Details

analyze0.0ms (0%)

Algorithm

1×

Search

True	Other	False	Iter
0%	100%	0%	0
0%	100%	0%	1
100%	0%	0%	2

Compiler

Compiled 10 to 8 computations (20% saved)

sample786.0ms (27.3%)

Results

775.0ms

8256×

body

256

valid

preprocess88.0ms (3%)

Algorithm

2×	egg-herbie

Rules

702×	`fma-def_binary64`
434×	`unswap-sqr_binary64`
345×	`fma-neg_binary64`
290×	`exp-prod_binary64`
264×	`*-commutative_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	8	13
1	15	13
2	21	13
3	28	13
4	47	13
5	87	13
6	184	13
7	434	13
8	1195	13
9	3176	13
10	4367	13
11	5548	13
12	7298	13
0	1	1

Stop Event

1×	saturated
1×	node limit

Calls

Call 1

Inputs
0

Outputs
0

Call 2

Inputs
(/.f64 2 (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x))))

Outputs
(/.f64 2 (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x))))

Compiler

Compiled 10 to 8 computations (20% saved)

simplify87.0ms (3%)

Algorithm

1×	egg-herbie

Rules

702×	`fma-def_binary64`
434×	`unswap-sqr_binary64`
345×	`fma-neg_binary64`
290×	`exp-prod_binary64`
264×	`*-commutative_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	8	13
1	15	13
2	21	13
3	28	13
4	47	13
5	87	13
6	184	13
7	434	13
8	1195	13
9	3176	13
10	4367	13
11	5548	13
12	7298	13

Stop Event

1×	node limit

Counts

1 → 1

Calls

Call 1

Inputs
(/.f64 2 (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x))))

Outputs
(/.f64 2 (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x))))

eval0.0ms (0%)

Compiler: Compiled 9 to 7 computations (22.2% saved)

prune1.0ms (0%)

Pruning

2 alts after pruning (2 fresh and 0 done)

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

Error

0.0b

Counts

2 → 1

Alt Table

Click to see full alt table

Status	Error	Program
▶	0.0b	(/.f64 2 (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x))))

Compiler

Compiled 9 to 7 computations (22.2% saved)

localize8.0ms (0.3%)

Local error

Found 1 expressions with local error:

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

Compiler

Compiled 24 to 8 computations (66.7% saved)

series3.0ms (0.1%)

Counts

1 → 12

Calls

3 calls:

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

rewrite35.0ms (1.2%)

Algorithm

1×	egg-rewrite-iter-limit
1×	batch-egg-rewrite

Rules

91×	`add-sqr-sqrt_binary64`
87×	`add-log-exp_binary64`
85×	`*-un-lft-identity_binary64`
85×	`add-exp-log_binary64`
85×	`pow1_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	8	9
1	176	9
2	2839	9
0	8	9

Stop Event

1×	iter limit
1×	unsound

Counts

1 → 10

Calls

Call 1

Inputs
(/.f64 2 (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x))))

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

Outputs

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

simplify95.0ms (3.3%)

Algorithm

1×	egg-herbie

Rules

722×	`fma-def_binary64`
402×	`associate-/l/_binary64`
370×	`*-commutative_binary64`
326×	`distribute-lft-out_binary64`
302×	`associate-/r/_binary64`

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	31	156
1	66	154
2	132	152
3	357	150
4	1279	150
5	3194	150
6	4371	150
7	7154	150

Stop Event

1×	node limit

Counts

22 → 19

Calls

Call 1

Inputs
1
(+.f64 1 (*.f64 -1/2 (pow.f64 x 2)))
(+.f64 1 (+.f64 (.f64 -1/2 (pow.f64 x 2)) (.f64 5/24 (pow.f64 x 4))))
(+.f64 1 (+.f64 (.f64 -1/2 (pow.f64 x 2)) (+.f64 (.f64 -61/720 (pow.f64 x 6)) (*.f64 5/24 (pow.f64 x 4)))))
(/.f64 2 (+.f64 (exp.f64 (neg.f64 x)) (exp.f64 x)))
(/.f64 2 (+.f64 (exp.f64 (neg.f64 x)) (exp.f64 x)))
(/.f64 2 (+.f64 (exp.f64 (neg.f64 x)) (exp.f64 x)))
(/.f64 2 (+.f64 (exp.f64 (neg.f64 x)) (exp.f64 x)))
(/.f64 2 (+.f64 (exp.f64 x) (exp.f64 (*.f64 -1 x))))
(/.f64 2 (+.f64 (exp.f64 x) (exp.f64 (*.f64 -1 x))))
(/.f64 2 (+.f64 (exp.f64 x) (exp.f64 (*.f64 -1 x))))
(/.f64 2 (+.f64 (exp.f64 x) (exp.f64 (*.f64 -1 x))))

Outputs
1
(+.f64 1 (*.f64 -1/2 (pow.f64 x 2)))
(+.f64 1 (.f64 -1/2 (.f64 x x)))
(fma.f64 -1/2 (*.f64 x x) 1)
(+.f64 1 (+.f64 (.f64 -1/2 (pow.f64 x 2)) (.f64 5/24 (pow.f64 x 4))))
(+.f64 1 (fma.f64 -1/2 (.f64 x x) (.f64 5/24 (pow.f64 x 4))))
(fma.f64 -1/2 (*.f64 x x) (fma.f64 5/24 (pow.f64 x 4) 1))
(+.f64 1 (+.f64 (.f64 -1/2 (pow.f64 x 2)) (+.f64 (.f64 -61/720 (pow.f64 x 6)) (*.f64 5/24 (pow.f64 x 4)))))
(+.f64 1 (fma.f64 -1/2 (.f64 x x) (fma.f64 -61/720 (pow.f64 x 6) (.f64 5/24 (pow.f64 x 4)))))
(+.f64 1 (fma.f64 -1/2 (.f64 x x) (fma.f64 5/24 (pow.f64 x 4) (.f64 -61/720 (pow.f64 x 6)))))
(+.f64 (fma.f64 -1/2 (.f64 x x) 1) (fma.f64 -61/720 (pow.f64 x 6) (.f64 5/24 (pow.f64 x 4))))
(fma.f64 -61/720 (pow.f64 x 6) (fma.f64 -1/2 (*.f64 x x) (fma.f64 5/24 (pow.f64 x 4) 1)))
(fma.f64 (.f64 x x) (fma.f64 (.f64 x x) 5/24 -1/2) (fma.f64 -61/720 (pow.f64 x 6) 1))
(fma.f64 -1/2 (*.f64 x x) (fma.f64 5/24 (pow.f64 x 4) (fma.f64 -61/720 (pow.f64 x 6) 1)))
(/.f64 2 (+.f64 (exp.f64 (neg.f64 x)) (exp.f64 x)))
(/.f64 2 (+.f64 (exp.f64 (neg.f64 x)) (exp.f64 x)))
(/.f64 2 (+.f64 (exp.f64 (neg.f64 x)) (exp.f64 x)))
(/.f64 2 (+.f64 (exp.f64 (neg.f64 x)) (exp.f64 x)))
(/.f64 2 (+.f64 (exp.f64 x) (exp.f64 (*.f64 -1 x))))
(/.f64 2 (+.f64 (exp.f64 (neg.f64 x)) (exp.f64 x)))
(/.f64 2 (+.f64 (exp.f64 x) (exp.f64 (*.f64 -1 x))))
(/.f64 2 (+.f64 (exp.f64 (neg.f64 x)) (exp.f64 x)))
(/.f64 2 (+.f64 (exp.f64 x) (exp.f64 (*.f64 -1 x))))
(/.f64 2 (+.f64 (exp.f64 (neg.f64 x)) (exp.f64 x)))
(/.f64 2 (+.f64 (exp.f64 x) (exp.f64 (*.f64 -1 x))))
(/.f64 2 (+.f64 (exp.f64 (neg.f64 x)) (exp.f64 x)))

eval5.0ms (0.2%)

Compiler: Compiled 206 to 155 computations (24.8% saved)

prune5.0ms (0.2%)

Pruning

5 alts after pruning (5 fresh and 0 done)

	Pruned	Kept	Total
New	14	5	19
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	15	5	20

Error

Counts

20 → 5

Alt Table

Click to see full alt table

Status	Error	Program
▶	33.9b	(+.f64 1 (+.f64 (.f64 -1/2 (pow.f64 x 2)) (.f64 5/24 (pow.f64 x 4))))
▶	33.8b	(fma.f64 -1/2 (*.f64 x x) 1)
	33.3b	1
▶	0.0b	(.f64 2 (/.f64 1 (.f64 2 (cosh.f64 x))))
▶	33.9b	(+.f64 1 (+.f64 (.f64 -1/2 (pow.f64 x 2)) (+.f64 (.f64 -61/720 (pow.f64 x 6)) (*.f64 5/24 (pow.f64 x 4)))))

Compiler

Compiled 52 to 44 computations (15.4% saved)

localize9.0ms (0.3%)

Local error

Found 1 expressions with local error:

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

Compiler

Compiled 24 to 16 computations (33.3% saved)

series4.0ms (0.1%)

Counts

1 → 12

Calls

3 calls:

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

rewrite51.0ms (1.8%)

Algorithm

1×	batch-egg-rewrite

Rules

618×	`pow1_binary64`
573×	`add-log-exp_binary64`
572×	`log1p-expm1-u_binary64`
572×	`expm1-log1p-u_binary64`
561×	`add-exp-log_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	7	6
1	145	6
2	1667	6

Stop Event

1×	node limit

Counts

1 → 24

Calls

Call 1

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

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

Outputs

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

simplify86.0ms (3%)

Algorithm

1×	egg-herbie

Rules

713×	`fma-def_binary64`
389×	`*-commutative_binary64`
372×	`associate-/l/_binary64`
326×	`distribute-lft-out_binary64`
315×	`associate-/r/_binary64`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	24	156
1	51	154
2	109	150
3	316	150
4	1190	150
5	3026	150
6	3792	150
7	4723	150
8	7687	150

Stop Event

1×	node limit

Counts

36 → 33

Calls

Call 1

Inputs
1/2
(+.f64 1/2 (*.f64 -1/4 (pow.f64 x 2)))
(+.f64 1/2 (+.f64 (.f64 -1/4 (pow.f64 x 2)) (.f64 5/48 (pow.f64 x 4))))
(+.f64 (.f64 -61/1440 (pow.f64 x 6)) (+.f64 1/2 (+.f64 (.f64 -1/4 (pow.f64 x 2)) (*.f64 5/48 (pow.f64 x 4)))))
(/.f64 1 (+.f64 (/.f64 1 (exp.f64 x)) (exp.f64 x)))
(/.f64 1 (+.f64 (/.f64 1 (exp.f64 x)) (exp.f64 x)))
(/.f64 1 (+.f64 (/.f64 1 (exp.f64 x)) (exp.f64 x)))
(/.f64 1 (+.f64 (/.f64 1 (exp.f64 x)) (exp.f64 x)))
(/.f64 1 (+.f64 (/.f64 1 (exp.f64 x)) (exp.f64 x)))
(/.f64 1 (+.f64 (/.f64 1 (exp.f64 x)) (exp.f64 x)))
(/.f64 1 (+.f64 (/.f64 1 (exp.f64 x)) (exp.f64 x)))
(/.f64 1 (+.f64 (/.f64 1 (exp.f64 x)) (exp.f64 x)))

