Details

analyze4.0ms (0.1%)

Algorithm

1×

Search

True	Other	False	Iter
0%	100%	0%	0
0%	100%	0%	1
0%	100%	0%	2
50%	50%	0%	3
50%	25%	25%	4
50%	12.5%	37.5%	5
50%	6.2%	43.8%	6
50%	3.1%	46.9%	7
50%	1.6%	48.5%	8
50%	0.8%	49.2%	9
50.4%	0.4%	49.2%	10
50.4%	0.2%	49.4%	11
50.4%	0.1%	49.5%	12

Compiler

Compiled 10 to 8 computations (20% saved)

sample2.8s (70.4%)

Results

1.8s	4124×	body	1024	valid
463.0ms	2031×	body	512	valid
201.0ms	417×	body	2048	valid
200.0ms	1684×	body	256	valid
1.0ms	8×	body	256	invalid

preprocess44.0ms (1.1%)

Algorithm

2×	egg-herbie

Rules

618×	`fma-neg_binary64`
579×	`fma-def_binary64`
525×	`cancel-sign-sub-inv_binary64`
508×	`associate-/l*_binary64`
425×	`times-frac_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	8	13
1	19	13
2	34	13
3	58	13
4	120	13
5	261	13
6	714	13
7	2100	13
8	4939	12
0	1	1

Stop Event

1×	saturated
1×	node limit

Calls

Call 1

Inputs
0

Outputs
0

Call 2

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

Outputs
(/.f64 (-.f64 (exp.f64 x) (exp.f64 (neg.f64 x))) 2)
(*.f64 -1/2 (-.f64 (exp.f64 (neg.f64 x)) (exp.f64 x)))
(*.f64 (-.f64 (exp.f64 (neg.f64 x)) (exp.f64 x)) -1/2)
(fma.f64 1/2 (exp.f64 x) (/.f64 -1/2 (exp.f64 x)))

Compiler

Compiled 10 to 8 computations (20% saved)

simplify32.0ms (0.8%)

Algorithm

1×	egg-herbie

Rules

618×	`fma-neg_binary64`
579×	`fma-def_binary64`
525×	`cancel-sign-sub-inv_binary64`
508×	`associate-/l*_binary64`
425×	`times-frac_binary64`

Iterations

Useful iterations: 8 (0.0ms)

Iter	Nodes	Cost
0	8	13
1	19	13
2	34	13
3	58	13
4	120	13
5	261	13
6	714	13
7	2100	13
8	4939	12

Stop Event

1×	node limit

Counts

1 → 2

Calls

Call 1

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

Outputs
(/.f64 (-.f64 (exp.f64 x) (exp.f64 (neg.f64 x))) 2)
(*.f64 -1/2 (-.f64 (exp.f64 (neg.f64 x)) (exp.f64 x)))
(*.f64 (-.f64 (exp.f64 (neg.f64 x)) (exp.f64 x)) -1/2)
(fma.f64 1/2 (exp.f64 x) (/.f64 -1/2 (exp.f64 x)))

eval1.0ms (0%)

Compiler: Compiled 17 to 11 computations (35.3% saved)

prune1.0ms (0%)

Pruning

2 alts after pruning (2 fresh and 0 done)

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

Error

58.1b

Counts

3 → 1

Alt Table

Click to see full alt table

Status	Error	Program
▶	58.1b	(/.f64 (-.f64 (exp.f64 x) (exp.f64 (neg.f64 x))) 2)

Compiler

Compiled 9 to 7 computations (22.2% saved)

localize5.0ms (0.1%)

Local error

Found 2 expressions with local error:

New	Error	Program
	5.2b	(-.f64 (exp.f64 x) (exp.f64 (neg.f64 x)))
✓	5.2b	(-.f64 (exp.f64 x) (exp.f64 (neg.f64 x)))

series1.0ms (0%)

Counts

1 → 8

Calls

3 calls:

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

rewrite39.0ms (1%)

Algorithm

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

Rules

70×	`add-sqr-sqrt_binary64`
67×	`add-log-exp_binary64`
66×	`*-un-lft-identity_binary64`
66×	`pow1_binary64`
65×	`add-exp-log_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	6	6
1	130	6
2	2149	6
0	6	6

Stop Event

1×	iter limit
1×	unsound

Counts

1 → 13

Calls

Call 1

Inputs
(-.f64 (exp.f64 x) (exp.f64 (neg.f64 x)))

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

Outputs

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

simplify135.0ms (3.5%)

Algorithm

1×	egg-herbie

Rules

700×	`fma-def_binary64`
676×	`unswap-sqr_binary64`
322×	`associate-l_binary64`
310×	`associate-*l/_binary64`
268×	`associate-*r/_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	27	98
1	68	98
2	151	98
3	388	98
4	739	98
5	1635	98
6	2539	98
7	4128	98
8	7050	98

Stop Event

1×	node limit

Counts

21 → 22

Calls

Call 1

Inputs
(*.f64 2 x)
(+.f64 (.f64 2 x) (.f64 1/3 (pow.f64 x 3)))
(+.f64 (.f64 2 x) (+.f64 (.f64 1/3 (pow.f64 x 3)) (*.f64 1/60 (pow.f64 x 5))))
(+.f64 (.f64 2 x) (+.f64 (.f64 1/3 (pow.f64 x 3)) (+.f64 (.f64 1/2520 (pow.f64 x 7)) (.f64 1/60 (pow.f64 x 5)))))
(-.f64 (exp.f64 x) (exp.f64 (*.f64 -1 x)))
(-.f64 (exp.f64 x) (exp.f64 (*.f64 -1 x)))
(-.f64 (exp.f64 x) (exp.f64 (*.f64 -1 x)))
(-.f64 (exp.f64 x) (exp.f64 (*.f64 -1 x)))

