow.f64 x -2)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 1 (fma.f64 1/12 x (/.f64 -1 x))) (pow.f64 (/.f64 1 (-.f64 (*.f64 (*.f64 x x) 1/144) (pow.f64 x -2))) -1))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (pow.f64 (cbrt.f64 (/.f64 1 (fma.f64 1/12 x (/.f64 1 x)))) 2) -1) (pow.f64 (cbrt.f64 (/.f64 1 (fma.f64 1/12 x (/.f64 1 x)))) -1))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (/.f64 1 (sqrt.f64 (fma.f64 1/12 x (/.f64 1 x)))) -1) (pow.f64 (/.f64 1 (sqrt.f64 (fma.f64 1/12 x (/.f64 1 x)))) -1))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (pow.f64 (cbrt.f64 (-.f64 (*.f64 (*.f64 x x) 1/144) (pow.f64 x -2))) 2) 1) (/.f64 (cbrt.f64 (-.f64 (*.f64 (*.f64 x x) 1/144) (pow.f64 x -2))) (fma.f64 1/12 x (/.f64 -1 x))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (hypot.f64 (*.f64 1/12 x) (sqrt.f64 (neg.f64 (pow.f64 x -2)))) 1) (/.f64 (hypot.f64 (*.f64 1/12 x) (sqrt.f64 (neg.f64 (pow.f64 x -2)))) (fma.f64 1/12 x (/.f64 -1 x))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 1 (pow.f64 (cbrt.f64 (fma.f64 1/12 x (/.f64 -1 x))) 2)) (/.f64 (-.f64 (*.f64 (*.f64 x x) 1/144) (pow.f64 x -2)) (cbrt.f64 (fma.f64 1/12 x (/.f64 -1 x)))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (pow.f64 (cbrt.f64 (-.f64 (*.f64 (*.f64 x x) 1/144) (pow.f64 x -2))) 2) (pow.f64 (cbrt.f64 (fma.f64 1/12 x (/.f64 -1 x))) 2)) (/.f64 (cbrt.f64 (-.f64 (*.f64 (*.f64 x x) 1/144) (pow.f64 x -2))) (cbrt.f64 (fma.f64 1/12 x (/.f64 -1 x)))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (hypot.f64 (*.f64 1/12 x) (sqrt.f64 (neg.f64 (pow.f64 x -2)))) (pow.f64 (cbrt.f64 (fma.f64 1/12 x (/.f64 -1 x))) 2)) (/.f64 (hypot.f64 (*.f64 1/12 x) (sqrt.f64 (neg.f64 (pow.f64 x -2)))) (cbrt.f64 (fma.f64 1/12 x (/.f64 -1 x)))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 1 (sqrt.f64 (fma.f64 1/12 x (/.f64 -1 x)))) (/.f64 (-.f64 (*.f64 (*.f64 x x) 1/144) (pow.f64 x -2)) (sqrt.f64 (fma.f64 1/12 x (/.f64 -1 x)))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (pow.f64 (cbrt.f64 (-.f64 (*.f64 (*.f64 x x) 1/144) (pow.f64 x -2))) 2) (sqrt.f64 (fma.f64 1/12 x (/.f64 -1 x)))) (/.f64 (cbrt.f64 (-.f64 (*.f64 (*.f64 x x) 1/144) (pow.f64 x -2))) (sqrt.f64 (fma.f64 1/12 x (/.f64 -1 x)))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (hypot.f64 (*.f64 1/12 x) (sqrt.f64 (neg.f64 (pow.f64 x -2)))) (sqrt.f64 (fma.f64 1/12 x (/.f64 -1 x)))) (/.f64 (hypot.f64 (*.f64 1/12 x) (sqrt.f64 (neg.f64 (pow.f64 x -2)))) (sqrt.f64 (fma.f64 1/12 x (/.f64 -1 x)))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 1 (neg.f64 (fma.f64 1/12 x (/.f64 -1 x)))) (neg.f64 (-.f64 (*.f64 (*.f64 x x) 1/144) (pow.f64 x -2))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (-.f64 (*.f64 (*.f64 x x) 1/144) (pow.f64 x -2)) (-.f64 (*.f64 (pow.f64 x 3) 1/1728) (pow.f64 x -3))) (+.f64 (fma.f64 x (*.f64 x 1/144) (pow.f64 x -2)) (/.f64 (*.f64 1/12 x) x)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (-.f64 (*.f64 (*.f64 x x) 1/144) (pow.f64 