Outputs
1/2
(+.f64 1/2 (*.f64 -1/4 (pow.f64 x 2)))
(+.f64 1/2 (.f64 -1/4 (.f64 x x)))
(fma.f64 -1/4 (*.f64 x x) 1/2)
(fma.f64 x (*.f64 -1/4 x) 1/2)
(+.f64 1/2 (+.f64 (.f64 -1/4 (pow.f64 x 2)) (.f64 5/48 (pow.f64 x 4))))
(+.f64 1/2 (fma.f64 -1/4 (.f64 x x) (.f64 5/48 (pow.f64 x 4))))
(fma.f64 -1/4 (*.f64 x x) (fma.f64 5/48 (pow.f64 x 4) 1/2))
(fma.f64 x (fma.f64 5/48 (pow.f64 x 3) (*.f64 -1/4 x)) 1/2)
(+.f64 (.f64 -61/1440 (pow.f64 x 6)) (+.f64 1/2 (+.f64 (.f64 -1/4 (pow.f64 x 2)) (*.f64 5/48 (pow.f64 x 4)))))
(fma.f64 -61/1440 (pow.f64 x 6) (+.f64 1/2 (fma.f64 -1/4 (.f64 x x) (.f64 5/48 (pow.f64 x 4)))))
(+.f64 (fma.f64 -1/4 (.f64 x x) (.f64 5/48 (pow.f64 x 4))) (fma.f64 -61/1440 (pow.f64 x 6) 1/2))
(fma.f64 -61/1440 (pow.f64 x 6) (fma.f64 -1/4 (*.f64 x x) (fma.f64 5/48 (pow.f64 x 4) 1/2)))
(fma.f64 -1/4 (*.f64 x x) (fma.f64 -61/1440 (pow.f64 x 6) (fma.f64 5/48 (pow.f64 x 4) 1/2)))
(fma.f64 -61/1440 (pow.f64 x 6) (fma.f64 x (fma.f64 5/48 (pow.f64 x 3) (*.f64 -1/4 x)) 1/2))
(fma.f64 x (fma.f64 5/48 (pow.f64 x 3) (*.f64 -1/4 x)) (fma.f64 -61/1440 (pow.f64 x 6) 1/2))
(/.f64 1 (+.f64 (/.f64 1 (exp.f64 x)) (exp.f64 x)))
(/.f64 1 (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x))))
(/.f64 1 (+.f64 (/.f64 1 (exp.f64 x)) (exp.f64 x)))
(/.f64 1 (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x))))
(/.f64 1 (+.f64 (/.f64 1 (exp.f64 x)) (exp.f64 x)))
(/.f64 1 (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x))))
(/.f64 1 (+.f64 (/.f64 1 (exp.f64 x)) (exp.f64 x)))
(/.f64 1 (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x))))
(/.f64 1 (+.f64 (/.f64 1 (exp.f64 x)) (exp.f64 x)))
(/.f64 1 (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x))))
(/.f64 1 (+.f64 (/.f64 1 (exp.f64 x)) (exp.f64 x)))
(/.f64 1 (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x))))
(/.f64 1 (+.f64 (/.f64 1 (exp.f64 x)) (exp.f64 x)))
(/.f64 1 (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x))))
(/.f64 1 (+.f64 (/.f64 1 (exp.f64 x)) (exp.f64 x)))
(/.f64 1 (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x))))

localize18.0ms (0.6%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.0b	(*.f64 -1/2 (pow.f64 x 2))
✓	0.1b	(*.f64 5/24 (pow.f64 x 4))
✓	14.2b	(+.f64 (.f64 -1/2 (pow.f64 x 2)) (.f64 5/24 (pow.f64 x 4)))

Compiler

Compiled 47 to 38 computations (19.1% saved)

series4.0ms (0.1%)

Counts

3 → 3

Calls

9 calls:

Time	Variable		Point	Expression
1.0ms	x	@	inf	(+.f64 (.f64 -1/2 (pow.f64 x 2)) (.f64 5/24 (pow.f64 x 4)))
1.0ms	x	@	0	(+.f64 (.f64 -1/2 (pow.f64 x 2)) (.f64 5/24 (pow.f64 x 4)))
0.0ms	x	@	inf	(*.f64 5/24 (pow.f64 x 4))
0.0ms	x	@	inf	(*.f64 -1/2 (pow.f64 x 2))
0.0ms	x	@	-inf	(+.f64 (.f64 -1/2 (pow.f64 x 2)) (.f64 5/24 (pow.f64 x 4)))

rewrite72.0ms (2.5%)

Algorithm

1×	batch-egg-rewrite

Rules

446×	`log-prod_binary64`
335×	`exp-prod_binary64`
304×	`fma-def_binary64`
298×	`prod-exp_binary64`
270×	`pow-prod-down_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	11	28
1	239	28
2	2732	28

Stop Event

1×	node limit

Counts

3 → 117

Calls

Call 1

Inputs
(+.f64 (.f64 -1/2 (pow.f64 x 2)) (.f64 5/24 (pow.f64 x 4)))
(*.f64 5/24 (pow.f64 x 4))
(*.f64 -1/2 (pow.f64 x 2))

Outputs

((#(struct:change #<rule egg-rr> (2) ((x -.f64 (exp.f64 (log1p.f64 (fma.f64 5/24 (pow.f64 x 4) (*.f64 -1/2 (*.f64 x x))))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (/.f64 (*.f64 (pow.f64 x 4) 1/4) (fma.f64 -1/2 (*.f64 x x) (*.f64 -5/24 (pow.f64 x 4)))) (/.f64 (*.f64 (pow.f64 x 8) 25/576) (fma.f64 -1/2 (*.f64 x x) (*.f64 -5/24 (pow.f64 x 4)))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (fma.f64 5/24 (pow.f64 x 4) (*.f64 -1/2 (*.f64 x x))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 1 (fma.f64 5/24 (pow.f64 x 4) (*.f64 -1/2 (*.f64 x x))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 (fma.f64 5/24 (pow.f64 x 4) (*.f64 -1/2 (*.f64 x x)))) (pow.f64 (cbrt.f64 (fma.f64 5/24 (pow.f64 x 4) (*.f64 -1/2 (*.f64 x x)))) 2))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (cbrt.f64 (fma.f64 5/24 (pow.f64 x 4) (*.f64 -1/2 (*.f64 x x)))) 2) (cbrt.f64 (fma.f64 5/24 (pow.f64 x 4) (*.f64 -1/2 (*.f64 x x)))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (sqrt.f64 (fma.f64 5/24 (pow.f64 x 4) (*.f64 -1/2 (*.f64 x x)))) (sqrt.f64 (fma.f64 5/24 (pow.f64 x 4) (*.f64 -1/2 (*.f64 x x)))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (fma.f64 (pow.f64 x 12) 125/13824 (*.f64 (pow.f64 x 6) -1/8)) (/.f64 1 (-.f64 (fma.f64 (pow.f64 x 4) 1/4 (*.f64 (pow.f64 x 8) 25/576)) (*.f64 -1/2 (*.f64 (*.f64 x x) (*.f64 5/24 (pow.f64 x 4)))))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (-.f64 (*.f64 (pow.f64 x 4) 1/4) (*.f64 (pow.f64 x 8) 25/576)) (/.f64 1 (fma.f64 -1/2 (*.f64 x x) (*.f64 -5/24 (pow.f64 x 4)))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 1 (/.f64 (-.f64 (fma.f64 (pow.f64 x 4) 1/4 (*.f64 (pow.f64 x 8) 25/576)) (*.f64 -1/2 (*.f64 (*.f64 x x) (*.f64 5/24 (pow.f64 x 4))))) (fma.f64 (pow.f64 x 12) 125/13824 (*.f64 (pow.f64 x 6) -1/8))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 1 (/.f64 (fma.f64 -1/2 (*.f64 x x) (*.f64 -5/24 (pow.f64 x 4))) (-.f64 (*.f64 (pow.f64 x 4) 1/4) (*.f64 (pow.f64 x 8) 25/576))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (fma.f64 (pow.f64 x 12) 125/13824 (*.f64 (pow.f64 x 6) -1/8)) (-.f64 (fma.f64 (pow.f64 x 4) 1/4 (*.f64 (pow.f64 x 8) 25/576)) (*.f64 -1/2 (*.f64 (*.f64 x x) (*.f64 5/24 (pow.f64 x 4))))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (fma.f64 (pow.f64 x 12) 125/13824 (*.f64 (pow.f64 x 6) -1/8)) (fma.f64 (pow.f64 x 8) 25/576 (-.f64 (*.f64 (pow.f64 x 4) 1/4) (*.f64 -1/2 (*.f64 (*.f64 x x) (*.f64 5/24 (pow.f64 x 4)))))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (-.f64 (*.f64 (pow.f64 x 4) 1/4) (*.f64 (pow.f64 x 8) 25/576)) (fma.f64 -1/2 (*.f64 x x) (*.f64 -5/24 (pow.f64 x 4))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (neg.f64 (fma.f64 (pow.f64 x 12) 125/13824 (*.f64 (pow.f64 x 6) -1/8))) (neg.f64 (-.f64 (fma.f64 (pow.f64 x 4) 1/4 (*.f64 (pow.f64 x 8) 25/576)) (*.f64 -1/2 (*.f64 (*.f64 x x) (*.f64 5/24 (pow.f64 x 4)))))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (neg.f64 (-.f64 (*.f64 (pow.f64 x 4) 1/4) (*.f64 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#<rule egg-rr> (2) ((x pow.f64 (/.f64 (-.f64 (fma.f64 (pow.f64 x 4) 1/4 (*.f64 (pow.f64 x 8) 25/576)) (*.f64 -1/2 (*.f64 (*.f64 x x) (*.f64 5/24 (pow.f64 x 4))))) (fma.f64 (pow.f64 x 12) 125/13824 (*.f64 (pow.f64 x 6) -1/8))) -1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (/.f64 (fma.f64 -1/2 (*.f64 x x) (*.f64 -5/24 (pow.f64 x 4))) (-.f64 (*.f64 (pow.f64 x 4) 1/4) (*.f64 (pow.f64 x 8) 25/576))) -1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (exp.f64 (pow.f64 (cbrt.f64 (log.f64 (fma.f64 5/24 (pow.f64 x 4) (*.f64 -1/2 (*.f64 x x))))) 2)) (cbrt.f64 (log.f64 (fma.f64 5/24 (pow.f64 x 4) (*.f64 -1/2 (*.f64 x x))))))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (exp.f64 (sqrt.f64 (log.f64 (fma.f64 5/24 (pow.f64 x 4) (*.f64 -1/2 (*.f64 x x)))))) (sqrt.f64 (log.f64 (fma.f64 5/24 (pow.f64 x 4) (*.f64 -1/2 (*.f64 x x))))))))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f64 (pow.f64 (fma.f64 5/24 (pow.f64 x 4) (*.f64 -1/2 (*.f64 x x))) 2))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (exp.f64 (fma.f64 5/24 (pow.f64 x 4) (*.f64 -1/2 (*.f64 x x)))))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (+.f64 1 (expm1.f64 (fma.f64 5/24 (pow.f64 x 4) (*.f64 -1/2 (*.f64 x x))))))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (*.f64 (+.f64 1 (expm1.f64 (*.f64 -1/2 (*.f64 x x)))) (pow.f64 (exp.f64 5/24) (pow.f64 x 4))))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (*.f64 (pow.f64 (exp.f64 x) (*.f64 x -1/2)) (+.f64 1 (expm1.f64 (*.f64 5/24 (pow.f64 x 4))))))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (*.f64 (+.f64 1 (expm1.f64 (*.f64 -1/2 (*.f64 x x)))) (+.f64 1 (expm1.f64 (*.f64 5/24 (pow.f64 x 4))))))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (*.f64 (+.f64 1 (expm1.f64 (*.f64 5/24 (pow.f64 x 4)))) (pow.f64 (exp.f64 x) (*.f64 x -1/2))))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (*.f64 (pow.f64 (exp.f64 5/24) (pow.f64 x 4)) (+.f64 1 (expm1.f64 (*.f64 -1/2 (*.f64 x x))))))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 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(*.f64 x x)))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (cbrt.f64 (*.f64 (pow.f64 x 8) 25/576)) (cbrt.f64 (*.f64 5/24 (pow.f64 x 4))) (*.f64 -1/2 (*.f64 x x)))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (*.f64 x (sqrt.f64 -1/2)) (*.f64 x (sqrt.f64 -1/2)) (*.f64 5/24 (pow.f64 x 4)))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (*.f64 (*.f64 x x) (sqrt.f64 5/24)) (*.f64 (*.f64 x x) (sqrt.f64 5/24)) (*.f64 -1/2 (*.f64 x x)))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (*.f64 -1/2 x) x (*.f64 5/24 (pow.f64 x 4)))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (*.f64 -1/2 (*.f64 (cbrt.f64 x) x)) (pow.f64 (cbrt.f64 x) 2) (*.f64 5/24 (pow.f64 x 4)))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (*.f64 5/24 (*.f64 x x)) (*.f64 x x) (*.f64 -1/2 (*.f64 x x)))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (*.f64 5/24 (pow.f64 (cbrt.f64 x) 8)) (*.f64 (cbrt.f64 x) x) (*.f64 -1/2 (*.f64 x x)))))))