Outputs
(*.f64 2 x)
(+.f64 (.f64 2 x) (.f64 1/3 (pow.f64 x 3)))
(fma.f64 2 x (*.f64 1/3 (pow.f64 x 3)))
(.f64 x (fma.f64 x (.f64 x 1/3) 2))
(.f64 x (fma.f64 1/3 (.f64 x x) 2))
(+.f64 (.f64 2 x) (+.f64 (.f64 1/3 (pow.f64 x 3)) (*.f64 1/60 (pow.f64 x 5))))
(fma.f64 2 x (fma.f64 1/3 (pow.f64 x 3) (*.f64 1/60 (pow.f64 x 5))))
(fma.f64 x (fma.f64 x (.f64 x 1/3) 2) (.f64 1/60 (pow.f64 x 5)))
(fma.f64 x (fma.f64 1/3 (.f64 x x) 2) (.f64 1/60 (pow.f64 x 5)))
(+.f64 (.f64 2 x) (+.f64 (.f64 1/3 (pow.f64 x 3)) (+.f64 (.f64 1/2520 (pow.f64 x 7)) (.f64 1/60 (pow.f64 x 5)))))
(fma.f64 2 x (fma.f64 1/3 (pow.f64 x 3) (fma.f64 1/2520 (pow.f64 x 7) (*.f64 1/60 (pow.f64 x 5)))))
(fma.f64 2 x (fma.f64 1/3 (pow.f64 x 3) (fma.f64 1/60 (pow.f64 x 5) (*.f64 1/2520 (pow.f64 x 7)))))
(fma.f64 1/3 (pow.f64 x 3) (fma.f64 1/60 (pow.f64 x 5) (fma.f64 1/2520 (pow.f64 x 7) (*.f64 2 x))))
(fma.f64 x (fma.f64 1/3 (.f64 x x) 2) (fma.f64 1/60 (pow.f64 x 5) (.f64 1/2520 (pow.f64 x 7))))
(fma.f64 1/60 (pow.f64 x 5) (fma.f64 x (fma.f64 1/3 (.f64 x x) 2) (.f64 1/2520 (pow.f64 x 7))))
(-.f64 (exp.f64 x) (exp.f64 (*.f64 -1 x)))
(-.f64 (exp.f64 x) (exp.f64 (neg.f64 x)))
(-.f64 (exp.f64 x) (exp.f64 (*.f64 -1 x)))
(-.f64 (exp.f64 x) (exp.f64 (neg.f64 x)))
(-.f64 (exp.f64 x) (exp.f64 (*.f64 -1 x)))
(-.f64 (exp.f64 x) (exp.f64 (neg.f64 x)))
(-.f64 (exp.f64 x) (exp.f64 (*.f64 -1 x)))
(-.f64 (exp.f64 x) (exp.f64 (neg.f64 x)))

eval6.0ms (0.2%)

Compiler: Compiled 286 to 186 computations (35% saved)

prune5.0ms (0.1%)

Pruning

4 alts after pruning (4 fresh and 0 done)

	Pruned	Kept	Total
New	18	4	22
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	19	4	23

Error

Counts

23 → 4

Alt Table

Click to see full alt table

Status	Error	Program
▶	0.5b	(/.f64 (+.f64 (.f64 2 x) (+.f64 (.f64 1/3 (pow.f64 x 3)) (+.f64 (.f64 1/2520 (pow.f64 x 7)) (.f64 1/60 (pow.f64 x 5))))) 2)
▶	0.0b	(/.f64 (*.f64 2 (sinh.f64 x)) 2)
▶	0.7b	(/.f64 (+.f64 (.f64 2 x) (.f64 1/3 (pow.f64 x 3))) 2)
▶	1.0b	(/.f64 (*.f64 2 x) 2)

Compiler

Compiled 49 to 41 computations (16.3% saved)

localize19.0ms (0.5%)

localize6.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.1b	(*.f64 1/3 (pow.f64 x 3))
	0.0b	(+.f64 (.f64 2 x) (.f64 1/3 (pow.f64 x 3)))
✓	0.0b	(+.f64 (.f64 2 x) (.f64 1/3 (pow.f64 x 3)))
✓	0.1b	(*.f64 1/3 (pow.f64 x 3))

series3.0ms (0.1%)

Counts

2 → 3

Calls

6 calls:

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

rewrite56.0ms (1.4%)

Algorithm

1×	batch-egg-rewrite

Rules

909×	`pow1_binary64`
854×	`add-log-exp_binary64`
853×	`log1p-expm1-u_binary64`
853×	`expm1-log1p-u_binary64`
837×	`add-exp-log_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	9	18
1	200	18
2	2372	18