x -2)) (-.f64 (*.f64 (*.f64 x x) 1/144) (pow.f64 x -2))) (fma.f64 1/12 x (/.f64 1 x)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (*.f64 (/.f64 1 (fma.f64 1/12 x (/.f64 -1 x))) 1) (-.f64 (*.f64 (*.f64 x x) 1/144) (pow.f64 x -2)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (*.f64 (/.f64 1 (fma.f64 1/12 x (/.f64 -1 x))) (pow.f64 (cbrt.f64 (-.f64 (*.f64 (*.f64 x x) 1/144) (pow.f64 x -2))) 2)) (cbrt.f64 (-.f64 (*.f64 (*.f64 x x) 1/144) (pow.f64 x -2))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (*.f64 (/.f64 1 (fma.f64 1/12 x (/.f64 -1 x))) (hypot.f64 (*.f64 1/12 x) (sqrt.f64 (neg.f64 (pow.f64 x -2))))) (hypot.f64 (*.f64 1/12 x) (sqrt.f64 (neg.f64 (pow.f64 x -2)))))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (/.f64 1 (fma.f64 1/12 x (/.f64 1 x))) -1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (fma.f64 1/12 x (/.f64 1 x)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (fma.f64 1/12 x (/.f64 1 x)) 3) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (cbrt.f64 (fma.f64 1/12 x (/.f64 1 x))) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (sqrt.f64 (fma.f64 1/12 x (/.f64 1 x))) 2)))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f64 (pow.f64 (fma.f64 1/12 x (/.f64 1 x)) 2))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (exp.f64 (fma.f64 1/12 x (/.f64 1 x))))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (+.f64 1 (expm1.f64 (fma.f64 1/12 x (/.f64 1 x)))))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (*.f64 (pow.f64 (exp.f64 1/12) x) (exp.f64 (/.f64 1 x))))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (*.f64 (+.f64 1 (expm1.f64 (*.f64 1/12 x))) (exp.f64 (/.f64 1 x))))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (*.f64 (pow.f64 (exp.f64 1/12) x) (+.f64 1 (expm1.f64 (/.f64 1 x)))))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (*.f64 (+.f64 1 (expm1.f64 (*.f64 1/12 x))) (+.f64 1 (expm1.f64 (/.f64 1 x)))))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (*.f64 (exp.f64 (/.f64 1 x)) (pow.f64 (exp.f64 1/12) x)))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (*.f64 (+.f64 1 (expm1.f64 (/.f64 1 x))) (pow.f64 (exp.f64 1/12) x)))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (*.f64 (exp.f64 (/.f64 1 x)) (+.f64 1 (expm1.f64 (*.f64 1/12 x)))))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (*.f64 (+.f64 1 (expm1.f64 (/.f64 1 x))) (+.f64 1 (expm1.f64 (*.f64 1/12 x)))))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (pow.f64 (fma.f64 1/12 x (/.f64 1 x)) 3))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (/.f64 (pow.f64 (-.f64 (*.f64 (*.f64 x x) 1/144) (pow.f64 x -2)) 3) (pow.f64 (fma.f64 1/12 x (/.f64 -1 x)) 3)))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (fma.f64 1/12 x (/.f64 1 x))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (log.f64 (fma.f64 1/12 x (/.f64 1 x))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (neg.f64 (log.f64 (fma.f64 1/12 x (/.f64 1 