((#(struct:change #<rule egg-rr> (2) ((x +.f64 0 (*.f64 5/24 (pow.f64 x 4)))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (log.f64 (pow.f64 (cbrt.f64 (pow.f64 (exp.f64 5/24) (pow.f64 x 4))) 2)) (log.f64 (cbrt.f64 (pow.f64 (exp.f64 5/24) (pow.f64 x 4)))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (log.f64 (sqrt.f64 (pow.f64 (exp.f64 5/24) (pow.f64 x 4)))) (log.f64 (sqrt.f64 (pow.f64 (exp.f64 5/24) (pow.f64 x 4)))))))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (exp.f64 (log1p.f64 (*.f64 5/24 (pow.f64 x 4)))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (*.f64 5/24 (pow.f64 x 4)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (*.f64 (pow.f64 x 8) 25/576) 1/2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (cbrt.f64 (*.f64 5/24 (pow.f64 x 4))) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (*.f64 (*.f64 x x) (sqrt.f64 5/24)) 2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (*.f64 (pow.f64 x 12) 125/13824) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (exp.f64 1) (log.f64 (*.f64 5/24 (pow.f64 x 4))))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (exp.f64 (pow.f64 (cbrt.f64 (log.f64 (*.f64 5/24 (pow.f64 x 4)))) 2)) (cbrt.f64 (log.f64 (*.f64 5/24 (pow.f64 x 4)))))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (exp.f64 (sqrt.f64 (log.f64 (*.f64 5/24 (pow.f64 x 4))))) (sqrt.f64 (log.f64 (*.f64 5/24 (pow.f64 x 4)))))))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f64 (*.f64 (pow.f64 x 8) 25/576))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (pow.f64 (exp.f64 5/24) (pow.f64 x 4)))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (+.f64 1 (expm1.f64 (*.f64 5/24 (pow.f64 x 4)))))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (*.f64 (pow.f64 x 12) 125/13824))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (*.f64 5/24 (pow.f64 x 4))))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (*.f64 5/24 (pow.f64 x 4))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (log.f64 (*.f64 5/24 (pow.f64 x 4))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (log.f64 (*.f64 5/24 (pow.f64 x 4))) 1))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (log.f64 (cbrt.f64 (*.f64 5/24 (pow.f64 x 4)))) 3))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (log.f64 (*.f64 (*.f64 x x) (sqrt.f64 5/24))) 2))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (log.f64 (*.f64 (pow.f64 x 12) 125/13824)) 1/3))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (*.f64 (log.f64 (*.f64 5/24 (pow.f64 x 4))) 1) 1))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (*.f64 (log.f64 (*.f64 5/24 (pow.f64 x 4))) 3) 1/3))))))

((#(struct:change #<rule egg-rr> (2) ((x +.f64 0 (*.f64 -1/2 (*.f64 x x)))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (log.f64 (pow.f64 (cbrt.f64 (pow.f64 (exp.f64 x) (*.f64 x -1/2))) 2)) (log.f64 (cbrt.f64 (pow.f64 (exp.f64 x) (*.f64 x -1/2)))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (log.f64 (sqrt.f64 (pow.f64 (exp.f64 x) (*.f64 x -1/2)))) (log.f64 (sqrt.f64 (pow.f64 (exp.f64 x) (*.f64 x -1/2)))))))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (exp.f64 (log1p.f64 (*.f64 -1/2 (*.f64 x x)))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (*.f64 -1/2 (*.f64 x x)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (*.f64 (pow.f64 x 4) 1/4) 1/2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (cbrt.f64 (*.f64 -1/2 (*.f64 x x))) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (*.f64 x (sqrt.f64 -1/2)) 2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (*.f64 (pow.f64 x 6) -1/8) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (exp.f64 1) (log.f64 (*.f64 -1/2 (*.f64 x x))))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (exp.f64 (pow.f64 (cbrt.f64 (log.f64 (*.f64 -1/2 (*.f64 x x)))) 2)) (cbrt.f64 (log.f64 (*.f64 -1/2 (*.f64 x x)))))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (exp.f64 (sqrt.f64 (log.f64 (*.f64 -1/2 (*.f64 x x))))) (sqrt.f64 (log.f64 (*.f64 -1/2 (*.f64 x x)))))))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f64 (*.f64 (pow.f64 x 4) 1/4))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (pow.f64 (exp.f64 x) (*.f64 x -1/2)))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (+.f64 1 (expm1.f64 (*.f64 -1/2 (*.f64 x x)))))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (*.f64 (pow.f64 x 6) -1/8))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (*.f64 -1/2 (*.f64 x x))))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (*.f64 -1/2 (*.f64 x x))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (log.f64 (*.f64 -1/2 (*.f64 x x))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (log.f64 (*.f64 -1/2 (*.f64 x x))) 1))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (log.f64 (cbrt.f64 (*.f64 -1/2 (*.f64 x x)))) 3))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (log.f64 (*.f64 x (sqrt.f64 -1/2))) 2))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (log.f64 (*.f64 (pow.f64 x 6) -1/8)) 1/3))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (*.f64 (log.f64 (*.f64 -1/2 (*.f64 x x))) 1) 1))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (*.f64 (log.f64 (*.f64 -1/2 (*.f64 x x))) 3) 1/3))))))

simplify188.0ms (6.5%)

Algorithm

1×	egg-herbie

Rules

1319×	`sqr-pow_binary64`
659×	`pow-sqr_binary64`
493×	`cube-prod_binary64`
406×	`fabs-mul_binary64`
386×	`associate-l_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	10	21
1	19	21
2	39	21
3	90	21
4	294	21
5	1173	21
6	1917	21
7	2041	21
8	2210	21
9	2409	21
10	2680	21
11	3037	21
12	3491	21
13	4022	21
14	4652	21
15	5403	21
16	5713	21
17	5939	21
18	6137	21
19	6195	21
20	6217	21
21	7051	21
22	7964	21

Stop Event

1×	node limit

Counts

120 → 120

Calls

Call 1

Inputs
(*.f64 -1/2 (pow.f64 x 2))
(*.f64 5/24 (pow.f64 x 4))
(*.f64 5/24 (pow.f64 x 4))

Outputs
(*.f64 -1/2 (pow.f64 x 2))
(.f64 -1/2 (.f64 x x))
(*.f64 5/24 (pow.f64 x 4))
(*.f64 5/24 (pow.f64 x 4))

localize34.0ms (1.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.0b	(*.f64 -1/2 (pow.f64 x 2))
✓	0.1b	(*.f64 -61/720 (pow.f64 x 6))
	0.1b	(*.f64 5/24 (pow.f64 x 4))
✓	26.3b	(+.f64 (.f64 -61/720 (pow.f64 x 6)) (.f64 5/24 (pow.f64 x 4)))

Compiler

Compiled 80 to 65 computations (18.8% saved)

series3.0ms (0.1%)

Counts

2 → 3

Calls

6 calls:

Time	Variable		Point	Expression
1.0ms	x	@	inf	(+.f64 (.f64 -61/720 (pow.f64 x 6)) (.f64 5/24 (pow.f64 x 4)))
1.0ms	x	@	0	(+.f64 (.f64 -61/720 (pow.f64 x 6)) (.f64 5/24 (pow.f64 x 4)))
0.0ms	x	@	inf	(*.f64 -61/720 (pow.f64 x 6))
0.0ms	x	@	0	(*.f64 -61/720 (pow.f64 x 6))
0.0ms	x	@	-inf	(+.f64 (.f64 -61/720 (pow.f64 x 6)) (.f64 5/24 (pow.f64 x 4)))

rewrite75.0ms (2.6%)

Algorithm

1×	batch-egg-rewrite

Rules

454×	`log-prod_binary64`
346×	`exp-prod_binary64`
312×	`prod-exp_binary64`
299×	`fma-def_binary64`
274×	`pow2_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	11	21
1	244	21
2	2884	21

Stop Event

1×	node limit

Counts

2 → 92

Calls

Call 1

Inputs
(+.f64 (.f64 -61/720 (pow.f64 x 6)) (.f64 5/24 (pow.f64 x 4)))
(*.f64 -61/720 (pow.f64 x 6))