Stop Event

1×	node limit

Counts

2 → 48

Calls

Call 1

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

Outputs
((#(struct:change #<rule egg-rr> (2) ((x -.f64 (+.f64 1 (.f64 1/3 (pow.f64 x 3))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (.f64 1/3 (pow.f64 x 3)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (.f64 x (cbrt.f64 1/3)) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (.f64 (sqrt.f64 1/3) (pow.f64 x 3/2)) 2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (.f64 (pow.f64 (pow.f64 x 3) 3) 1/27) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f64 (.f64 (pow.f64 x 6) 1/9))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (pow.f64 (exp.f64 1/3) (pow.f64 x 3)))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (.f64 (pow.f64 (pow.f64 x 3) 3) 1/27))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (.f64 1/3 (pow.f64 x 3))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (log.f64 (.f64 1/3 (pow.f64 x 3))))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (.f64 1/3 (pow.f64 x 3))))))))
((#(struct:change #<rule egg-rr> (2) ((x -.f64 (+.f64 1 (fma.f64 1/3 (pow.f64 x 3) (.f64 x 2))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (/.f64 (.f64 (.f64 x x) 4) (+.f64 (.f64 x 2) (.f64 -1/3 (pow.f64 x 3)))) (/.f64 (.f64 (pow.f64 x 6) 1/9) (+.f64 (.f64 x 2) (.f64 -1/3 (pow.f64 x 3)))))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (fma.f64 1/3 (pow.f64 x 3) (.f64 x 2)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x .f64 1 (fma.f64 1/3 (pow.f64 x 3) (.f64 x 2)))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (cbrt.f64 (fma.f64 1/3 (pow.f64 x 3) (.f64 x 2))) (pow.f64 (cbrt.f64 (fma.f64 1/3 (pow.f64 x 3) (.f64 x 2))) 2))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (pow.f64 (cbrt.f64 (fma.f64 1/3 (pow.f64 x 3) (.f64 x 2))) 2) (cbrt.f64 (fma.f64 1/3 (pow.f64 x 3) (.f64 x 2))))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (sqrt.f64 (fma.f64 1/3 (pow.f64 x 3) (.f64 x 2))) (sqrt.f64 (fma.f64 1/3 (pow.f64 x 3) (.f64 x 2))))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (+.f64 (.f64 (pow.f64 x 3) 8) (.f64 (pow.f64 (pow.f64 x 3) 3) 1/27)) (/.f64 1 (+.f64 (.f64 (.f64 x x) 4) (-.f64 (.f64 (pow.f64 x 6) 1/9) (.f64 (.f64 1/3 (pow.f64 x 3)) (.f64 x 2))))))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (-.f64 (.f64 (.f64 x x) 4) (.f64 (pow.f64 x 6) 1/9)) (/.f64 1 (+.f64 (.f64 x 2) (.f64 -1/3 (pow.f64 x 3)))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 1 (/.f64 (+.f64 (.f64 (.f64 x x) 4) (-.f64 (.f64 (pow.f64 x 6) 1/9) (.f64 (.f64 1/3 (pow.f64 x 3)) (.f64 x 2)))) (+.f64 (.f64 (pow.f64 x 3) 8) (.f64 (pow.f64 (pow.f64 x 3) 3) 1/27))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 1 (/.f64 (+.f64 (.f64 x 2) (.f64 -1/3 (pow.f64 x 3))) (-.f64 (.f64 (.f64 x x) 4) (.f64 (pow.f64 x 6) 1/9))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (+.f64 (.f64 (pow.f64 x 3) 8) (.f64 (pow.f64 (pow.f64 x 3) 3) 1/27)) (+.f64 (.f64 (.f64 x x) 4) (-.f64 (.f64 (pow.f64 x 6) 1/9) (.f64 (.f64 1/3 (pow.f64 x 3)) (.f64 x 2)))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (+.f64 (.f64 (pow.f64 x 3) 8) (.f64 (pow.f64 (pow.f64 x 3) 3) 1/27)) (+.f64 (.f64 (pow.f64 x 6) 1/9) (-.f64 (.f64 (.f64 x x) 4) (.f64 (.f64 1/3 (pow.f64 x 3)) (.f64 x 2)))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (-.f64 (.f64 (.f64 x x) 4) (.f64 (pow.f64 x 6) 1/9)) (+.f64 (.f64 x 2) (.f64 -1/3 (pow.f64 x 3))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (neg.f64 (+.f64 (.f64 (pow.f64 x 3) 8) (.f64 (pow.f64 (pow.f64 x 3) 3) 1/27))) (neg.f64 (+.f64 (.f64 (.f64 x x) 4) (-.f64 (.f64 (pow.f64 x 6) 1/9) (.f64 (.f64 1/3 (pow.f64 x 3)) (.f64 x 2))))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (neg.f64 (-.f64 (.f64 (.f64 x x) 4) (.f64 (pow.f64 x 6) 1/9))) (neg.f64 (+.f64 (.f64 x 2) (.f64 -1/3 (pow.f64 x 3)))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (-.f64 (.f64 (pow.f64 x 6) 1/9) (.f64 (.f64 x x) 4)) (-.f64 (.f64 1/3 (pow.f64 x 3)) (.f64 x 2)))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (fma.f64 1/3 (pow.f64 x 3) (.f64 x 2)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (fma.f64 1/3 (pow.f64 x 3) (.f64 x 2)) 3) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (cbrt.f64 (fma.f64 1/3 (pow.f64 x 3) (.f64 x 2))) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (sqrt.f64 (fma.f64 1/3 (pow.f64 x 3) (.f64 x 2))) 2)))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f64 (pow.f64 (fma.f64 1/3 (pow.f64 x 3) (.f64 x 2)) 2))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (exp.f64 (fma.f64 1/3 (pow.f64 x 3) (.f64 x 2))))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (pow.f64 (fma.f64 1/3 (pow.f64 x 3) (.f64 x 2)) 3))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (fma.f64 1/3 (pow.f64 x 3) (.f64 x 2))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (log.f64 (fma.f64 1/3 (pow.f64 x 3) (.f64 x 2))))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (fma.f64 1/3 (pow.f64 x 3) (.f64 x 2))))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 1/3 (pow.f64 x 3) (.f64 x 2))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 x 2 (.f64 1/3 (pow.f64 x 3)))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (pow.f64 x 3) 1/3 (.f64 x 2))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 2 x (.f64 1/3 (pow.f64 x 3)))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 1 (.f64 1/3 (pow.f64 x 3)) (.f64 x 2))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 1 (.f64 x 2) (.f64 1/3 (pow.f64 x 3)))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (cbrt.f64 (.f64 (.f64 x x) 4)) (cbrt.f64 (.f64 x 2)) (.f64 1/3 (pow.f64 x 3)))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (pow.f64 (.f64 x (cbrt.f64 1/3)) 2) (.f64 x (cbrt.f64 1/3)) (.f64 x 2))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (sqrt.f64 (.f64 x 2)) (sqrt.f64 (.f64 x 2)) (.f64 1/3 (pow.f64 x 3)))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (.f64 (sqrt.f64 1/3) (pow.f64 x 3/2)) (.f64 (sqrt.f64 1/3) (pow.f64 x 3/2)) (*.f64 x 2))))))

Outputs

((#(struct:change #<rule egg-rr> (2) ((x -.f64 (+.f64 1 (*.f64 1/3 (pow.f64 x 3))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (*.f64 1/3 (pow.f64 x 3)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (*.f64 x (cbrt.f64 1/3)) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (*.f64 (sqrt.f64 1/3) (pow.f64 x 3/2)) 2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (*.f64 (pow.f64 (pow.f64 x 3) 3) 1/27) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f64 (*.f64 (pow.f64 x 6) 1/9))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (pow.f64 (exp.f64 1/3) (pow.f64 x 3)))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (*.f64 (pow.f64 (pow.f64 x 3) 3) 1/27))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (*.f64 1/3 (pow.f64 x 3))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (log.f64 (*.f64 1/3 (pow.f64 x 3))))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (*.f64 1/3 (pow.f64 x 3))))))))