x)))) -1))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (log.f64 (fma.f64 1/12 x (/.f64 1 x))) 1))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (fma.f64 1/12 x (/.f64 1 x))))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 1/12 x (/.f64 1 x))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 x 1/12 (/.f64 1 x))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (*.f64 1/12 x) 1 (/.f64 1 x))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 1 (*.f64 1/12 x) (/.f64 1 x))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 1 (/.f64 1 x) (*.f64 1/12 x))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (/.f64 1 x) 1 (*.f64 1/12 x))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (*.f64 (*.f64 x x) 1/144) (/.f64 1 (fma.f64 1/12 x (/.f64 -1 x))) (*.f64 (neg.f64 (pow.f64 x -2)) (/.f64 1 (fma.f64 1/12 x (/.f64 -1 x)))))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (cbrt.f64 (pow.f64 x -2)) (/.f64 1 (cbrt.f64 x)) (*.f64 1/12 x))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (/.f64 1 (cbrt.f64 x)) (cbrt.f64 (pow.f64 x -2)) (*.f64 1/12 x))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (pow.f64 (cbrt.f64 x) 2) (*.f64 (cbrt.f64 x) 1/12) (/.f64 1 x))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (cbrt.f64 (*.f64 1/12 x)) (pow.f64 (cbrt.f64 (*.f64 1/12 x)) 2) (/.f64 1 x))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (pow.f64 (cbrt.f64 (*.f64 1/12 x)) 2) (cbrt.f64 (*.f64 1/12 x)) (/.f64 1 x))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (pow.f64 x -1/2) (pow.f64 x -1/2) (*.f64 1/12 x))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (sqrt.f64 x) (sqrt.f64 (*.f64 x 1/144)) (/.f64 1 x))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (sqrt.f64 x) (*.f64 (sqrt.f64 x) 1/12) (/.f64 1 x))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (sqrt.f64 (*.f64 1/12 x)) (sqrt.f64 (*.f64 1/12 x)) (/.f64 1 x))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 -1 (/.f64 -1 x) (*.f64 1/12 x))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (/.f64 1 (fma.f64 1/12 x (/.f64 -1 x))) (*.f64 (*.f64 x x) 1/144) (*.f64 (/.f64 1 (fma.f64 1/12 x (/.f64 -1 x))) (neg.f64 (pow.f64 x -2))))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (sqrt.f64 (cbrt.f64 (*.f64 1/20736 (pow.f64 x 4)))) (sqrt.f64 (pow.f64 (cbrt.f64 (*.f64 1/12 x)) 2)) (/.f64 1 x))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (sqrt.f64 (cbrt.f64 (pow.f64 x -4))) (sqrt.f64 (cbrt.f64 (pow.f64 x -2))) (*.f64 1/12 x))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (pow.f64 (pow.f64 (cbrt.f64 x) 2) -1) (pow.f64 (cbrt.f64 x) -1) (*.f64 1/12 x))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (pow.f64 (sqrt.f64 x) -1) (pow.f64 (sqrt.f64 x) -1) (*.f64 1/12 x))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (*.f64 1/12 (pow.f64 (cbrt.f64 x) 2)) (cbrt.f64 x) (/.f64 1 x))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (*.f64 1/12 (sqrt.f64 x)) (sqrt.f64 x) (/.f64 1 x))))))