Outputs

((#(struct:change #<rule egg-rr> (2) ((x -.f64 (exp.f64 (log1p.f64 (fma.f64 -61/720 (pow.f64 x 6) (*.f64 5/24 (pow.f64 x 4))))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (/.f64 (*.f64 (pow.f64 x 12) 3721/518400) (fma.f64 -61/720 (pow.f64 x 6) (*.f64 -5/24 (pow.f64 x 4)))) (/.f64 (*.f64 (pow.f64 x 8) 25/576) (fma.f64 -61/720 (pow.f64 x 6) (*.f64 -5/24 (pow.f64 x 4)))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (fma.f64 -61/720 (pow.f64 x 6) (*.f64 5/24 (pow.f64 x 4))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 1 (fma.f64 -61/720 (pow.f64 x 6) (*.f64 5/24 (pow.f64 x 4))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 (fma.f64 -61/720 (pow.f64 x 6) (*.f64 5/24 (pow.f64 x 4)))) (pow.f64 (cbrt.f64 (fma.f64 -61/720 (pow.f64 x 6) (*.f64 5/24 (pow.f64 x 4)))) 2))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (cbrt.f64 (fma.f64 -61/720 (pow.f64 x 6) (*.f64 5/24 (pow.f64 x 4)))) 2) (cbrt.f64 (fma.f64 -61/720 (pow.f64 x 6) (*.f64 5/24 (pow.f64 x 4)))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (sqrt.f64 (fma.f64 -61/720 (pow.f64 x 6) (*.f64 5/24 (pow.f64 x 4)))) (sqrt.f64 (fma.f64 -61/720 (pow.f64 x 6) (*.f64 5/24 (pow.f64 x 4)))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (fma.f64 (pow.f64 x 12) 125/13824 (*.f64 (pow.f64 x 18) -226981/373248000)) (/.f64 1 (-.f64 (fma.f64 (pow.f64 x 12) 3721/518400 (*.f64 (pow.f64 x 8) 25/576)) (*.f64 -61/720 (*.f64 (pow.f64 x 6) (*.f64 5/24 (pow.f64 x 4)))))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (-.f64 (*.f64 (pow.f64 x 12) 3721/518400) (*.f64 (pow.f64 x 8) 25/576)) (/.f64 1 (fma.f64 -61/720 (pow.f64 x 6) (*.f64 -5/24 (pow.f64 x 4)))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 1 (/.f64 (-.f64 (fma.f64 (pow.f64 x 12) 3721/518400 (*.f64 (pow.f64 x 8) 25/576)) (*.f64 -61/720 (*.f64 (pow.f64 x 6) (*.f64 5/24 (pow.f64 x 4))))) (fma.f64 (pow.f64 x 12) 125/13824 (*.f64 (pow.f64 x 18) -226981/373248000))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 1 (/.f64 (fma.f64 -61/720 (pow.f64 x 6) (*.f64 -5/24 (pow.f64 x 4))) (-.f64 (*.f64 (pow.f64 x 12) 3721/518400) (*.f64 (pow.f64 x 8) 25/576))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (fma.f64 (pow.f64 x 12) 125/13824 (*.f64 (pow.f64 x 18) -226981/373248000)) (-.f64 (fma.f64 (pow.f64 x 12) 3721/518400 (*.f64 (pow.f64 x 8) 25/576)) (*.f64 -61/720 (*.f64 (pow.f64 x 6) (*.f64 5/24 (pow.f64 x 4))))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (fma.f64 (pow.f64 x 12) 125/13824 (*.f64 (pow.f64 x 18) -226981/373248000)) (fma.f64 (pow.f64 x 8) 25/576 (-.f64 (*.f64 (pow.f64 x 12) 3721/518400) (*.f64 -61/720 (*.f64 (pow.f64 x 6) (*.f64 5/24 (pow.f64 x 4)))))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (-.f64 (*.f64 (pow.f64 x 12) 3721/518400) (*.f64 (pow.f64 x 8) 25/576)) (fma.f64 -61/720 (pow.f64 x 6) (*.f64 -5/24 (pow.f64 x 4))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (neg.f64 (fma.f64 (pow.f64 x 12) 125/13824 (*.f64 (pow.f64 x 18) -226981/373248000))) (neg.f64 (-.f64 (fma.f64 (pow.f64 x 12) 3721/518400 (*.f64 (pow.f64 x 8) 25/576)) (*.f64 -61/720 (*.f64 (pow.f64 x 6) (*.f64 5/24 (pow.f64 x 4)))))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (neg.f64 (-.f64 (*.f64 (pow.f64 x 12) 3721/518400) (*.f64 (pow.f64 x 8) 25/576))) (neg.f64 (fma.f64 -61/720 (pow.f64 x 6) (*.f64 -5/24 (pow.f64 x 4)))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (-.f64 (*.f64 (pow.f64 x 8) 25/576) (*.f64 (pow.f64 x 12) 3721/518400)) (-.f64 (*.f64 5/24 (pow.f64 x 4)) (*.f64 -61/720 (pow.f64 x 6))))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (fma.f64 -61/720 (pow.f64 x 6) (*.f64 5/24 (pow.f64 x 4))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (fma.f64 -61/720 (pow.f64 x 6) (*.f64 5/24 (pow.f64 x 4))) 2) 1/2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (fma.f64 -61/720 (pow.f64 x 6) (*.f64 5/24 (pow.f64 x 4))) 3) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (cbrt.f64 (fma.f64 -61/720 (pow.f64 x 6) (*.f64 5/24 (pow.f64 x 4)))) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (sqrt.f64 (fma.f64 -61/720 (pow.f64 x 6) (*.f64 5/24 (pow.f64 x 4)))) 2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (exp.f64 1) (log.f64 (fma.f64 -61/720 (pow.f64 x 6) (*.f64 5/24 (pow.f64 x 4)))))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (/.f64 (-.f64 (fma.f64 (pow.f64 x 12) 3721/518400 (*.f64 (pow.f64 x 8) 25/576)) (*.f64 -61/720 (*.f64 (pow.f64 x 6) (*.f64 5/24 (pow.f64 x 4))))) (fma.f64 (pow.f64 x 12) 125/13824 (*.f64 (pow.f64 x 18) -226981/373248000))) -1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (/.f64 (fma.f64 -61/720 (pow.f64 x 6) (*.f64 -5/24 (pow.f64 x 4))) (-.f64 (*.f64 (pow.f64 x 12) 3721/518400) (*.f64 (pow.f64 x 8) 25/576))) -1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (exp.f64 (pow.f64 (cbrt.f64 (log.f64 (fma.f64 -61/720 (pow.f64 x 6) (*.f64 5/24 (pow.f64 x 4))))) 2)) (cbrt.f64 (log.f64 (fma.f64 -61/720 (pow.f64 x 6) (*.f64 5/24 (pow.f64 x 4))))))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (exp.f64 (sqrt.f64 (log.f64 (fma.f64 -61/720 (pow.f64 x 6) (*.f64 5/24 (pow.f64 x 4)))))) (sqrt.f64 (log.f64 (fma.f64 -61/720 (pow.f64 x 6) (*.f64 5/24 (pow.f64 x 4))))))))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f64 (pow.f64 (fma.f64 -61/720 (pow.f64 x 6) (*.f64 5/24 (pow.f64 x 4))) 2))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (exp.f64 (fma.f64 -61/720 (pow.f64 x 6) (*.f64 5/24 (pow.f64 x 4)))))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (+.f64 1 (expm1.f64 (fma.f64 -61/720 (pow.f64 x 6) (*.f64 5/24 (pow.f64 x 4))))))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (*.f64 (+.f64 1 (expm1.f64 (*.f64 -61/720 (pow.f64 x 6)))) (pow.f64 (exp.f64 5/24) (pow.f64 x 4))))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (*.f64 (pow.f64 (exp.f64 -61/720) (pow.f64 x 6)) (+.f64 1 (expm1.f64 (*.f64 5/24 (pow.f64 x 4))))))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (*.f64 (+.f64 1 (expm1.f64 (*.f64 -61/720 (pow.f64 x 6)))) (+.f64 1 (expm1.f64 (*.f64 5/24 (pow.f64 x 4))))))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (*.f64 (+.f64 1 (expm1.f64 (*.f64 5/24 (pow.f64 x 4)))) (pow.f64 (exp.f64 -61/720) (pow.f64 x 6))))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (*.f64 (pow.f64 (exp.f64 5/24) (pow.f64 x 4)) (+.f64 1 (expm1.f64 (*.f64 -61/720 (pow.f64 x 6))))))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (*.f64 (+.f64 1 (expm1.f64 (*.f64 5/24 (pow.f64 x 4)))) (+.f64 1 (expm1.f64 (*.f64 -61/720 (pow.f64 x 6))))))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (pow.f64 (fma.f64 -61/720 (pow.f64 x 6) (*.f64 5/24 (pow.f64 x 4))) 3))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (fma.f64 -61/720 (pow.f64 x 6) (*.f64 5/24 (pow.f64 x 4)))))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (fma.f64 -61/720 (pow.f64 x 6) (*.f64 5/24 (pow.f64 x 4)))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (log.f64 (fma.f64 -61/720 (pow.f64 x 6) (*.f64 5/24 (pow.f64 x 4)))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (log.f64 (fma.f64 -61/720 (pow.f64 x 6) (*.f64 5/24 (pow.f64 x 4)))) 1))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (*.f64 3 (log.f64 (fma.f64 -61/720 (pow.f64 x 6) (*.f64 5/24 (pow.f64 x 4))))) 1/3))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (log.f64 (cbrt.f64 (fma.f64 -61/720 (pow.f64 x 6) (*.f64 5/24 (pow.f64 x 4))))) 3))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (log.f64 (sqrt.f64 (fma.f64 -61/720 (pow.f64 x 6) (*.f64 5/24 (pow.f64 x 4))))) 2))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (*.f64 (log.f64 (fma.f64 -61/720 (pow.f64 x 6) (*.f64 5/24 (pow.f64 x 4)))) 1) 1))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 -61/720 (pow.f64 x 6) (*.f64 5/24 (pow.f64 x 4)))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (pow.f64 x 6) -61/720 (*.f64 5/24 (pow.f64 x 4)))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (*.f64 -61/720 (pow.f64 x 6)) 1 (*.f64 5/24 (pow.f64 x 4)))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 5/24 (pow.f64 x 4) (*.f64 -61/720 (pow.f64 x 6)))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (pow.f64 x 4) 5/24 (*.f64 -61/720 (pow.f64 x 6)))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (pow.f64 x 4) (*.f64 (*.f64 x x) -61/720) (*.f64 5/24 (pow.f64 x 4)))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (*.f64 5/24 (pow.f64 x 4)) 1 (*.f64 -61/720 (pow.f64 x 6)))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 1 (*.f64 -61/720 (pow.f64 x 6)) (*.f64 5/24 (pow.f64 x 4)))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 1 (*.f64 5/24 (pow.f64 x 4)) (*.f64 -61/720 (pow.f64 x 6)))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (*.f64 x x) (*.f64 (*.f64 x x) 5/24) (*.f64 -61/720 (pow.f64 x 6)))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (pow.f64 x 3) (*.f64 (pow.f64 x 3) -61/720) (*.f64 5/24 (pow.f64 x 4)))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (cbrt.f64 (pow.f64 x 8)) (*.f64 (*.f64 (cbrt.f64 x) x) 5/24) (*.f64 -61/720 (pow.f64 x 6)))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (*.f64 (*.f64 x x) (cbrt.f64 -61/720)) (cbrt.f64 (*.f64 (pow.f64 x 12) 3721/518400)) (*.f64 5/24 (pow.f64 x 4)))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (cbrt.f64 (*.f64 (pow.f64 x 12) 3721/518400)) (*.f64 (*.f64 x x) (cbrt.f64 -61/720)) (*.f64 5/24 (pow.f64 x 4)))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (cbrt.f64 (*.f64 5/24 (pow.f64 x 4))) (cbrt.f64 (*.f64 (pow.f64 x 8) 25/576)) (*.f64 -61/720 (pow.f64 x 6)))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (cbrt.f64 (*.f64 (pow.f64 x 8) 25/576)) (cbrt.f64 (*.f64 5/24 (pow.f64 x 4))) (*.f64 -61/720 (pow.f64 x 6)))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (*.f64 (pow.f64 x 3) (sqrt.f64 -61/720)) (*.f64 (pow.f64 x 3) (sqrt.f64 -61/720)) (*.f64 5/24 (pow.f64 x 4)))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (*.f64 (*.f64 x x) (sqrt.f64 5/24)) (*.f64 (*.f64 x x) (sqrt.f64 5/24)) (*.f64 -61/720 (pow.f64 x 6)))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (*.f64 -61/720 (pow.f64 x 4)) (*.f64 x x) (*.f64 5/24 (pow.f64 x 4)))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (*.f64 -61/720 (pow.f64 x 3)) (pow.f64 x 3) (*.f64 5/24 (pow.f64 x 4)))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (*.f64 5/24 (cbrt.f64 (pow.f64 x 8))) (*.f64 (cbrt.f64 x) x) (*.f64 -61/720 (pow.f64 x 6)))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (*.f64 5/24 (*.f64 x x)) (*.f64 x x) (*.f64 -61/720 (pow.f64 x 6)))))))

((#(struct:change #<rule egg-rr> (2) ((x +.f64 0 (*.f64 -61/720 (pow.f64 x 6)))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (log.f64 (pow.f64 (cbrt.f64 (pow.f64 (exp.f64 -61/720) (pow.f64 x 6))) 2)) (log.f64 (cbrt.f64 (pow.f64 (exp.f64 -61/720) (pow.f64 x 6)))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (log.f64 (sqrt.f64 (pow.f64 (exp.f64 -61/720) (pow.f64 x 6)))) (log.f64 (sqrt.f64 (pow.f64 (exp.f64 -61/720) (pow.f64 x 6)))))))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (exp.f64 (log1p.f64 (*.f64 -61/720 (pow.f64 x 6)))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (*.f64 -61/720 (pow.f64 x 6)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (*.f64 (pow.f64 x 12) 3721/518400) 1/2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (*.f64 (*.f64 x x) (cbrt.f64 -61/720)) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (*.f64 (pow.f64 x 3) (sqrt.f64 -61/720)) 2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (*.f64 (pow.f64 x 18) -226981/373248000) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (exp.f64 1) (fma.f64 6 (log.f64 x) (log1p.f64 -781/720)))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (exp.f64 (pow.f64 (cbrt.f64 (fma.f64 6 (log.f64 x) (log1p.f64 -781/720))) 2)) (cbrt.f64 (fma.f64 6 (log.f64 x) (log1p.f64 -781/720))))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (exp.f64 (sqrt.f64 (fma.f64 6 (log.f64 x) (log1p.f64 -781/720)))) (sqrt.f64 (fma.f64 6 (log.f64 x) (log1p.f64 -781/720))))))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f64 (*.f64 (pow.f64 x 12) 3721/518400))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (pow.f64 (exp.f64 -61/720) (pow.f64 x 6)))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (+.f64 1 (expm1.f64 (*.f64 -61/720 (pow.f64 x 6)))))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (*.f64 (pow.f64 x 18) -226981/373248000))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (*.f64 -61/720 (pow.f64 x 6))))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (*.f64 -61/720 (pow.f64 x 6))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (fma.f64 6 (log.f64 x) (log1p.f64 -781/720)))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (fma.f64 6 (log.f64 x) (log1p.f64 -781/720)) 1))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (log.f64 (*.f64 (*.f64 x x) (cbrt.f64 -61/720))) 3))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (log.f64 (*.f64 (pow.f64 x 3) (sqrt.f64 -61/720))) 2))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (log.f64 (*.f64 (pow.f64 x 18) -226981/373248000)) 1/3))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (*.f64 (fma.f64 6 (log.f64 x) (log1p.f64 -781/720)) 1) 1))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (*.f64 (fma.f64 6 (log.f64 x) (log1p.f64 -781/720)) 3) 1/3))))))

simplify128.0ms (4.5%)