((#(struct:change #<rule egg-rr> (2) ((x -.f64 (+.f64 1 (fma.f64 1/3 (pow.f64 x 3) (*.f64 x 2))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (/.f64 (*.f64 (*.f64 x x) 4) (+.f64 (*.f64 x 2) (*.f64 -1/3 (pow.f64 x 3)))) (/.f64 (*.f64 (pow.f64 x 6) 1/9) (+.f64 (*.f64 x 2) (*.f64 -1/3 (pow.f64 x 3)))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (fma.f64 1/3 (pow.f64 x 3) (*.f64 x 2)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 1 (fma.f64 1/3 (pow.f64 x 3) (*.f64 x 2)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 (fma.f64 1/3 (pow.f64 x 3) (*.f64 x 2))) (pow.f64 (cbrt.f64 (fma.f64 1/3 (pow.f64 x 3) (*.f64 x 2))) 2))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (cbrt.f64 (fma.f64 1/3 (pow.f64 x 3) (*.f64 x 2))) 2) (cbrt.f64 (fma.f64 1/3 (pow.f64 x 3) (*.f64 x 2))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (sqrt.f64 (fma.f64 1/3 (pow.f64 x 3) (*.f64 x 2))) (sqrt.f64 (fma.f64 1/3 (pow.f64 x 3) (*.f64 x 2))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (+.f64 (*.f64 (pow.f64 x 3) 8) (*.f64 (pow.f64 (pow.f64 x 3) 3) 1/27)) (/.f64 1 (+.f64 (*.f64 (*.f64 x x) 4) (-.f64 (*.f64 (pow.f64 x 6) 1/9) (*.f64 (*.f64 1/3 (pow.f64 x 3)) (*.f64 x 2))))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (-.f64 (*.f64 (*.f64 x x) 4) (*.f64 (pow.f64 x 6) 1/9)) (/.f64 1 (+.f64 (*.f64 x 2) (*.f64 -1/3 (pow.f64 x 3)))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 1 (/.f64 (+.f64 (*.f64 (*.f64 x x) 4) (-.f64 (*.f64 (pow.f64 x 6) 1/9) (*.f64 (*.f64 1/3 (pow.f64 x 3)) (*.f64 x 2)))) (+.f64 (*.f64 (pow.f64 x 3) 8) (*.f64 (pow.f64 (pow.f64 x 3) 3) 1/27))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 1 (/.f64 (+.f64 (*.f64 x 2) (*.f64 -1/3 (pow.f64 x 3))) (-.f64 (*.f64 (*.f64 x x) 4) (*.f64 (pow.f64 x 6) 1/9))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (+.f64 (*.f64 (pow.f64 x 3) 8) (*.f64 (pow.f64 (pow.f64 x 3) 3) 1/27)) (+.f64 (*.f64 (*.f64 x x) 4) (-.f64 (*.f64 (pow.f64 x 6) 1/9) (*.f64 (*.f64 1/3 (pow.f64 x 3)) (*.f64 x 2)))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (+.f64 (*.f64 (pow.f64 x 3) 8) (*.f64 (pow.f64 (pow.f64 x 3) 3) 1/27)) (+.f64 (*.f64 (pow.f64 x 6) 1/9) (-.f64 (*.f64 (*.f64 x x) 4) (*.f64 (*.f64 1/3 (pow.f64 x 3)) (*.f64 x 2)))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (-.f64 (*.f64 (*.f64 x x) 4) (*.f64 (pow.f64 x 6) 1/9)) (+.f64 (*.f64 x 2) (*.f64 -1/3 (pow.f64 x 3))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (neg.f64 (+.f64 (*.f64 (pow.f64 x 3) 8) (*.f64 (pow.f64 (pow.f64 x 3) 3) 1/27))) (neg.f64 (+.f64 (*.f64 (*.f64 x x) 4) (-.f64 (*.f64 (pow.f64 x 6) 1/9) (*.f64 (*.f64 1/3 (pow.f64 x 3)) (*.f64 x 2))))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (neg.f64 (-.f64 (*.f64 (*.f64 x x) 4) (*.f64 (pow.f64 x 6) 1/9))) (neg.f64 (+.f64 (*.f64 x 2) (*.f64 -1/3 (pow.f64 x 3)))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (-.f64 (*.f64 (pow.f64 x 6) 1/9) (*.f64 (*.f64 x x) 4)) (-.f64 (*.f64 1/3 (pow.f64 x 3)) (*.f64 x 2)))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (fma.f64 1/3 (pow.f64 x 3) (*.f64 x 2)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (fma.f64 1/3 (pow.f64 x 3) (*.f64 x 2)) 3) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (cbrt.f64 (fma.f64 1/3 (pow.f64 x 3) (*.f64 x 2))) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (sqrt.f64 (fma.f64 1/3 (pow.f64 x 3) (*.f64 x 2))) 2)))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f64 (pow.f64 (fma.f64 1/3 (pow.f64 x 3) (*.f64 x 2)) 2))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (exp.f64 (fma.f64 1/3 (pow.f64 x 3) (*.f64 x 2))))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (pow.f64 (fma.f64 1/3 (pow.f64 x 3) (*.f64 x 2)) 3))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (fma.f64 1/3 (pow.f64 x 3) (*.f64 x 2))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (log.f64 (fma.f64 1/3 (pow.f64 x 3) (*.f64 x 2))))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (fma.f64 1/3 (pow.f64 x 3) (*.f64 x 2))))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 1/3 (pow.f64 x 3) (*.f64 x 2))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 x 2 (*.f64 1/3 (pow.f64 x 3)))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (pow.f64 x 3) 1/3 (*.f64 x 2))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 2 x (*.f64 1/3 (pow.f64 x 3)))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 1 (*.f64 1/3 (pow.f64 x 3)) (*.f64 x 2))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 1 (*.f64 x 2) (*.f64 1/3 (pow.f64 x 3)))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (cbrt.f64 (*.f64 (*.f64 x x) 4)) (cbrt.f64 (*.f64 x 2)) (*.f64 1/3 (pow.f64 x 3)))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (pow.f64 (*.f64 x (cbrt.f64 1/3)) 2) (*.f64 x (cbrt.f64 1/3)) (*.f64 x 2))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (sqrt.f64 (*.f64 x 2)) (sqrt.f64 (*.f64 x 2)) (*.f64 1/3 (pow.f64 x 3)))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (*.f64 (sqrt.f64 1/3) (pow.f64 x 3/2)) (*.f64 (sqrt.f64 1/3) (pow.f64 x 3/2)) (*.f64 x 2))))))

simplify119.0ms (3%)

Algorithm

1×	egg-herbie

Rules

1331×	`sqr-pow_binary64`
715×	`pow-sqr_binary64`
530×	`cube-prod_binary64`
476×	`fabs-mul_binary64`
449×	`associate-l_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	8	18
1	17	18
2	34	18
3	62	18
4	120	18
5	335	18
6	1184	18
7	1870	18
8	1957	18
9	2090	18
10	2248	18
11	2478	18
12	2800	18
13	3221	18
14	3721	18
15	4318	18
16	5038	18
17	5359	18
18	5647	18
19	5871	18
20	6053	18
21	6137	18
22	7077	18

Stop Event

1×	node limit

Counts

51 → 50

Calls

Call 1

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

Outputs
(*.f64 2 x)
(*.f64 1/3 (pow.f64 x 3))
(*.f64 1/3 (pow.f64 x 3))

localize3.0ms (0.1%)

Local error

Found 2 expressions with local error:

New	Error	Program
	0.0b	(sinh.f64 x)
✓	0.0b	(sinh.f64 x)

series3.0ms (0.1%)

Counts

1 → 12

Calls

3 calls:

Time	Variable		Point	Expression
1.0ms	x	@	inf	(sinh.f64 x)
1.0ms	x	@	-inf	(sinh.f64 x)
1.0ms	x	@	0	(sinh.f64 x)

rewrite47.0ms (1.2%)

Algorithm

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

Rules

318×	`pow1_binary64`
311×	`add-sqr-sqrt_binary64`
302×	`*-un-lft-identity_binary64`
297×	`add-log-exp_binary64`
296×	`log1p-expm1-u_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	3	3
1	63	3
2	785	3
0	3	3

Stop Event

1×	iter limit
1×	node limit

Counts

1 → 10

Calls

Call 1

Inputs
(sinh.f64 x)

Outputs

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

simplify55.0ms (1.4%)

Algorithm

1×	egg-herbie

Rules

872×	`fma-def_binary64`
626×	`distribute-rgt-neg-in_binary64`
624×	`unswap-sqr_binary64`
560×	`distribute-lft-neg-in_binary64`
311×	`neg-mul-1_binary64`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	25	150
1	67	150
2	151	142
3	372	142
4	686	142
5	1466	142
6	2299	142
7	3552	142
8	4529	142
9	7199	142