simplify62.0ms (1.5%)

Algorithm

1×	egg-herbie

Rules

796×	`distribute-neg-frac_binary64`
735×	`fma-def_binary64`
673×	`associate-l_binary64`
592×	`associate-/r*_binary64`
450×	`associate-r_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	45	354
1	117	354
2	280	354
3	741	354
4	1997	354
5	7410	354

Stop Event

1×	node limit

Counts

194 → 177

Calls

Call 1

Inputs
x
(+.f64 (*.f64 -1/12 (pow.f64 x 3)) x)
(+.f64 (.f64 1/144 (pow.f64 x 5)) (+.f64 (.f64 -1/12 (pow.f64 x 3)) x))
(+.f64 (.f64 1/144 (pow.f64 x 5)) (+.f64 (.f64 -1/12 (pow.f64 x 3)) (+.f64 (*.f64 -1/1728 (pow.f64 x 7)) x)))
(/.f64 12 x)
(-.f64 (.f64 12 (/.f64 1 x)) (.f64 144 (/.f64 1 (pow.f64 x 3))))
(-.f64 (+.f64 (.f64 1728 (/.f64 1 (pow.f64 x 5))) (.f64 12 (/.f64 1 x))) (*.f64 144 (/.f64 1 (pow.f64 x 3))))
(-.f64 (+.f64 (.f64 1728 (/.f64 1 (pow.f64 x 5))) (.f64 12 (/.f64 1 x))) (+.f64 (.f64 144 (/.f64 1 (pow.f64 x 3))) (.f64 20736 (/.f64 1 (pow.f64 x 7)))))
(/.f64 12 x)
(-.f64 (.f64 12 (/.f64 1 x)) (.f64 144 (/.f64 1 (pow.f64 x 3))))
(-.f64 (+.f64 (.f64 1728 (/.f64 1 (pow.f64 x 5))) (.f64 12 (/.f64 1 x))) (*.f64 144 (/.f64 1 (pow.f64 x 3))))
(-.f64 (+.f64 (.f64 1728 (/.f64 1 (pow.f64 x 5))) (.f64 12 (/.f64 1 x))) (+.f64 (.f64 144 (/.f64 1 (pow.f64 x 3))) (.f64 20736 (/.f64 1 (pow.f64 x 7)))))
(*.f64 1/144 (pow.f64 x 2))
(*.f64 1/144 (pow.f64 x 2))
(*.f64 1/144 (pow.f64 x 2))
(*.f64 1/144 (pow.f64 x 2))
(*.f64 1/144 (pow.f64 x 2))
(*.f64 1/144 (pow.f64 x 2))
(*.f64 1/144 (pow.f64 x 2))
(*.f64 1/144 (pow.f64 x 2))
(*.f64 1/144 (pow.f64 x 2))
(*.f64 1/144 (pow.f64 x 2))
(*.f64 1/144 (pow.f64 x 2))
(*.f64 1/144 (pow.f64 x 2))
(/.f64 1 x)
(+.f64 (*.f64 1/12 x) (/.f64 1 x))
(+.f64 (*.f64 1/12 x) (/.f64 1 x))
(+.f64 (*.f64 1/12 x) (/.f64 1 x))
(*.f64 1/12 x)
(+.f64 (/.f64 1 x) (*.f64 1/12 x))
(+.f64 (/.f64 1 x) (*.f64 1/12 x))
(+.f64 (/.f64 1 x) (*.f64 1/12 x))
(*.f64 1/12 x)
(+.f64 (/.f64 1 x) (*.f64 1/12 x))
(+.f64 (/.f64 1 x) (*.f64 1/12 x))
(+.f64 (/.f64 1 x) (*.f64 1/12 x))