Algorithm

1×	egg-herbie

Rules

811×	`sqr-pow_binary64`
687×	`cube-prod_binary64`
603×	`fabs-mul_binary64`
492×	`associate-l_binary64`
467×	`unswap-sqr_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	10	21
1	20	21
2	42	21
3	106	21
4	350	21
5	1581	21
6	2627	21
7	2784	21
8	3048	21
9	3312	21
10	3658	21
11	4115	21
12	4639	21
13	5280	21
14	6046	21
15	6489	21
16	6993	21
17	7507	21

Stop Event

1×	node limit

Counts

95 → 94

Calls

Call 1

Inputs
(*.f64 5/24 (pow.f64 x 4))
(*.f64 -61/720 (pow.f64 x 6))
(*.f64 -61/720 (pow.f64 x 6))

Outputs
(*.f64 5/24 (pow.f64 x 4))
(*.f64 -61/720 (pow.f64 x 6))
(*.f64 -61/720 (pow.f64 x 6))

localize5.0ms (0.2%)

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

eval167.0ms (5.8%)

Compiler: Compiled 6110 to 4920 computations (19.5% saved)

prune44.0ms (1.5%)

Pruning

5 alts after pruning (4 fresh and 1 done)

	Pruned	Kept	Total
New	294	3	297
Fresh	0	1	1
Picked	1	0	1
Done	2	1	3
Total	297	5	302

Error

Counts

302 → 5

Alt Table

Click to see full alt table

Status	Error	Program
	33.3b	1
▶	33.8b	(+.f64 1 (.f64 -1/2 (.f64 x x)))
▶	33.9b	(+.f64 1 (+.f64 (+.f64 0 (.f64 -1/2 (.f64 x x))) (*.f64 5/24 (pow.f64 x 4))))
✓	0.0b	(.f64 2 (/.f64 1 (.f64 2 (cosh.f64 x))))
▶	0.0b	(*.f64 2 (-.f64 (+.f64 1 (/.f64 1/2 (cosh.f64 x))) 1))

Compiler

Compiled 46 to 39 computations (15.2% saved)

localize13.0ms (0.4%)

Local error

Found 2 expressions with local error:

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

Compiler

Compiled 35 to 25 computations (28.6% saved)

series5.0ms (0.2%)

Counts

2 → 24

Calls

6 calls:

Time	Variable		Point	Expression
2.0ms	x	@	inf	(-.f64 (+.f64 1 (/.f64 1/2 (cosh.f64 x))) 1)
1.0ms	x	@	-inf	(-.f64 (+.f64 1 (/.f64 1/2 (cosh.f64 x))) 1)
0.0ms	x	@	0	(-.f64 (+.f64 1 (/.f64 1/2 (cosh.f64 x))) 1)
0.0ms	x	@	0	(/.f64 1/2 (cosh.f64 x))
0.0ms	x	@	inf	(/.f64 1/2 (cosh.f64 x))

rewrite63.0ms (2.2%)

Algorithm

1×	batch-egg-rewrite

Rules

920×	`pow1_binary64`
866×	`add-log-exp_binary64`
864×	`log1p-expm1-u_binary64`
864×	`expm1-log1p-u_binary64`
97×	`add-sqr-sqrt_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	8	12
1	187	12
2	2591	12

Stop Event

1×	node limit

Counts

2 → 87

Calls

Call 1

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

Outputs

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

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

simplify85.0ms (3%)

Algorithm

1×	egg-herbie

Rules

713×	`fma-def_binary64`
389×	`*-commutative_binary64`
372×	`associate-/l/_binary64`
326×	`distribute-lft-out_binary64`
315×	`associate-/r/_binary64`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	24	312
1	51	308
2	109	300
3	316	300
4	1190	300
5	3026	300
6	3792	300
7	4723	300
8	7687	300

Stop Event

1×	node limit

Counts

111 → 63

Calls

Call 1

Inputs
1/2
(+.f64 1/2 (*.f64 -1/4 (pow.f64 x 2)))
(+.f64 1/2 (+.f64 (.f64 -1/4 (pow.f64 x 2)) (.f64 5/48 (pow.f64 x 4))))
(+.f64 (.f64 -61/1440 (pow.f64 x 6)) (+.f64 1/2 (+.f64 (.f64 -1/4 (pow.f64 x 2)) (*.f64 5/48 (pow.f64 x 4)))))
(/.f64 1 (+.f64 (/.f64 1 (exp.f64 x)) (exp.f64 x)))
(/.f64 1 (+.f64 (/.f64 1 (exp.f64 x)) (exp.f64 x)))
(/.f64 1 (+.f64 (/.f64 1 (exp.f64 x)) (exp.f64 x)))
(/.f64 1 (+.f64 (/.f64 1 (exp.f64 x)) (exp.f64 x)))
(/.f64 1 (+.f64 (/.f64 1 (exp.f64 x)) (exp.f64 x)))
(/.f64 1 (+.f64 (/.f64 1 (exp.f64 x)) (exp.f64 x)))
(/.f64 1 (+.f64 (/.f64 1 (exp.f64 x)) (exp.f64 x)))
(/.f64 1 (+.f64 (/.f64 1 (exp.f64 x)) (exp.f64 x)))
1/2
(+.f64 1/2 (*.f64 -1/4 (pow.f64 x 2)))
(+.f64 1/2 (+.f64 (.f64 -1/4 (pow.f64 x 2)) (.f64 5/48 (pow.f64 x 4))))
(+.f64 (.f64 -61/1440 (pow.f64 x 6)) (+.f64 1/2 (+.f64 (.f64 -1/4 (pow.f64 x 2)) (*.f64 5/48 (pow.f64 x 4)))))
(/.f64 1 (+.f64 (/.f64 1 (exp.f64 x)) (exp.f64 x)))
(/.f64 1 (+.f64 (/.f64 1 (exp.f64 x)) (exp.f64 x)))
(/.f64 1 (+.f64 (/.f64 1 (exp.f64 x)) (exp.f64 x)))
(/.f64 1 (+.f64 (/.f64 1 (exp.f64 x)) (exp.f64 x)))
(/.f64 1 (+.f64 (/.f64 1 (exp.f64 x)) (exp.f64 x)))
(/.f64 1 (+.f64 (/.f64 1 (exp.f64 x)) (exp.f64 x)))
(/.f64 1 (+.f64 (/.f64 1 (exp.f64 x)) (exp.f64 x)))
(/.f64 1 (+.f64 (/.f64 1 (exp.f64 x)) (exp.f64 x)))

Outputs
1/2
(+.f64 1/2 (*.f64 -1/4 (pow.f64 x 2)))
(+.f64 1/2 (.f64 -1/4 (.f64 x x)))
(fma.f64 -1/4 (*.f64 x x) 1/2)
(fma.f64 x (*.f64 -1/4 x) 1/2)
(+.f64 1/2 (+.f64 (.f64 -1/4 (pow.f64 x 2)) (.f64 5/48 (pow.f64 x 4))))
(+.f64 1/2 (fma.f64 -1/4 (.f64 x x) (.f64 5/48 (pow.f64 x 4))))
(fma.f64 -1/4 (*.f64 x x) (fma.f64 5/48 (pow.f64 x 4) 1/2))
(fma.f64 x (fma.f64 5/48 (pow.f64 x 3) (*.f64 -1/4 x)) 1/2)
(+.f64 (.f64 -61/1440 (pow.f64 x 6)) (+.f64 1/2 (+.f64 (.f64 -1/4 (pow.f64 x 2)) (*.f64 5/48 (pow.f64 x 4)))))
(fma.f64 -61/1440 (pow.f64 x 6) (+.f64 1/2 (fma.f64 -1/4 (.f64 x x) (.f64 5/48 (pow.f64 x 4)))))
(+.f64 (fma.f64 -1/4 (.f64 x x) (.f64 5/48 (pow.f64 x 4))) (fma.f64 -61/1440 (pow.f64 x 6) 1/2))
(fma.f64 -61/1440 (pow.f64 x 6) (fma.f64 -1/4 (*.f64 x x) (fma.f64 5/48 (pow.f64 x 4) 1/2)))
(fma.f64 -1/4 (*.f64 x x) (fma.f64 -61/1440 (pow.f64 x 6) (fma.f64 5/48 (pow.f64 x 4) 1/2)))
(fma.f64 -61/1440 (pow.f64 x 6) (fma.f64 x (fma.f64 5/48 (pow.f64 x 3) (*.f64 -1/4 x)) 1/2))
(fma.f64 x (fma.f64 5/48 (pow.f64 x 3) (*.f64 -1/4 x)) (fma.f64 -61/1440 (pow.f64 x 6) 1/2))
(/.f64 1 (+.f64 (/.f64 1 (exp.f64 x)) (exp.f64 x)))
(/.f64 1 (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x))))
(/.f64 1 (+.f64 (/.f64 1 (exp.f64 x)) (exp.f64 x)))
(/.f64 1 (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x))))
(/.f64 1 (+.f64 (/.f64 1 (exp.f64 x)) (exp.f64 x)))
(/.f64 1 (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x))))
(/.f64 1 (+.f64 (/.f64 1 (exp.f64 x)) (exp.f64 x)))
(/.f64 1 (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x))))
(/.f64 1 (+.f64 (/.f64 1 (exp.f64 x)) (exp.f64 x)))
(/.f64 1 (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x))))
(/.f64 1 (+.f64 (/.f64 1 (exp.f64 x)) (exp.f64 x)))
(/.f64 1 (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x))))
(/.f64 1 (+.f64 (/.f64 1 (exp.f64 x)) (exp.f64 x)))
(/.f64 1 (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x))))
(/.f64 1 (+.f64 (/.f64 1 (exp.f64 x)) (exp.f64 x)))
(/.f64 1 (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x))))
1/2
(+.f64 1/2 (*.f64 -1/4 (pow.f64 x 2)))
(+.f64 1/2 (.f64 -1/4 (.f64 x x)))
(fma.f64 -1/4 (*.f64 x x) 1/2)
(fma.f64 x (*.f64 -1/4 x) 1/2)
(+.f64 1/2 (+.f64 (.f64 -1/4 (pow.f64 x 2)) (.f64 5/48 (pow.f64 x 4))))
(+.f64 1/2 (fma.f64 -1/4 (.f64 x x) (.f64 5/48 (pow.f64 x 4))))
(fma.f64 -1/4 (*.f64 x x) (fma.f64 5/48 (pow.f64 x 4) 1/2))
(fma.f64 x (fma.f64 5/48 (pow.f64 x 3) (*.f64 -1/4 x)) 1/2)
(+.f64 (.f64 -61/1440 (pow.f64 x 6)) (+.f64 1/2 (+.f64 (.f64 -1/4 (pow.f64 x 2)) (*.f64 5/48 (pow.f64 x 4)))))
(fma.f64 -61/1440 (pow.f64 x 6) (+.f64 1/2 (fma.f64 -1/4 (.f64 x x) (.f64 5/48 (pow.f64 x 4)))))
(+.f64 (fma.f64 -1/4 (.f64 x x) (.f64 5/48 (pow.f64 x 4))) (fma.f64 -61/1440 (pow.f64 x 6) 1/2))
(fma.f64 -61/1440 (pow.f64 x 6) (fma.f64 -1/4 (*.f64 x x) (fma.f64 5/48 (pow.f64 x 4) 1/2)))
(fma.f64 -1/4 (*.f64 x x) (fma.f64 -61/1440 (pow.f64 x 6) (fma.f64 5/48 (pow.f64 x 4) 1/2)))
(fma.f64 -61/1440 (pow.f64 x 6) (fma.f64 x (fma.f64 5/48 (pow.f64 x 3) (*.f64 -1/4 x)) 1/2))
(fma.f64 x (fma.f64 5/48 (pow.f64 x 3) (*.f64 -1/4 x)) (fma.f64 -61/1440 (pow.f64 x 6) 1/2))
(/.f64 1 (+.f64 (/.f64 1 (exp.f64 x)) (exp.f64 x)))
(/.f64 1 (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x))))
(/.f64 1 (+.f64 (/.f64 1 (exp.f64 x)) (exp.f64 x)))
(/.f64 1 (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x))))
(/.f64 1 (+.f64 (/.f64 1 (exp.f64 x)) (exp.f64 x)))
(/.f64 1 (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x))))
(/.f64 1 (+.f64 (/.f64 1 (exp.f64 x)) (exp.f64 x)))
(/.f64 1 (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x))))
(/.f64 1 (+.f64 (/.f64 1 (exp.f64 x)) (exp.f64 x)))
(/.f64 1 (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x))))
(/.f64 1 (+.f64 (/.f64 1 (exp.f64 x)) (exp.f64 x)))
(/.f64 1 (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x))))
(/.f64 1 (+.f64 (/.f64 1 (exp.f64 x)) (exp.f64 x)))
(/.f64 1 (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x))))
(/.f64 1 (+.f64 (/.f64 1 (exp.f64 x)) (exp.f64 x)))
(/.f64 1 (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x))))