Stop Event

1×	node limit

Counts

22 → 19

Calls

Call 1

Inputs
x
(+.f64 (*.f64 1/6 (pow.f64 x 3)) x)
(+.f64 (.f64 1/6 (pow.f64 x 3)) (+.f64 (.f64 1/120 (pow.f64 x 5)) x))
(+.f64 (.f64 1/6 (pow.f64 x 3)) (+.f64 (.f64 1/5040 (pow.f64 x 7)) (+.f64 (*.f64 1/120 (pow.f64 x 5)) x)))
(*.f64 1/2 (-.f64 (exp.f64 x) (/.f64 1 (exp.f64 x))))
(*.f64 1/2 (-.f64 (exp.f64 x) (/.f64 1 (exp.f64 x))))
(*.f64 1/2 (-.f64 (exp.f64 x) (/.f64 1 (exp.f64 x))))
(*.f64 1/2 (-.f64 (exp.f64 x) (/.f64 1 (exp.f64 x))))
(*.f64 1/2 (-.f64 (exp.f64 x) (/.f64 1 (exp.f64 x))))
(*.f64 1/2 (-.f64 (exp.f64 x) (/.f64 1 (exp.f64 x))))
(*.f64 1/2 (-.f64 (exp.f64 x) (/.f64 1 (exp.f64 x))))
(*.f64 1/2 (-.f64 (exp.f64 x) (/.f64 1 (exp.f64 x))))

Outputs
x
(+.f64 (*.f64 1/6 (pow.f64 x 3)) x)
(fma.f64 1/6 (pow.f64 x 3) x)
(+.f64 (.f64 1/6 (pow.f64 x 3)) (+.f64 (.f64 1/120 (pow.f64 x 5)) x))
(fma.f64 1/6 (pow.f64 x 3) (fma.f64 1/120 (pow.f64 x 5) x))
(+.f64 (.f64 1/6 (pow.f64 x 3)) (+.f64 (.f64 1/5040 (pow.f64 x 7)) (+.f64 (*.f64 1/120 (pow.f64 x 5)) x)))
(fma.f64 1/6 (pow.f64 x 3) (fma.f64 1/5040 (pow.f64 x 7) (fma.f64 1/120 (pow.f64 x 5) x)))
(fma.f64 1/6 (pow.f64 x 3) (fma.f64 1/120 (pow.f64 x 5) (fma.f64 1/5040 (pow.f64 x 7) x)))
(*.f64 1/2 (-.f64 (exp.f64 x) (/.f64 1 (exp.f64 x))))
(*.f64 1/2 (-.f64 (exp.f64 x) (exp.f64 (neg.f64 x))))
(fma.f64 1/2 (exp.f64 x) (/.f64 -1/2 (exp.f64 x)))
(*.f64 1/2 (-.f64 (exp.f64 x) (/.f64 1 (exp.f64 x))))
(*.f64 1/2 (-.f64 (exp.f64 x) (exp.f64 (neg.f64 x))))
(fma.f64 1/2 (exp.f64 x) (/.f64 -1/2 (exp.f64 x)))
(*.f64 1/2 (-.f64 (exp.f64 x) (/.f64 1 (exp.f64 x))))
(*.f64 1/2 (-.f64 (exp.f64 x) (exp.f64 (neg.f64 x))))
(fma.f64 1/2 (exp.f64 x) (/.f64 -1/2 (exp.f64 x)))
(*.f64 1/2 (-.f64 (exp.f64 x) (/.f64 1 (exp.f64 x))))
(*.f64 1/2 (-.f64 (exp.f64 x) (exp.f64 (neg.f64 x))))
(fma.f64 1/2 (exp.f64 x) (/.f64 -1/2 (exp.f64 x)))
(*.f64 1/2 (-.f64 (exp.f64 x) (/.f64 1 (exp.f64 x))))
(*.f64 1/2 (-.f64 (exp.f64 x) (exp.f64 (neg.f64 x))))
(fma.f64 1/2 (exp.f64 x) (/.f64 -1/2 (exp.f64 x)))
(*.f64 1/2 (-.f64 (exp.f64 x) (/.f64 1 (exp.f64 x))))
(*.f64 1/2 (-.f64 (exp.f64 x) (exp.f64 (neg.f64 x))))
(fma.f64 1/2 (exp.f64 x) (/.f64 -1/2 (exp.f64 x)))
(*.f64 1/2 (-.f64 (exp.f64 x) (/.f64 1 (exp.f64 x))))
(*.f64 1/2 (-.f64 (exp.f64 x) (exp.f64 (neg.f64 x))))
(fma.f64 1/2 (exp.f64 x) (/.f64 -1/2 (exp.f64 x)))
(*.f64 1/2 (-.f64 (exp.f64 x) (/.f64 1 (exp.f64 x))))
(*.f64 1/2 (-.f64 (exp.f64 x) (exp.f64 (neg.f64 x))))
(fma.f64 1/2 (exp.f64 x) (/.f64 -1/2 (exp.f64 x)))

localize13.0ms (0.3%)

Local error

Found 8 expressions with local error:

New	Error	Program
	0.1b	(*.f64 1/60 (pow.f64 x 5))
	0.0b	(*.f64 1/2520 (pow.f64 x 7))
	0.0b	(+.f64 (.f64 1/3 (pow.f64 x 3)) (+.f64 (.f64 1/2520 (pow.f64 x 7)) (*.f64 1/60 (pow.f64 x 5))))
	0.0b	(+.f64 (.f64 1/2520 (pow.f64 x 7)) (.f64 1/60 (pow.f64 x 5)))
✓	0.0b	(+.f64 (.f64 1/3 (pow.f64 x 3)) (+.f64 (.f64 1/2520 (pow.f64 x 7)) (*.f64 1/60 (pow.f64 x 5))))
✓	0.0b	(*.f64 1/2520 (pow.f64 x 7))
✓	0.1b	(*.f64 1/60 (pow.f64 x 5))
	0.1b	(*.f64 1/3 (pow.f64 x 3))

series5.0ms (0.1%)

Counts

3 → 8

Calls

9 calls:

Time	Variable		Point	Expression
1.0ms	x	@	0	(*.f64 1/60 (pow.f64 x 5))
1.0ms	x	@	0	(*.f64 1/2520 (pow.f64 x 7))
1.0ms	x	@	inf	(*.f64 1/60 (pow.f64 x 5))
1.0ms	x	@	inf	(*.f64 1/2520 (pow.f64 x 7))
1.0ms	x	@	-inf	(*.f64 1/2520 (pow.f64 x 7))

rewrite168.0ms (4.3%)

Algorithm

1×	batch-egg-rewrite

Rules

716×	`log-prod_binary64`
632×	`fma-def_binary64`
336×	`fma-neg_binary64`
295×	`expm1-udef_binary64`
295×	`log1p-udef_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	16	35
1	367	35
2	4465	35