Outputs
x
(+.f64 (*.f64 -1/12 (pow.f64 x 3)) x)
(fma.f64 -1/12 (pow.f64 x 3) x)
(+.f64 (.f64 1/144 (pow.f64 x 5)) (+.f64 (.f64 -1/12 (pow.f64 x 3)) x))
(fma.f64 1/144 (pow.f64 x 5) (fma.f64 -1/12 (pow.f64 x 3) x))
(fma.f64 -1/12 (pow.f64 x 3) (fma.f64 1/144 (pow.f64 x 5) x))
(+.f64 (.f64 1/144 (pow.f64 x 5)) (+.f64 (.f64 -1/12 (pow.f64 x 3)) (+.f64 (*.f64 -1/1728 (pow.f64 x 7)) x)))
(fma.f64 1/144 (pow.f64 x 5) (fma.f64 -1/12 (pow.f64 x 3) (fma.f64 -1/1728 (pow.f64 x 7) x)))
(fma.f64 -1/12 (pow.f64 x 3) (fma.f64 -1/1728 (pow.f64 x 7) (fma.f64 1/144 (pow.f64 x 5) x)))
(/.f64 12 x)
(-.f64 (.f64 12 (/.f64 1 x)) (.f64 144 (/.f64 1 (pow.f64 x 3))))
(-.f64 (/.f64 12 x) (/.f64 144 (pow.f64 x 3)))
(+.f64 (/.f64 12 x) (/.f64 -144 (pow.f64 x 3)))
(-.f64 (+.f64 (.f64 1728 (/.f64 1 (pow.f64 x 5))) (.f64 12 (/.f64 1 x))) (*.f64 144 (/.f64 1 (pow.f64 x 3))))
(+.f64 (/.f64 1728 (pow.f64 x 5)) (-.f64 (/.f64 12 x) (/.f64 144 (pow.f64 x 3))))
(+.f64 (/.f64 12 x) (-.f64 (/.f64 1728 (pow.f64 x 5)) (/.f64 144 (pow.f64 x 3))))
(+.f64 (/.f64 12 x) (+.f64 (/.f64 1728 (pow.f64 x 5)) (/.f64 -144 (pow.f64 x 3))))
(-.f64 (+.f64 (.f64 1728 (/.f64 1 (pow.f64 x 5))) (.f64 12 (/.f64 1 x))) (+.f64 (.f64 144 (/.f64 1 (pow.f64 x 3))) (.f64 20736 (/.f64 1 (pow.f64 x 7)))))
(-.f64 (+.f64 (/.f64 12 x) (/.f64 1728 (pow.f64 x 5))) (+.f64 (/.f64 144 (pow.f64 x 3)) (/.f64 20736 (pow.f64 x 7))))
(+.f64 (+.f64 (/.f64 12 x) (/.f64 1728 (pow.f64 x 5))) (-.f64 (/.f64 -20736 (pow.f64 x 7)) (/.f64 144 (pow.f64 x 3))))
(+.f64 (/.f64 12 x) (+.f64 (/.f64 -20736 (pow.f64 x 7)) (-.f64 (/.f64 1728 (pow.f64 x 5)) (/.f64 144 (pow.f64 x 3)))))
(+.f64 (/.f64 1728 (pow.f64 x 5)) (+.f64 (/.f64 12 x) (+.f64 (/.f64 -144 (pow.f64 x 3)) (/.f64 -20736 (pow.f64 x 7)))))
(+.f64 (/.f64 12 x) (+.f64 (/.f64 -20736 (pow.f64 x 7)) (+.f64 (/.f64 1728 (pow.f64 x 5)) (/.f64 -144 (pow.f64 x 3)))))
(/.f64 12 x)
(-.f64 (.f64 12 (/.f64 1 x)) (.f64 144 (/.f64 1 (pow.f64 x 3))))
(-.f64 (/.f64 12 x) (/.f64 144 (pow.f64 x 3)))
(+.f64 (/.f64 12 x) (/.f64 -144 (pow.f64 x 3)))
(-.f64 (+.f64 (.f64 1728 (/.f64 1 (pow.f64 x 5))) (.f64 12 (/.f64 1 x))) (*.f64 144 (/.f64 1 (pow.f64 x 3))))
(+.f64 (/.f64 1728 (pow.f64 x 5)) (-.f64 (/.f64 12 x) (/.f64 144 (pow.f64 x 3))))
(+.f64 (/.f64 12 x) (-.f64 (/.f64 1728 (pow.f64 x 5)) (/.f64 144 (pow.f64 x 3))))
(+.f64 (/.f64 12 x) (+.f64 (/.f64 1728 (pow.f64 x 5)) (/.f64 -144 (pow.f64 x 3))))
(-.f64 (+.f64 (.f64 1728 (/.f64 1 (pow.f64 x 5))) (.f64 12 (/.f64 1 x))) (+.f64 (.f64 144 (/.f64 1 (pow.f64 x 3))) (.f64 20736 (/.f64 1 (pow.f64 x 7)))))