localize6.0ms (0.2%)

Local error

Found 1 expressions with local error:

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

Compiler

Compiled 19 to 10 computations (47.4% saved)

series1.0ms (0%)

Counts

1 → 12

Calls

3 calls:

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

rewrite46.0ms (1.6%)

Algorithm

1×	batch-egg-rewrite

Rules

432×	`pow1_binary64`
420×	`add-sqr-sqrt_binary64`
411×	`*-un-lft-identity_binary64`
401×	`add-log-exp_binary64`
401×	`log1p-expm1-u_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	5	7
1	102	7
2	1148	7

Stop Event

1×	node limit

Counts

1 → 14

Calls

Call 1

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

Outputs

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

simplify178.0ms (6.2%)

Algorithm

1×	egg-herbie

Rules

1082×	`sqr-pow_binary64`
617×	`cube-prod_binary64`
554×	`fabs-mul_binary64`
523×	`pow-sqr_binary64`
441×	`associate-l_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	6	84
1	12	84
2	23	84
3	44	84
4	105	84
5	331	84
6	1250	84
7	2123	84
8	2287	84
9	2471	84
10	2679	84
11	2976	84
12	3371	84
13	3852	84
14	4418	84
15	5102	84
16	5935	84
17	6327	84
18	6619	84
19	6895	84
20	6969	84
21	7003	84
22	7944	84

Stop Event

1×	node limit

Counts

26 → 16

Calls

Call 1

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

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

localize23.0ms (0.8%)

Local error

Found 3 expressions with local error:

New	Error	Program
	0.0b	(.f64 -1/2 (.f64 x x))
	0.1b	(*.f64 5/24 (pow.f64 x 4))
✓	14.2b	(+.f64 (+.f64 0 (.f64 -1/2 (.f64 x x))) (*.f64 5/24 (pow.f64 x 4)))

Compiler

Compiled 58 to 39 computations (32.8% saved)

series1.0ms (0%)

Counts

1 → 12

Calls

3 calls:

Time

Variable

Point

Expression

0.0ms

(+.f64 (+.f64 0 (*.f64 -1/2 (*.f64 x x))) (*.f64 5/24 (pow.f64 x 4)))

0.0ms

inf

(+.f64 (+.f64 0 (*.f64 -1/2 (*.f64 x x))) (*.f64 5/24 (pow.f64 x 4)))

0.0ms

-inf

(+.f64 (+.f64 0 (*.f64 -1/2 (*.f64 x x))) (*.f64 5/24 (pow.f64 x 4)))

rewrite68.0ms (2.4%)

Algorithm

1×	batch-egg-rewrite

Rules

477×	`fma-def_binary64`
456×	`log-prod_binary64`
344×	`exp-prod_binary64`
297×	`pow-prod-down_binary64`
262×	`pow2_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	12	16
1	271	14
2	3130	14

Stop Event

1×	node limit

Counts

1 → 81

Calls

Call 1

Inputs
(+.f64 (+.f64 0 (.f64 -1/2 (.f64 x x))) (*.f64 5/24 (pow.f64 x 4)))