Stop Event

1×	node limit

Counts

3 → 122

Calls

Call 1

Inputs
(*.f64 1/60 (pow.f64 x 5))
(*.f64 1/2520 (pow.f64 x 7))
(+.f64 (.f64 1/3 (pow.f64 x 3)) (+.f64 (.f64 1/2520 (pow.f64 x 7)) (*.f64 1/60 (pow.f64 x 5))))

Outputs

((#(struct:change #<rule egg-rr> (2) ((x +.f64 0 (*.f64 1/60 (pow.f64 x 5)))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (log.f64 (*.f64 (cbrt.f64 (pow.f64 (exp.f64 (pow.f64 x 5)) 1/60)) (cbrt.f64 (pow.f64 (exp.f64 (pow.f64 x 5)) 1/60)))) (log.f64 (cbrt.f64 (pow.f64 (exp.f64 (pow.f64 x 5)) 1/60))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (log.f64 (sqrt.f64 (pow.f64 (exp.f64 (pow.f64 x 5)) 1/60))) (log.f64 (sqrt.f64 (pow.f64 (exp.f64 (pow.f64 x 5)) 1/60))))))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (exp.f64 (log1p.f64 (*.f64 1/60 (pow.f64 x 5)))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (*.f64 1/60 (pow.f64 x 5)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (cbrt.f64 (*.f64 1/60 (pow.f64 x 5))) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (*.f64 (sqrt.f64 1/60) (pow.f64 x 5/2)) 2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (*.f64 (pow.f64 (pow.f64 x 5) 3) 1/216000) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f64 (*.f64 (pow.f64 x 10) 1/3600))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (pow.f64 (exp.f64 (pow.f64 x 5)) 1/60))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (+.f64 1 (expm1.f64 (*.f64 1/60 (pow.f64 x 5)))))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (*.f64 (pow.f64 (pow.f64 x 5) 3) 1/216000))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (*.f64 1/60 (pow.f64 x 5))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (fma.f64 5 (log.f64 x) (log.f64 1/60)))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (fma.f64 5 (log.f64 x) (log.f64 1/60)) 1))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (*.f64 1/60 (pow.f64 x 5))))))))

((#(struct:change #<rule egg-rr> (2) ((x +.f64 0 (*.f64 1/2520 (pow.f64 x 7)))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (log.f64 (*.f64 (cbrt.f64 (pow.f64 (exp.f64 (pow.f64 x 7)) 1/2520)) (cbrt.f64 (pow.f64 (exp.f64 (pow.f64 x 7)) 1/2520)))) (log.f64 (cbrt.f64 (pow.f64 (exp.f64 (pow.f64 x 7)) 1/2520))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (log.f64 (sqrt.f64 (pow.f64 (exp.f64 (pow.f64 x 7)) 1/2520))) (log.f64 (sqrt.f64 (pow.f64 (exp.f64 (pow.f64 x 7)) 1/2520))))))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (exp.f64 (log1p.f64 (*.f64 1/2520 (pow.f64 x 7)))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (*.f64 1/2520 (pow.f64 x 7)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (cbrt.f64 (*.f64 1/2520 (pow.f64 x 7))) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (*.f64 (sqrt.f64 1/2520) (pow.f64 x 7/2)) 2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (*.f64 (pow.f64 (pow.f64 x 7) 3) 1/16003008000) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f64 (*.f64 (pow.f64 x 14) 1/6350400))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (pow.f64 (exp.f64 (pow.f64 x 7)) 1/2520))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (+.f64 1 (expm1.f64 (*.f64 1/2520 (pow.f64 x 7)))))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (*.f64 (pow.f64 (pow.f64 x 7) 3) 1/16003008000))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (*.f64 1/2520 (pow.f64 x 7))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (fma.f64 7 (log.f64 x) (log1p.f64 -2519/2520)))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (fma.f64 7 (log.f64 x) (log1p.f64 -2519/2520)) 1))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (*.f64 1/2520 (pow.f64 x 7))))))))