(-.f64 (+.f64 (/.f64 12 x) (/.f64 1728 (pow.f64 x 5))) (+.f64 (/.f64 144 (pow.f64 x 3)) (/.f64 20736 (pow.f64 x 7))))
(+.f64 (+.f64 (/.f64 12 x) (/.f64 1728 (pow.f64 x 5))) (-.f64 (/.f64 -20736 (pow.f64 x 7)) (/.f64 144 (pow.f64 x 3))))
(+.f64 (/.f64 12 x) (+.f64 (/.f64 -20736 (pow.f64 x 7)) (-.f64 (/.f64 1728 (pow.f64 x 5)) (/.f64 144 (pow.f64 x 3)))))
(+.f64 (/.f64 1728 (pow.f64 x 5)) (+.f64 (/.f64 12 x) (+.f64 (/.f64 -144 (pow.f64 x 3)) (/.f64 -20736 (pow.f64 x 7)))))
(+.f64 (/.f64 12 x) (+.f64 (/.f64 -20736 (pow.f64 x 7)) (+.f64 (/.f64 1728 (pow.f64 x 5)) (/.f64 -144 (pow.f64 x 3)))))
(*.f64 1/144 (pow.f64 x 2))
(.f64 1/144 (.f64 x x))
(.f64 x (.f64 x 1/144))
(*.f64 1/144 (pow.f64 x 2))
(.f64 1/144 (.f64 x x))
(.f64 x (.f64 x 1/144))
(*.f64 1/144 (pow.f64 x 2))
(.f64 1/144 (.f64 x x))
(.f64 x (.f64 x 1/144))
(*.f64 1/144 (pow.f64 x 2))
(.f64 1/144 (.f64 x x))
(.f64 x (.f64 x 1/144))
(*.f64 1/144 (pow.f64 x 2))
(.f64 1/144 (.f64 x x))
(.f64 x (.f64 x 1/144))
(*.f64 1/144 (pow.f64 x 2))
(.f64 1/144 (.f64 x x))
(.f64 x (.f64 x 1/144))
(*.f64 1/144 (pow.f64 x 2))
(.f64 1/144 (.f64 x x))
(.f64 x (.f64 x 1/144))
(*.f64 1/144 (pow.f64 x 2))
(.f64 1/144 (.f64 x x))
(.f64 x (.f64 x 1/144))
(*.f64 1/144 (pow.f64 x 2))
(.f64 1/144 (.f64 x x))
(.f64 x (.f64 x 1/144))
(*.f64 1/144 (pow.f64 x 2))
(.f64 1/144 (.f64 x x))
(.f64 x (.f64 x 1/144))
(*.f64 1/144 (pow.f64 x 2))
(.f64 1/144 (.f64 x x))
(.f64 x (.f64 x 1/144))
(*.f64 1/144 (pow.f64 x 2))
(.f64 1/144 (.f64 x x))
(.f64 x (.f64 x 1/144))
(/.f64 1 x)
(+.f64 (*.f64 1/12 x) (/.f64 1 x))
(fma.f64 1/12 x (/.f64 1 x))
(fma.f64 x 1/12 (/.f64 1 x))
(+.f64 (*.f64 1/12 x) (/.f64 1 x))
(fma.f64 1/12 x (/.f64 1 x))
(fma.f64 x 1/12 (/.f64 1 x))
(+.f64 (*.f64 1/12 x) (/.f64 1 x))
(fma.f64 1/12 x (/.f64 1 x))
(fma.f64 x 1/12 (/.f64 1 x))
(*.f64 1/12 x)
(*.f64 x 1/12)
(+.f64 (/.f64 1 x) (*.f64 1/12 x))
(fma.f64 1/12 x (/.f64 1 x))
(fma.f64 x 1/12 (/.f64 1 x))
(+.f64 (/.f64 1 x) (*.f64 1/12 x))
(fma.f64 1/12 x (/.f64 1 x))
(fma.f64 x 1/12 (/.f64 1 x))
(+.f64 (/.f64 1 x) (*.f64 1/12 x))
(fma.f64 1/12 x (/.f64 1 x))
(fma.f64 x 1/12 (/.f64 1 x))
(*.f64 1/12 x)
(*.f64 x 1/12)
(+.f64 (/.f64 1 x) (*.f64 1/12 x))
(fma.f64 1/12 x (/.f64 1 x))
(fma.f64 x 1/12 (/.f64 1 x))
(+.f64 (/.f64 1 x) (*.f64 1/12 x))
(fma.f64 1/12 x (/.f64 1 x))
(fma.f64 x 1/12 (/.f64 1 x))
(+.f64 (/.f64 1 x) (*.f64 1/12 x))
(fma.f64 1/12 x (/.f64 1 x))
(fma.f64 x 1/12 (/.f64 1 x))