Outputs

((#(struct:change #<rule egg-rr> (2) ((x -.f64 (exp.f64 (log1p.f64 (fma.f64 5/24 (pow.f64 x 4) (*.f64 -1/2 (*.f64 x x))))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (/.f64 (*.f64 (pow.f64 x 4) 1/4) (fma.f64 -1/2 (*.f64 x x) (*.f64 -5/24 (pow.f64 x 4)))) (/.f64 (*.f64 25/576 (pow.f64 x 8)) (fma.f64 -1/2 (*.f64 x x) (*.f64 -5/24 (pow.f64 x 4)))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (fma.f64 5/24 (pow.f64 x 4) (*.f64 -1/2 (*.f64 x x))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 1 (fma.f64 5/24 (pow.f64 x 4) (*.f64 -1/2 (*.f64 x x))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 (fma.f64 5/24 (pow.f64 x 4) (*.f64 -1/2 (*.f64 x x)))) (pow.f64 (cbrt.f64 (fma.f64 5/24 (pow.f64 x 4) (*.f64 -1/2 (*.f64 x x)))) 2))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (cbrt.f64 (fma.f64 5/24 (pow.f64 x 4) (*.f64 -1/2 (*.f64 x x)))) 2) (cbrt.f64 (fma.f64 5/24 (pow.f64 x 4) (*.f64 -1/2 (*.f64 x x)))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (sqrt.f64 (fma.f64 5/24 (pow.f64 x 4) (*.f64 -1/2 (*.f64 x x)))) (sqrt.f64 (fma.f64 5/24 (pow.f64 x 4) (*.f64 -1/2 (*.f64 x x)))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (fma.f64 125/13824 (pow.f64 x 12) (*.f64 (pow.f64 x 6) -1/8)) (/.f64 1 (-.f64 (fma.f64 (pow.f64 x 4) 1/4 (*.f64 25/576 (pow.f64 x 8))) (*.f64 (*.f64 (*.f64 -1/2 (*.f64 x x)) 5/24) (pow.f64 x 4)))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (-.f64 (*.f64 (pow.f64 x 4) 1/4) (*.f64 25/576 (pow.f64 x 8))) (/.f64 1 (fma.f64 -1/2 (*.f64 x x) (*.f64 -5/24 (pow.f64 x 4)))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 1 (/.f64 (-.f64 (fma.f64 (pow.f64 x 4) 1/4 (*.f64 25/576 (pow.f64 x 8))) (*.f64 (*.f64 (*.f64 -1/2 (*.f64 x x)) 5/24) (pow.f64 x 4))) (fma.f64 125/13824 (pow.f64 x 12) (*.f64 (pow.f64 x 6) -1/8))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 1 (/.f64 (fma.f64 -1/2 (*.f64 x x) (*.f64 -5/24 (pow.f64 x 4))) (-.f64 (*.f64 (pow.f64 x 4) 1/4) (*.f64 25/576 (pow.f64 x 8)))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (fma.f64 125/13824 (pow.f64 x 12) (*.f64 (pow.f64 x 6) -1/8)) (-.f64 (fma.f64 (pow.f64 x 4) 1/4 (*.f64 25/576 (pow.f64 x 8))) (*.f64 (*.f64 (*.f64 -1/2 (*.f64 x x)) 5/24) (pow.f64 x 4))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (fma.f64 125/13824 (pow.f64 x 12) (*.f64 (pow.f64 x 6) -1/8)) (fma.f64 25/576 (pow.f64 x 8) (-.f64 (*.f64 (pow.f64 x 4) 1/4) (*.f64 (*.f64 (*.f64 -1/2 (*.f64 x x)) 5/24) (pow.f64 x 4)))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (-.f64 (*.f64 (pow.f64 x 4) 1/4) (*.f64 25/576 (pow.f64 x 8))) (fma.f64 -1/2 (*.f64 x x) (*.f64 -5/24 (pow.f64 x 4))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (neg.f64 (fma.f64 125/13824 (pow.f64 x 12) (*.f64 (pow.f64 x 6) -1/8))) (neg.f64 (-.f64 (fma.f64 (pow.f64 x 4) 1/4 (*.f64 25/576 (pow.f64 x 8))) (*.f64 (*.f64 (*.f64 -1/2 (*.f64 x x)) 5/24) (pow.f64 x 4)))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (neg.f64 (-.f64 (*.f64 (pow.f64 x 4) 1/4) (*.f64 25/576 (pow.f64 x 8)))) (neg.f64 (fma.f64 -1/2 (*.f64 x x) (*.f64 -5/24 (pow.f64 x 4)))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (+.f64 0 (pow.f64 (fma.f64 5/24 (pow.f64 x 4) (*.f64 -1/2 (*.f64 x x))) 3)) (+.f64 0 (-.f64 (pow.f64 (fma.f64 5/24 (pow.f64 x 4) (*.f64 -1/2 (*.f64 x x))) 2) (*.f64 0 (fma.f64 5/24 (pow.f64 x 4) (*.f64 -1/2 (*.f64 x x)))))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (-.f64 0 (pow.f64 (fma.f64 5/24 (pow.f64 x 4) (*.f64 -1/2 (*.f64 x x))) 2)) (-.f64 0 (fma.f64 5/24 (pow.f64 x 4) (*.f64 -1/2 (*.f64 x x)))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (-.f64 (*.f64 25/576 (pow.f64 x 8)) (*.f64 (pow.f64 x 4) 1/4)) (fma.f64 5/24 (pow.f64 x 4) (neg.f64 (*.f64 -1/2 (*.f64 x x)))))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (fma.f64 5/24 (pow.f64 x 4) (*.f64 -1/2 (*.f64 x x))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (fma.f64 5/24 (pow.f64 x 4) (*.f64 -1/2 (*.f64 x x))) 2) 1/2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (fma.f64 5/24 (pow.f64 x 4) (*.f64 -1/2 (*.f64 x x))) 3) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (cbrt.f64 (fma.f64 5/24 (pow.f64 x 4) (*.f64 -1/2 (*.f64 x x)))) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (sqrt.f64 (fma.f64 5/24 (pow.f64 x 4) (*.f64 -1/2 (*.f64 x x)))) 2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (exp.f64 1) (log.f64 (fma.f64 5/24 (pow.f64 x 4) (*.f64 -1/2 (*.f64 x x)))))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (/.f64 (-.f64 (fma.f64 (pow.f64 x 4) 1/4 (*.f64 25/576 (pow.f64 x 8))) (*.f64 (*.f64 (*.f64 -1/2 (*.f64 x x)) 5/24) (pow.f64 x 4))) (fma.f64 125/13824 (pow.f64 x 12) (*.f64 (pow.f64 x 6) -1/8))) -1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (/.f64 (fma.f64 -1/2 (*.f64 x x) (*.f64 -5/24 (pow.f64 x 4))) (-.f64 (*.f64 (pow.f64 x 4) 1/4) (*.f64 25/576 (pow.f64 x 8)))) -1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (exp.f64 (pow.f64 (cbrt.f64 (log.f64 (fma.f64 5/24 (pow.f64 x 4) (*.f64 -1/2 (*.f64 x x))))) 2)) (cbrt.f64 (log.f64 (fma.f64 5/24 (pow.f64 x 4) (*.f64 -1/2 (*.f64 x x))))))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (exp.f64 (sqrt.f64 (log.f64 (fma.f64 5/24 (pow.f64 x 4) (*.f64 -1/2 (*.f64 x x)))))) (sqrt.f64 (log.f64 (fma.f64 5/24 (pow.f64 x 4) (*.f64 -1/2 (*.f64 x x))))))))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f64 (pow.f64 (fma.f64 5/24 (pow.f64 x 4) (*.f64 -1/2 (*.f64 x x))) 2))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (exp.f64 (fma.f64 5/24 (pow.f64 x 4) (*.f64 -1/2 (*.f64 x x)))))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (+.f64 1 (expm1.f64 (fma.f64 5/24 (pow.f64 x 4) (*.f64 -1/2 (*.f64 x x))))))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (*.f64 (+.f64 1 (expm1.f64 (*.f64 -1/2 (*.f64 x x)))) (pow.f64 (exp.f64 5/24) (pow.f64 x 4))))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (*.f64 (pow.f64 (pow.f64 (exp.f64 -1/2) x) x) (+.f64 1 (expm1.f64 (*.f64 5/24 (pow.f64 x 4))))))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (*.f64 (+.f64 1 (expm1.f64 (*.f64 -1/2 (*.f64 x x)))) (+.f64 1 (expm1.f64 (*.f64 5/24 (pow.f64 x 4))))))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (*.f64 (+.f64 1 (expm1.f64 (*.f64 5/24 (pow.f64 x 4)))) (pow.f64 (pow.f64 (exp.f64 -1/2) x) x)))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (*.f64 (pow.f64 (exp.f64 5/24) (pow.f64 x 4)) (+.f64 1 (expm1.f64 (*.f64 -1/2 (*.f64 x x))))))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (*.f64 (+.f64 1 (expm1.f64 (*.f64 5/24 (pow.f64 x 4)))) (+.f64 1 (expm1.f64 (*.f64 -1/2 (*.f64 x x))))))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (pow.f64 (fma.f64 5/24 (pow.f64 x 4) (*.f64 -1/2 (*.f64 x x))) 3))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (fma.f64 5/24 (pow.f64 x 4) (*.f64 -1/2 (*.f64 x x)))))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (fma.f64 5/24 (pow.f64 x 4) (*.f64 -1/2 (*.f64 x x)))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (log.f64 (fma.f64 5/24 (pow.f64 x 4) (*.f64 -1/2 (*.f64 x x)))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (log.f64 (fma.f64 5/24 (pow.f64 x 4) (*.f64 -1/2 (*.f64 x x)))) 1))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (log.f64 (pow.f64 (fma.f64 5/24 (pow.f64 x 4) (*.f64 -1/2 (*.f64 x x))) 3)) 1/3))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (log.f64 (cbrt.f64 (fma.f64 5/24 (pow.f64 x 4) (*.f64 -1/2 (*.f64 x x))))) 3))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (log.f64 (sqrt.f64 (fma.f64 5/24 (pow.f64 x 4) (*.f64 -1/2 (*.f64 x x))))) 2))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (*.f64 (log.f64 (fma.f64 5/24 (pow.f64 x 4) (*.f64 -1/2 (*.f64 x x)))) 1) 1))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 -1/2 (*.f64 x x) (*.f64 5/24 (pow.f64 x 4)))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 x (*.f64 -1/2 x) (*.f64 5/24 (pow.f64 x 4)))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (*.f64 x x) -1/2 (*.f64 5/24 (pow.f64 x 4)))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (*.f64 x x) (*.f64 (*.f64 x x) 5/24) (*.f64 -1/2 (*.f64 x x)))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (*.f64 -1/2 (*.f64 x x)) 1 (*.f64 5/24 (pow.f64 x 4)))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 5/24 (pow.f64 x 4) (*.f64 -1/2 (*.f64 x x)))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (pow.f64 x 4) 5/24 (*.f64 -1/2 (*.f64 x x)))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (*.f64 5/24 (pow.f64 x 4)) 1 (*.f64 -1/2 (*.f64 x x)))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (fma.f64 5/24 (pow.f64 x 4) (*.f64 -1/2 (*.f64 x x))) 1 0)))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 1 (*.f64 -1/2 (*.f64 x x)) (*.f64 5/24 (pow.f64 x 4)))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 1 (*.f64 5/24 (pow.f64 x 4)) (*.f64 -1/2 (*.f64 x x)))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 1 (fma.f64 5/24 (pow.f64 x 4) (*.f64 -1/2 (*.f64 x x))) 0)))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (cbrt.f64 (*.f64 5/24 (pow.f64 x 4))) (cbrt.f64 (*.f64 25/576 (pow.f64 x 8))) (*.f64 -1/2 (*.f64 x x)))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (cbrt.f64 (*.f64 25/576 (pow.f64 x 8))) (cbrt.f64 (*.f64 5/24 (pow.f64 x 4))) (*.f64 -1/2 (*.f64 x x)))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (cbrt.f64 (fma.f64 5/24 (pow.f64 x 4) (*.f64 -1/2 (*.f64 x x)))) (pow.f64 (cbrt.f64 (fma.f64 5/24 (pow.f64 x 4) (*.f64 -1/2 (*.f64 x x)))) 2) 0)))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (pow.f64 (cbrt.f64 (fma.f64 5/24 (pow.f64 x 4) (*.f64 -1/2 (*.f64 x x)))) 2) (cbrt.f64 (fma.f64 5/24 (pow.f64 x 4) (*.f64 -1/2 (*.f64 x x)))) 0)))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (*.f64 (cbrt.f64 x) x) (*.f64 (pow.f64 (cbrt.f64 x) 2) -1/2) (*.f64 5/24 (pow.f64 x 4)))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (pow.f64 (cbrt.f64 x) 8) (*.f64 (*.f64 (cbrt.f64 x) x) 5/24) (*.f64 -1/2 (*.f64 x x)))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (cbrt.f64 (*.f64 -1/2 (*.f64 x x))) (cbrt.f64 (*.f64 (pow.f64 x 4) 1/4)) (*.f64 5/24 (pow.f64 x 4)))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (cbrt.f64 (*.f64 (pow.f64 x 4) 1/4)) (cbrt.f64 (*.f64 -1/2 (*.f64 x x))) (*.f64 5/24 (pow.f64 x 4)))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (*.f64 (*.f64 x x) (sqrt.f64 5/24)) (*.f64 (*.f64 x x) (sqrt.f64 5/24)) (*.f64 -1/2 (*.f64 x x)))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (sqrt.f64 (fma.f64 5/24 (pow.f64 x 4) (*.f64 -1/2 (*.f64 x x)))) (sqrt.f64 (fma.f64 5/24 (pow.f64 x 4) (*.f64 -1/2 (*.f64 x x)))) 0)))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (*.f64 x (sqrt.f64 -1/2)) (*.f64 x (sqrt.f64 -1/2)) (*.f64 5/24 (pow.f64 x 4)))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (*.f64 (pow.f64 x 6) -1/8) (pow.f64 (*.f64 -1/2 (*.f64 x x)) -2) (*.f64 5/24 (pow.f64 x 4)))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (fma.f64 125/13824 (pow.f64 x 12) (*.f64 (pow.f64 x 6) -1/8)) (/.f64 1 (-.f64 (fma.f64 (pow.f64 x 4) 1/4 (*.f64 25/576 (pow.f64 x 8))) (*.f64 (*.f64 (*.f64 -1/2 (*.f64 x x)) 5/24) (pow.f64 x 4)))) 0)))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (neg.f64 (*.f64 (pow.f64 x 4) 1/4)) (/.f64 1 (neg.f64 (*.f64 -1/2 (*.f64 x x)))) (*.f64 5/24 (pow.f64 x 4)))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (-.f64 (*.f64 (pow.f64 x 4) 1/4) (*.f64 25/576 (pow.f64 x 8))) (/.f64 1 (fma.f64 -1/2 (*.f64 x x) (*.f64 -5/24 (pow.f64 x 4)))) 0)))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (*.f64 -1/2 x) x (*.f64 5/24 (pow.f64 x 4)))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (*.f64 5/24 (*.f64 x x)) (*.f64 x x) (*.f64 -1/2 (*.f64 x x)))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (*.f64 5/24 (pow.f64 (cbrt.f64 x) 8)) (*.f64 (cbrt.f64 x) x) (*.f64 -1/2 (*.f64 x x)))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (*.f64 -1/2 (*.f64 (cbrt.f64 x) x)) (pow.f64 (cbrt.f64 x) 2) (*.f64 5/24 (pow.f64 x 4)))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (*.f64 (*.f64 -1/2 x) 1) x (*.f64 5/24 (pow.f64 x 4)))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (*.f64 (*.f64 -1/2 x) (pow.f64 (cbrt.f64 x) 2)) (cbrt.f64 x) (*.f64 5/24 (pow.f64 x 4)))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (*.f64 (*.f64 -1/2 x) (sqrt.f64 x)) (sqrt.f64 x) (*.f64 5/24 (pow.f64 x 4)))))))

simplify187.0ms (6.5%)

Algorithm

1×	egg-herbie

Rules

1057×	`sqr-pow_binary64`
538×	`fma-def_binary64`
506×	`pow-sqr_binary64`
443×	`cube-prod_binary64`
425×	`associate-l_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	11	147
1	22	147
2	45	147
3	114	147
4	355	147
5	1427	147
6	2658	147
7	3120	147
8	3289	147
9	3488	147
10	3761	147
11	4118	147
12	4568	147
13	5099	147
14	5729	147
15	6484	147
16	6794	147
17	7018	147
18	7216	147
19	7270	147
20	7292	147

Stop Event

1×	node limit

Counts

93 → 86

Calls

Call 1

Inputs
(*.f64 -1/2 (pow.f64 x 2))
(+.f64 (.f64 -1/2 (pow.f64 x 2)) (.f64 5/24 (pow.f64 x 4)))
(+.f64 (.f64 -1/2 (pow.f64 x 2)) (.f64 5/24 (pow.f64 x 4)))
(+.f64 (.f64 -1/2 (pow.f64 x 2)) (.f64 5/24 (pow.f64 x 4)))
(*.f64 5/24 (pow.f64 x 4))
(+.f64 (.f64 -1/2 (pow.f64 x 2)) (.f64 5/24 (pow.f64 x 4)))
(+.f64 (.f64 -1/2 (pow.f64 x 2)) (.f64 5/24 (pow.f64 x 4)))
(+.f64 (.f64 -1/2 (pow.f64 x 2)) (.f64 5/24 (pow.f64 x 4)))
(*.f64 5/24 (pow.f64 x 4))
(+.f64 (.f64 -1/2 (pow.f64 x 2)) (.f64 5/24 (pow.f64 x 4)))
(+.f64 (.f64 -1/2 (pow.f64 x 2)) (.f64 5/24 (pow.f64 x 4)))
(+.f64 (.f64 -1/2 (pow.f64 x 2)) (.f64 5/24 (pow.f64 x 4)))