((#(struct:change #<rule egg-rr> (2) ((x -.f64 (exp.f64 (log1p.f64 (fma.f64 1/2520 (pow.f64 x 7) (fma.f64 1/60 (pow.f64 x 5) (*.f64 1/3 (pow.f64 x 3)))))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (/.f64 (*.f64 1/9 (pow.f64 x 6)) (-.f64 (*.f64 1/3 (pow.f64 x 3)) (fma.f64 1/60 (pow.f64 x 5) (*.f64 1/2520 (pow.f64 x 7))))) (/.f64 (pow.f64 (fma.f64 1/60 (pow.f64 x 5) (*.f64 1/2520 (pow.f64 x 7))) 2) (-.f64 (*.f64 1/3 (pow.f64 x 3)) (fma.f64 1/60 (pow.f64 x 5) (*.f64 1/2520 (pow.f64 x 7))))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (fma.f64 1/2520 (pow.f64 x 7) (fma.f64 1/60 (pow.f64 x 5) (*.f64 1/3 (pow.f64 x 3)))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 1 (fma.f64 1/2520 (pow.f64 x 7) (fma.f64 1/60 (pow.f64 x 5) (*.f64 1/3 (pow.f64 x 3)))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 (fma.f64 1/2520 (pow.f64 x 7) (fma.f64 1/60 (pow.f64 x 5) (*.f64 1/3 (pow.f64 x 3))))) (pow.f64 (cbrt.f64 (fma.f64 1/2520 (pow.f64 x 7) (fma.f64 1/60 (pow.f64 x 5) (*.f64 1/3 (pow.f64 x 3))))) 2))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (cbrt.f64 (fma.f64 1/2520 (pow.f64 x 7) (fma.f64 1/60 (pow.f64 x 5) (*.f64 1/3 (pow.f64 x 3))))) 2) (cbrt.f64 (fma.f64 1/2520 (pow.f64 x 7) (fma.f64 1/60 (pow.f64 x 5) (*.f64 1/3 (pow.f64 x 3))))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (sqrt.f64 (fma.f64 1/2520 (pow.f64 x 7) (fma.f64 1/60 (pow.f64 x 5) (*.f64 1/3 (pow.f64 x 3))))) (sqrt.f64 (fma.f64 1/2520 (pow.f64 x 7) (fma.f64 1/60 (pow.f64 x 5) (*.f64 1/3 (pow.f64 x 3))))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (fma.f64 1/27 (pow.f64 (pow.f64 x 3) 3) (pow.f64 (fma.f64 1/60 (pow.f64 x 5) (*.f64 1/2520 (pow.f64 x 7))) 3)) (/.f64 1 (fma.f64 (fma.f64 1/60 (pow.f64 x 5) (*.f64 1/2520 (pow.f64 x 7))) (-.f64 (fma.f64 1/60 (pow.f64 x 5) (*.f64 1/2520 (pow.f64 x 7))) (*.f64 1/3 (pow.f64 x 3))) (*.f64 1/9 (pow.f64 x 6)))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (-.f64 (*.f64 1/9 (pow.f64 x 6)) (pow.f64 (fma.f64 1/60 (pow.f64 x 5) (*.f64 1/2520 (pow.f64 x 7))) 2)) (/.f64 1 (-.f64 (*.f64 1/3 (pow.f64 x 3)) (fma.f64 1/60 (pow.f64 x 5) (*.f64 1/2520 (pow.f64 x 7))))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 1 (/.f64 (fma.f64 (fma.f64 1/60 (pow.f64 x 5) (*.f64 1/2520 (pow.f64 x 7))) (-.f64 (fma.f64 1/60 (pow.f64 x 5) (*.f64 1/2520 (pow.f64 x 7))) (*.f64 1/3 (pow.f64 x 3))) (*.f64 1/9 (pow.f64 x 6))) (fma.f64 1/27 (pow.f64 (pow.f64 x 3) 3) (pow.f64 (fma.f64 1/60 (pow.f64 x 5) (*.f64 1/2520 (pow.f64 x 7))) 3))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 1 (/.f64 (-.f64 (*.f64 1/3 (pow.f64 x 3)) (fma.f64 1/60 (pow.f64 x 5) (*.f64 1/2520 (pow.f64 x 7)))) (-.f64 (*.f64 1/9 (pow.f64 x 6)) (pow.f64 (fma.f64 1/60 (pow.f64 x 5) (*.f64 1/2520 (pow.f64 x 7))) 2))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (fma.f64 1/27 (pow.f64 (pow.f64 x 3) 3) (pow.f64 (fma.f64 1/60 (pow.f64 x 5) (*.f64 1/2520 (pow.f64 x 7))) 3)) (fma.f64 (fma.f64 1/60 (pow.f64 x 5) (*.f64 1/2520 (pow.f64 x 7))) (-.f64 (fma.f64 1/60 (pow.f64 x 5) (*.f64 1/2520 (pow.f64 x 7))) (*.f64 1/3 (pow.f64 x 3))) (*.f64 1/9 (pow.f64 x 6))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (fma.f64 1/27 (pow.f64 (pow.f64 x 3) 3) (pow.f64 (fma.f64 1/60 (pow.f64 x 5) (*.f64 1/2520 (pow.f64 x 7))) 3)) (+.f64 (pow.f64 (fma.f64 1/60 (pow.f64 x 5) (*.f64 1/2520 (pow.f64 x 7))) 2) (-.f64 (*.f64 1/9 (pow.f64 x 6)) (*.f64 1/3 (*.f64 (pow.f64 x 3) (fma.f64 1/60 (pow.f64 x 5) (*.f64 1/2520 (pow.f64 x 7))))))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (-.f64 (*.f64 1/9 (pow.f64 x 6)) (pow.f64 (fma.f64 1/60 (pow.f64 x 5) (*.f64 1/2520 (pow.f64 x 7))) 2)) (-.f64 (*.f64 1/3 (pow.f64 x 3)) (fma.f64 1/60 (pow.f64 x 5) (*.f64 1/2520 (pow.f64 x 7)))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (neg.f64 (fma.f64 1/27 (pow.f64 (pow.f64 x 3) 3) (pow.f64 (fma.f64 1/60 (pow.f64 x 5) (*.f64 1/2520 (pow.f64 x 7))) 3))) (neg.f64 (fma.f64 (fma.f64 1/60 (pow.f64 x 5) (*.f64 1/2520 (pow.f64 x 7))) (-.f64 (fma.f64 1/60 (pow.f64 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(*.f64 1/3 (pow.f64 x 3))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (-.f64 (*.f64 (fma.f64 1/2520 (pow.f64 x 7) (*.f64 1/3 (pow.f64 x 3))) (fma.f64 1/2520 (pow.f64 x 7) (*.f64 1/3 (pow.f64 x 3)))) (*.f64 (pow.f64 x 10) 1/3600)) (-.f64 (fma.f64 1/2520 (pow.f64 x 7) (*.f64 1/3 (pow.f64 x 3))) (*.f64 1/60 (pow.f64 x 5))))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (fma.f64 1/2520 (pow.f64 x 7) (fma.f64 1/60 (pow.f64 x 5) (*.f64 1/3 (pow.f64 x 3)))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (fma.f64 1/2520 (pow.f64 x 7) (fma.f64 1/60 (pow.f64 x 5) (*.f64 1/3 (pow.f64 x 3)))) 3) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (cbrt.f64 (fma.f64 1/2520 (pow.f64 x 7) (fma.f64 1/60 (pow.f64 x 5) (*.f64 1/3 (pow.f64 x 3))))) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (sqrt.f64 (fma.f64 1/2520 (pow.f64 x 7) (fma.f64 1/60 (pow.f64 x 5) (*.f64 1/3 (pow.f64 x 3))))) 2)))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f64 (pow.f64 (fma.f64 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x 14))) (cbrt.f64 (pow.f64 x 7)) (fma.f64 1/60 (pow.f64 x 5) (*.f64 1/3 (pow.f64 x 3))))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (*.f64 1/2520 (pow.f64 x 7/2)) (pow.f64 x 7/2) (fma.f64 1/60 (pow.f64 x 5) (*.f64 1/3 (pow.f64 x 3))))))))

simplify141.0ms (3.6%)

Algorithm

1×	egg-herbie

Rules

1116×	`sqr-pow_binary64`
672×	`cube-prod_binary64`
624×	`unswap-sqr_binary64`
620×	`fabs-mul_binary64`
414×	`pow-sqr_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	17	105
1	44	105
2	93	105
3	210	105
4	406	105
5	1071	105
6	1589	105
7	2538	105
8	2692	105
9	2939	105
10	3254	105
11	3735	105
12	4414	105
13	5308	105
14	5950	105
15	6455	105
16	6858	105
17	7241	105
18	7455	105

Stop Event

1×	node limit

Counts

130 → 130

Calls

Call 1

Inputs
(*.f64 1/3 (pow.f64 x 3))
(+.f64 (.f64 1/3 (pow.f64 x 3)) (.f64 1/60 (pow.f64 x 5)))
(+.f64 (.f64 1/2520 (pow.f64 x 7)) (+.f64 (.f64 1/3 (pow.f64 x 3)) (*.f64 1/60 (pow.f64 x 5))))
(+.f64 (.f64 1/2520 (pow.f64 x 7)) (+.f64 (.f64 1/3 (pow.f64 x 3)) (*.f64 1/60 (pow.f64 x 5))))
(*.f64 1/2520 (pow.f64 x 7))
(+.f64 (.f64 1/2520 (pow.f64 x 7)) (.f64 1/60 (pow.f64 x 5)))
(*.f64 1/2520 (pow.f64 x 7))
(+.f64 (.f64 1/2520 (pow.f64 x 7)) (.f64 1/60 (pow.f64 x 5)))