localize5.0ms (0.1%)

Compiler: Compiled 11 to 8 computations (27.3% saved)

eval97.0ms (2.4%)

Compiler: Compiled 4555 to 3505 computations (23.1% saved)

prune29.0ms (0.7%)

Pruning

10 alts after pruning (0 fresh and 10 done)

	Pruned	Kept	Total
New	214	0	214
Fresh	0	0	0
Picked	0	1	1
Done	0	9	9
Total	214	10	224

Error

0.2b

Counts

224 → 10

Alt Table

Click to see full alt table

Status	Error	Program
✓	38.6b	(/.f64 (exp.f64 x) (-.f64 (exp.f64 x) 1))
✓	24.4b	(+.f64 1/2 (+.f64 (.f64 -1/720 (pow.f64 x 3)) (+.f64 (.f64 1/12 x) (/.f64 1 x))))
✓	44.0b	(+.f64 1/2 (/.f64 1 (/.f64 (-.f64 (.f64 1/12 x) (/.f64 1 x)) (-.f64 (.f64 (*.f64 x x) 1/144) (pow.f64 x -2)))))
✓	24.3b	(+.f64 1 (/.f64 1 x))
✓	0.5b	(/.f64 (exp.f64 x) (expm1.f64 x))
✓	1.8b	(/.f64 (exp.f64 x) x)
✓	24.1b	(+.f64 (/.f64 1 x) 1/2)
✓	62.0b	(+.f64 1/2 (*.f64 x 1/12))
✓	24.0b	(+.f64 1/2 (+.f64 (*.f64 1/12 x) (/.f64 1 x)))
✓	24.0b	(/.f64 1 x)

Compiler

Compiled 89 to 68 computations (23.6% saved)

regimes18.0ms (0.4%)

Counts

10 → 1

Calls

Call 1

Inputs
(/.f64 1 x)
(+.f64 1 (/.f64 1 x))
(+.f64 1/2 (*.f64 x 1/12))
(+.f64 (/.f64 1 x) 1/2)
(+.f64 1/2 (+.f64 (*.f64 1/12 x) (/.f64 1 x)))
(/.f64 (exp.f64 x) x)
(+.f64 1/2 (+.f64 (.f64 -1/720 (pow.f64 x 3)) (+.f64 (.f64 1/12 x) (/.f64 1 x))))
(+.f64 1/2 (/.f64 1 (/.f64 (-.f64 (.f64 1/12 x) (/.f64 1 x)) (-.f64 (.f64 (*.f64 x x) 1/144) (pow.f64 x -2)))))
(/.f64 (exp.f64 x) (expm1.f64 x))
(/.f64 (exp.f64 x) (-.f64 (exp.f64 x) 1))

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

Calls

3 calls:

10.0ms	x
3.0ms	(/.f64 (exp.f64 x) (-.f64 (exp.f64 x) 1))
2.0ms	(exp.f64 x)