Outputs
(*.f64 -1/2 (pow.f64 x 2))
(.f64 -1/2 (.f64 x x))
(+.f64 (.f64 -1/2 (pow.f64 x 2)) (.f64 5/24 (pow.f64 x 4)))
(fma.f64 -1/2 (.f64 x x) (.f64 5/24 (pow.f64 x 4)))
(fma.f64 5/24 (pow.f64 x 4) (.f64 -1/2 (.f64 x x)))
(.f64 x (.f64 x (fma.f64 (*.f64 x x) 5/24 -1/2)))
(.f64 (.f64 x x) (fma.f64 (*.f64 x x) 5/24 -1/2))
(.f64 x (fma.f64 -1/2 x (.f64 5/24 (pow.f64 x 3))))
(+.f64 (.f64 -1/2 (pow.f64 x 2)) (.f64 5/24 (pow.f64 x 4)))
(fma.f64 -1/2 (.f64 x x) (.f64 5/24 (pow.f64 x 4)))
(fma.f64 5/24 (pow.f64 x 4) (.f64 -1/2 (.f64 x x)))
(.f64 x (.f64 x (fma.f64 (*.f64 x x) 5/24 -1/2)))
(.f64 (.f64 x x) (fma.f64 (*.f64 x x) 5/24 -1/2))
(.f64 x (fma.f64 -1/2 x (.f64 5/24 (pow.f64 x 3))))
(+.f64 (.f64 -1/2 (pow.f64 x 2)) (.f64 5/24 (pow.f64 x 4)))
(fma.f64 -1/2 (.f64 x x) (.f64 5/24 (pow.f64 x 4)))
(fma.f64 5/24 (pow.f64 x 4) (.f64 -1/2 (.f64 x x)))
(.f64 x (.f64 x (fma.f64 (*.f64 x x) 5/24 -1/2)))
(.f64 (.f64 x x) (fma.f64 (*.f64 x x) 5/24 -1/2))
(.f64 x (fma.f64 -1/2 x (.f64 5/24 (pow.f64 x 3))))
(*.f64 5/24 (pow.f64 x 4))
(+.f64 (.f64 -1/2 (pow.f64 x 2)) (.f64 5/24 (pow.f64 x 4)))
(fma.f64 -1/2 (.f64 x x) (.f64 5/24 (pow.f64 x 4)))
(fma.f64 5/24 (pow.f64 x 4) (.f64 -1/2 (.f64 x x)))
(.f64 x (.f64 x (fma.f64 (*.f64 x x) 5/24 -1/2)))
(.f64 (.f64 x x) (fma.f64 (*.f64 x x) 5/24 -1/2))
(.f64 x (fma.f64 -1/2 x (.f64 5/24 (pow.f64 x 3))))
(+.f64 (.f64 -1/2 (pow.f64 x 2)) (.f64 5/24 (pow.f64 x 4)))
(fma.f64 -1/2 (.f64 x x) (.f64 5/24 (pow.f64 x 4)))
(fma.f64 5/24 (pow.f64 x 4) (.f64 -1/2 (.f64 x x)))
(.f64 x (.f64 x (fma.f64 (*.f64 x x) 5/24 -1/2)))
(.f64 (.f64 x x) (fma.f64 (*.f64 x x) 5/24 -1/2))
(.f64 x (fma.f64 -1/2 x (.f64 5/24 (pow.f64 x 3))))
(+.f64 (.f64 -1/2 (pow.f64 x 2)) (.f64 5/24 (pow.f64 x 4)))
(fma.f64 -1/2 (.f64 x x) (.f64 5/24 (pow.f64 x 4)))
(fma.f64 5/24 (pow.f64 x 4) (.f64 -1/2 (.f64 x x)))
(.f64 x (.f64 x (fma.f64 (*.f64 x x) 5/24 -1/2)))
(.f64 (.f64 x x) (fma.f64 (*.f64 x x) 5/24 -1/2))
(.f64 x (fma.f64 -1/2 x (.f64 5/24 (pow.f64 x 3))))
(*.f64 5/24 (pow.f64 x 4))
(+.f64 (.f64 -1/2 (pow.f64 x 2)) (.f64 5/24 (pow.f64 x 4)))
(fma.f64 -1/2 (.f64 x x) (.f64 5/24 (pow.f64 x 4)))
(fma.f64 5/24 (pow.f64 x 4) (.f64 -1/2 (.f64 x x)))
(.f64 x (.f64 x (fma.f64 (*.f64 x x) 5/24 -1/2)))
(.f64 (.f64 x x) (fma.f64 (*.f64 x x) 5/24 -1/2))
(.f64 x (fma.f64 -1/2 x (.f64 5/24 (pow.f64 x 3))))
(+.f64 (.f64 -1/2 (pow.f64 x 2)) (.f64 5/24 (pow.f64 x 4)))
(fma.f64 -1/2 (.f64 x x) (.f64 5/24 (pow.f64 x 4)))
(fma.f64 5/24 (pow.f64 x 4) (.f64 -1/2 (.f64 x x)))
(.f64 x (.f64 x (fma.f64 (*.f64 x x) 5/24 -1/2)))
(.f64 (.f64 x x) (fma.f64 (*.f64 x x) 5/24 -1/2))
(.f64 x (fma.f64 -1/2 x (.f64 5/24 (pow.f64 x 3))))
(+.f64 (.f64 -1/2 (pow.f64 x 2)) (.f64 5/24 (pow.f64 x 4)))
(fma.f64 -1/2 (.f64 x x) (.f64 5/24 (pow.f64 x 4)))
(fma.f64 5/24 (pow.f64 x 4) (.f64 -1/2 (.f64 x x)))
(.f64 x (.f64 x (fma.f64 (*.f64 x x) 5/24 -1/2)))
(.f64 (.f64 x x) (fma.f64 (*.f64 x x) 5/24 -1/2))
(.f64 x (fma.f64 -1/2 x (.f64 5/24 (pow.f64 x 3))))

eval87.0ms (3%)

Compiler: Compiled 3759 to 2878 computations (23.4% saved)

prune28.0ms (1%)

Pruning

5 alts after pruning (2 fresh and 3 done)

	Pruned	Kept	Total
New	205	1	206
Fresh	0	1	1
Picked	0	1	1
Done	1	2	3
Total	206	5	211

Error

Counts

211 → 5

Alt Table

Click to see full alt table

Status	Error	Program
	33.3b	1
✓	33.8b	(+.f64 1 (.f64 -1/2 (.f64 x x)))
✓	33.9b	(+.f64 1 (+.f64 (+.f64 0 (.f64 -1/2 (.f64 x x))) (*.f64 5/24 (pow.f64 x 4))))
▶	0.0b	(*.f64 2 (/.f64 1/2 (cosh.f64 x)))
✓	0.0b	(*.f64 2 (-.f64 (+.f64 1 (/.f64 1/2 (cosh.f64 x))) 1))

Compiler

Compiled 44 to 37 computations (15.9% saved)

localize7.0ms (0.2%)

Local error

Found 1 expressions with local error:

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

Compiler

Compiled 16 to 10 computations (37.5% saved)

eval15.0ms (0.5%)

Compiler: Compiled 568 to 446 computations (21.5% saved)

prune8.0ms (0.3%)

Pruning

5 alts after pruning (1 fresh and 4 done)

	Pruned	Kept	Total
New	45	0	45
Fresh	0	1	1
Picked	0	1	1
Done	0	3	3
Total	45	5	50

Error

Counts

50 → 5

Alt Table

Click to see full alt table

Status	Error	Program
	33.3b	1
✓	33.8b	(+.f64 1 (.f64 -1/2 (.f64 x x)))
✓	33.9b	(+.f64 1 (+.f64 (+.f64 0 (.f64 -1/2 (.f64 x x))) (*.f64 5/24 (pow.f64 x 4))))
✓	0.0b	(*.f64 2 (/.f64 1/2 (cosh.f64 x)))
✓	0.0b	(*.f64 2 (-.f64 (+.f64 1 (/.f64 1/2 (cosh.f64 x))) 1))

Compiler

Compiled 44 to 37 computations (15.9% saved)

regimes20.0ms (0.7%)

Counts

10 → 1

Calls

Call 1

Inputs
1
(+.f64 1 (.f64 -1/2 (.f64 x x)))
(*.f64 2 (/.f64 1/2 (cosh.f64 x)))
(fma.f64 -1/2 (*.f64 x x) 1)
(.f64 2 (/.f64 1 (.f64 2 (cosh.f64 x))))
(*.f64 2 (-.f64 (+.f64 1 (/.f64 1/2 (cosh.f64 x))) 1))
(+.f64 1 (+.f64 (+.f64 0 (.f64 -1/2 (.f64 x x))) (*.f64 5/24 (pow.f64 x 4))))
(/.f64 2 (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x))))
(+.f64 1 (+.f64 (.f64 -1/2 (pow.f64 x 2)) (.f64 5/24 (pow.f64 x 4))))
(+.f64 1 (+.f64 (.f64 -1/2 (pow.f64 x 2)) (+.f64 (.f64 -61/720 (pow.f64 x 6)) (*.f64 5/24 (pow.f64 x 4)))))

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

Calls

5 calls:

6.0ms	x
4.0ms	(/.f64 2 (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x))))
2.0ms	(/.f64 2 (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x))))
2.0ms	(+.f64 (exp.f64 x) (exp.f64 (neg.f64 x)))
2.0ms	(+.f64 (exp.f64 x) (exp.f64 (neg.f64 x)))

Results

Error	Segments	Branch
0.0b	1	`x`
0.0b	1	`(/.f64 2 (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x))))`
0.0b	1	`(/.f64 2 (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x))))`
0.0b	1	`(+.f64 (exp.f64 x) (exp.f64 (neg.f64 x)))`
0.0b	1	`(+.f64 (exp.f64 x) (exp.f64 (neg.f64 x)))`

Compiler

Compiled 128 to 98 computations (23.4% saved)

regimes6.0ms (0.2%)

Counts

5 → 1

Calls

Call 1

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

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

Calls

1 calls:

4.0ms

Results

Error	Segments	Branch
0.0b	1	`x`

Compiler

Compiled 31 to 22 computations (29% saved)

regimes4.0ms (0.1%)

Accuracy

Total -0.7b remaining (-2.1%)

Threshold costs -0.7b (-2.1%)

Counts

2 → 1

Calls

Call 1

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

Outputs
1

Calls

1 calls:

3.0ms

Results

Error	Segments	Branch
33.3b	1	`x`

Compiler

Compiled 11 to 8 computations (27.3% saved)

simplify6.0ms (0.2%)

Algorithm

1×	egg-herbie

Rules

2×	`+-commutative_binary64`
2×	`*-commutative_binary64`
1×	`sub-neg_binary64`
1×	`1-exp_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	11	25
1	19	25
2	20	25

Stop Event

1×	fuel
1×	saturated

Calls

Call 1

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

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

Compiler

Compiled 20 to 18 computations (10% saved)

soundness0.0ms (0%)

end23.0ms (0.8%)

Compiler: Compiled 18 to 15 computations (16.7% saved)

Details

analyze0.0ms (0%)

sample786.0ms (27.3%)

preprocess88.0ms (3%)

simplify87.0ms (3%)

eval0.0ms (0%)

prune1.0ms (0%)

localize8.0ms (0.3%)

series3.0ms (0.1%)

rewrite35.0ms (1.2%)

simplify95.0ms (3.3%)

eval5.0ms (0.2%)

prune5.0ms (0.2%)

localize9.0ms (0.3%)

series4.0ms (0.1%)

rewrite51.0ms (1.8%)

simplify86.0ms (3%)

localize18.0ms (0.6%)

series4.0ms (0.1%)

rewrite72.0ms (2.5%)

simplify188.0ms (6.5%)

localize34.0ms (1.2%)

series3.0ms (0.1%)

rewrite75.0ms (2.6%)

simplify128.0ms (4.5%)

localize5.0ms (0.2%)

eval167.0ms (5.8%)

prune44.0ms (1.5%)

localize13.0ms (0.4%)

series5.0ms (0.2%)

rewrite63.0ms (2.2%)

simplify85.0ms (3%)

localize6.0ms (0.2%)

series1.0ms (0%)

rewrite46.0ms (1.6%)

simplify178.0ms (6.2%)

localize23.0ms (0.8%)

series1.0ms (0%)

rewrite68.0ms (2.4%)

simplify187.0ms (6.5%)

eval87.0ms (3%)

prune28.0ms (1%)

localize7.0ms (0.2%)

eval15.0ms (0.5%)

prune8.0ms (0.3%)

regimes20.0ms (0.7%)

regimes6.0ms (0.2%)

regimes4.0ms (0.1%)

simplify6.0ms (0.2%)

soundness0.0ms (0%)

end23.0ms (0.8%)

Profiling