Outputs
(*.f64 1/3 (pow.f64 x 3))
(+.f64 (.f64 1/3 (pow.f64 x 3)) (.f64 1/60 (pow.f64 x 5)))
(fma.f64 1/3 (pow.f64 x 3) (*.f64 1/60 (pow.f64 x 5)))
(+.f64 (.f64 1/2520 (pow.f64 x 7)) (+.f64 (.f64 1/3 (pow.f64 x 3)) (*.f64 1/60 (pow.f64 x 5))))
(fma.f64 1/2520 (pow.f64 x 7) (fma.f64 1/3 (pow.f64 x 3) (*.f64 1/60 (pow.f64 x 5))))
(fma.f64 1/3 (pow.f64 x 3) (fma.f64 1/60 (pow.f64 x 5) (*.f64 1/2520 (pow.f64 x 7))))
(fma.f64 1/3 (pow.f64 x 3) (fma.f64 1/2520 (pow.f64 x 7) (*.f64 1/60 (pow.f64 x 5))))
(fma.f64 1/60 (pow.f64 x 5) (fma.f64 1/3 (pow.f64 x 3) (*.f64 1/2520 (pow.f64 x 7))))
(+.f64 (.f64 1/2520 (pow.f64 x 7)) (+.f64 (.f64 1/3 (pow.f64 x 3)) (*.f64 1/60 (pow.f64 x 5))))
(fma.f64 1/2520 (pow.f64 x 7) (fma.f64 1/3 (pow.f64 x 3) (*.f64 1/60 (pow.f64 x 5))))
(fma.f64 1/3 (pow.f64 x 3) (fma.f64 1/60 (pow.f64 x 5) (*.f64 1/2520 (pow.f64 x 7))))
(fma.f64 1/3 (pow.f64 x 3) (fma.f64 1/2520 (pow.f64 x 7) (*.f64 1/60 (pow.f64 x 5))))
(fma.f64 1/60 (pow.f64 x 5) (fma.f64 1/3 (pow.f64 x 3) (*.f64 1/2520 (pow.f64 x 7))))
(*.f64 1/2520 (pow.f64 x 7))
(+.f64 (.f64 1/2520 (pow.f64 x 7)) (.f64 1/60 (pow.f64 x 5)))
(fma.f64 1/2520 (pow.f64 x 7) (*.f64 1/60 (pow.f64 x 5)))
(fma.f64 1/60 (pow.f64 x 5) (*.f64 1/2520 (pow.f64 x 7)))
(*.f64 1/2520 (pow.f64 x 7))
(+.f64 (.f64 1/2520 (pow.f64 x 7)) (.f64 1/60 (pow.f64 x 5)))
(fma.f64 1/2520 (pow.f64 x 7) (*.f64 1/60 (pow.f64 x 5)))
(fma.f64 1/60 (pow.f64 x 5) (*.f64 1/2520 (pow.f64 x 7)))

eval170.0ms (4.3%)

Compiler: Compiled 5137 to 4226 computations (17.7% saved)

prune27.0ms (0.7%)

Pruning

4 alts after pruning (0 fresh and 4 done)

	Pruned	Kept	Total
New	210	0	210
Fresh	0	0	0
Picked	0	1	1
Done	0	3	3
Total	210	4	214

Error

Counts

214 → 4

Alt Table

Click to see full alt table

Status	Error	Program
✓	0.5b	(/.f64 (+.f64 (.f64 2 x) (+.f64 (.f64 1/3 (pow.f64 x 3)) (+.f64 (.f64 1/2520 (pow.f64 x 7)) (.f64 1/60 (pow.f64 x 5))))) 2)
✓	0.0b	(/.f64 (*.f64 2 (sinh.f64 x)) 2)
✓	0.7b	(/.f64 (+.f64 (.f64 2 x) (.f64 1/3 (pow.f64 x 3))) 2)
✓	1.0b	(/.f64 (*.f64 2 x) 2)

Compiler

Compiled 49 to 41 computations (16.3% saved)

regimes11.0ms (0.3%)

Accuracy

Total -58.9b remaining (-754095.9%)

Threshold costs -58.9b (-754095.9%)

Counts

5 → 1

Calls

Call 1

Inputs
(/.f64 (*.f64 2 x) 2)
(/.f64 (*.f64 2 (sinh.f64 x)) 2)
(/.f64 (+.f64 (.f64 2 x) (.f64 1/3 (pow.f64 x 3))) 2)
(/.f64 (-.f64 (exp.f64 x) (exp.f64 (neg.f64 x))) 2)
(/.f64 (+.f64 (.f64 2 x) (+.f64 (.f64 1/3 (pow.f64 x 3)) (+.f64 (.f64 1/2520 (pow.f64 x 7)) (.f64 1/60 (pow.f64 x 5))))) 2)

Outputs
(/.f64 (*.f64 2 (sinh.f64 x)) 2)

Calls

3 calls:

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

Results

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

Compiler

Compiled 72 to 57 computations (20.8% saved)

simplify2.0ms (0%)

Algorithm

1×	egg-herbie

Rules

2×	`*-commutative_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	8	16
1	10	16

Stop Event

1×

saturated

Calls

Call 1

Inputs
(/.f64 (*.f64 2 (sinh.f64 x)) 2)
(/.f64 (*.f64 2 x) 2)

Outputs
(/.f64 (*.f64 2 (sinh.f64 x)) 2)
(/.f64 (*.f64 2 x) 2)

end38.0ms (1%)

Stop Event

1×

done

Compiler

Compiled 25 to 21 computations (16% saved)

Details

analyze4.0ms (0.1%)

sample2.8s (70.4%)

preprocess44.0ms (1.1%)

simplify32.0ms (0.8%)

eval1.0ms (0%)

prune1.0ms (0%)

localize5.0ms (0.1%)

series1.0ms (0%)

rewrite39.0ms (1%)

simplify135.0ms (3.5%)

eval6.0ms (0.2%)

prune5.0ms (0.1%)

localize19.0ms (0.5%)

localize6.0ms (0.2%)

series3.0ms (0.1%)

rewrite56.0ms (1.4%)

simplify119.0ms (3%)

localize3.0ms (0.1%)

series3.0ms (0.1%)

rewrite47.0ms (1.2%)

simplify55.0ms (1.4%)

localize13.0ms (0.3%)

series5.0ms (0.1%)

rewrite168.0ms (4.3%)

simplify141.0ms (3.6%)

eval170.0ms (4.3%)

prune27.0ms (0.7%)

regimes11.0ms (0.3%)

simplify2.0ms (0%)

end38.0ms (1%)

Profiling