Results

Error	Segments	Branch
0.5b	1	`x`
0.5b	1	`(/.f64 (exp.f64 x) (-.f64 (exp.f64 x) 1))`
0.5b	1	`(exp.f64 x)`

Compiler

Compiled 93 to 65 computations (30.1% saved)

regimes8.0ms (0.2%)

Counts

8 → 1

Calls

Call 1

Inputs
(/.f64 1 x)
(+.f64 1 (/.f64 1 x))
(+.f64 1/2 (*.f64 x 1/12))
(+.f64 (/.f64 1 x) 1/2)
(+.f64 1/2 (+.f64 (*.f64 1/12 x) (/.f64 1 x)))
(/.f64 (exp.f64 x) x)
(+.f64 1/2 (+.f64 (.f64 -1/720 (pow.f64 x 3)) (+.f64 (.f64 1/12 x) (/.f64 1 x))))
(+.f64 1/2 (/.f64 1 (/.f64 (-.f64 (.f64 1/12 x) (/.f64 1 x)) (-.f64 (.f64 (*.f64 x x) 1/144) (pow.f64 x -2)))))

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

Calls

1 calls:

5.0ms

Results

Error	Segments	Branch
1.8b	1	`x`

Compiler

Compiled 70 to 53 computations (24.3% saved)

regimes6.0ms (0.1%)

Accuracy

Total -38.0b remaining (-158.8%)

Threshold costs -38.0b (-158.8%)

Counts

5 → 1

Calls

Call 1

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

Outputs
(/.f64 1 x)

Calls

1 calls:

4.0ms

Results

Error	Segments	Branch
24.0b	1	`x`

Compiler

Compiled 30 to 23 computations (23.3% saved)

simplify3.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

1×	`1-exp_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	8	18
1	10	18

Stop Event

1×	done
1×	saturated

Calls

Call 1

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

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

Compiler

Compiled 15 to 10 computations (33.3% saved)

soundness8.0ms (0.2%)

Algorithm

1×	egg-herbie

Rules

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

Iterations

Useful iterations: 0 (0.0ms)

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

Stop Event

1×

saturated

Compiler

Compiled 14 to 9 computations (35.7% saved)

end19.0ms (0.5%)

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

Details

analyze438.0ms (10.6%)

sample2.1s (50.6%)

preprocess19.0ms (0.5%)

simplify7.0ms (0.2%)

eval1.0ms (0%)

prune1.0ms (0%)

localize6.0ms (0.1%)

series2.0ms (0.1%)

rewrite44.0ms (1.1%)

simplify180.0ms (4.4%)

localize7.0ms (0.2%)

series2.0ms (0.1%)

rewrite53.0ms (1.3%)

simplify113.0ms (2.8%)

eval21.0ms (0.5%)

prune23.0ms (0.6%)

localize4.0ms (0.1%)

series2.0ms (0%)

rewrite44.0ms (1.1%)

simplify120.0ms (2.9%)

localize3.0ms (0.1%)

localize5.0ms (0.1%)

localize11.0ms (0.3%)

series3.0ms (0.1%)

rewrite56.0ms (1.4%)

simplify9.0ms (0.2%)

localize25.0ms (0.6%)

series3.0ms (0.1%)

rewrite74.0ms (1.8%)

simplify170.0ms (4.1%)

eval102.0ms (2.5%)

prune34.0ms (0.8%)

localize5.0ms (0.1%)

series1.0ms (0%)

rewrite43.0ms (1%)

simplify8.0ms (0.2%)

localize36.0ms (0.9%)

series6.0ms (0.2%)

rewrite98.0ms (2.4%)

simplify62.0ms (1.5%)

localize5.0ms (0.1%)

eval97.0ms (2.4%)

prune29.0ms (0.7%)

regimes18.0ms (0.4%)

regimes8.0ms (0.2%)

regimes6.0ms (0.1%)

simplify3.0ms (0.1%)

soundness8.0ms (0.2%)

end19.0ms (0.5%)

Profiling