Details

analyze9.0ms (0.2%)

Algorithm

1×

Search

True	Other	False	Iter
0%	100%	0%	0
0%	100%	0%	1
0%	100%	0%	2
50%	50%	0%	3
75%	25%	0%	4
87.5%	12.5%	0%	5
93.7%	6.2%	0%	6
96.8%	3.1%	0%	7
98.4%	1.6%	0%	8
99.2%	0.8%	0%	9
99.6%	0.4%	0%	10
99.8%	0.2%	0%	11
99.9%	0.1%	0%	12

Compiler

Compiled 8 to 7 computations (12.5% saved)

sample1.1s (18.4%)

Results

1.1s	8256×	body	256	valid
0.0ms	3×	body	256	invalid

preprocess172.0ms (3%)

Algorithm

2×	egg-herbie

Rules

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

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	6	9
1	12	9
2	23	9
3	44	9
4	108	9
5	330	9
6	1255	9
7	2129	9
8	2293	9
9	2477	9
10	2685	9
11	2984	9
12	3375	9
13	3856	9
14	4422	9
15	5110	9
16	5947	9
17	6337	9
18	6625	9
19	6903	9
20	6977	9
21	7013	9
22	7954	9
0	1	1

Stop Event

1×	saturated
1×	node limit

Calls

Call 1

Inputs
0

Outputs
0

Call 2

Inputs
(sqrt.f64 (*.f64 2 (pow.f64 x 2)))

Outputs
(sqrt.f64 (*.f64 2 (pow.f64 x 2)))
(sqrt.f64 (.f64 2 (.f64 x x)))

Compiler

Compiled 8 to 7 computations (12.5% saved)

simplify171.0ms (3%)

Algorithm

1×	egg-herbie

Rules

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

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	6	9
1	12	9
2	23	9
3	44	9
4	108	9
5	330	9
6	1255	9
7	2129	9
8	2293	9
9	2477	9
10	2685	9
11	2984	9
12	3375	9
13	3856	9
14	4422	9
15	5110	9
16	5947	9
17	6337	9
18	6625	9
19	6903	9
20	6977	9
21	7013	9
22	7954	9

Stop Event

1×	node limit

Counts

1 → 2

Calls

Call 1

Inputs
(sqrt.f64 (*.f64 2 (pow.f64 x 2)))

Outputs
(sqrt.f64 (*.f64 2 (pow.f64 x 2)))
(sqrt.f64 (.f64 2 (.f64 x x)))

eval1.0ms (0%)

Compiler: Compiled 13 to 10 computations (23.1% saved)

prune1.0ms (0%)

Pruning

1 alts after pruning (1 fresh and 0 done)

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

Error

34.1b

Counts

3 → 1

Alt Table

Click to see full alt table

Status	Error	Program
▶	34.1b	(sqrt.f64 (.f64 2 (.f64 x x)))

Compiler

Compiled 7 to 5 computations (28.6% saved)

localize7.0ms (0.1%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.0b	(.f64 2 (.f64 x x))
✓	32.7b	(sqrt.f64 (.f64 2 (.f64 x x)))

Compiler

Compiled 17 to 8 computations (52.9% saved)

series3.0ms (0.1%)

Counts

2 → 24

Calls

6 calls:

Time	Variable		Point	Expression
1.0ms	x	@	0	(sqrt.f64 (.f64 2 (.f64 x x)))
1.0ms	x	@	0	(.f64 2 (.f64 x x))
1.0ms	x	@	inf	(sqrt.f64 (.f64 2 (.f64 x x)))
0.0ms	x	@	inf	(.f64 2 (.f64 x x))
0.0ms	x	@	-inf	(.f64 2 (.f64 x x))

rewrite99.0ms (1.7%)

Algorithm

1×	batch-egg-rewrite

Rules

503×	`pow1_binary64`
486×	`add-sqr-sqrt_binary64`
466×	`add-log-exp_binary64`
466×	`log1p-expm1-u_binary64`
466×	`expm1-log1p-u_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	6	16
1	122	13
2	1367	13

Stop Event

1×	node limit

Counts

2 → 36

Calls

Call 1

Inputs
(sqrt.f64 (.f64 2 (.f64 x x)))
(.f64 2 (.f64 x x))

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

Outputs

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

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

simplify88.0ms (1.5%)

Algorithm

1×	egg-herbie

Rules

964×	`fma-def_binary64`
402×	`distribute-rgt-neg-out_binary64`
365×	`fma-neg_binary64`
337×	`distribute-rgt-neg-in_binary64`
318×	`fabs-mul_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	9	164
1	20	164
2	43	164
3	83	164
4	205	164
5	632	164
6	988	164
7	1635	164
8	2038	164
9	2907	164
10	3744	164
11	4611	164
12	5738	164

Stop Event

1×	node limit

Counts

60 → 40

Calls

Call 1

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

Outputs
(*.f64 (sqrt.f64 2) x)
(*.f64 (sqrt.f64 2) x)
(*.f64 (sqrt.f64 2) x)
(*.f64 (sqrt.f64 2) x)
(*.f64 (sqrt.f64 2) x)
(*.f64 (sqrt.f64 2) x)
(*.f64 (sqrt.f64 2) x)
(*.f64 (sqrt.f64 2) x)
(.f64 -1 (.f64 (sqrt.f64 2) x))
(neg.f64 (*.f64 (sqrt.f64 2) x))
(*.f64 (sqrt.f64 2) (neg.f64 x))
(*.f64 x (neg.f64 (sqrt.f64 2)))
(.f64 -1 (.f64 (sqrt.f64 2) x))
(neg.f64 (*.f64 (sqrt.f64 2) x))
(*.f64 (sqrt.f64 2) (neg.f64 x))
(*.f64 x (neg.f64 (sqrt.f64 2)))
(.f64 -1 (.f64 (sqrt.f64 2) x))
(neg.f64 (*.f64 (sqrt.f64 2) x))
(*.f64 (sqrt.f64 2) (neg.f64 x))
(*.f64 x (neg.f64 (sqrt.f64 2)))
(.f64 -1 (.f64 (sqrt.f64 2) x))
(neg.f64 (*.f64 (sqrt.f64 2) x))
(*.f64 (sqrt.f64 2) (neg.f64 x))
(*.f64 x (neg.f64 (sqrt.f64 2)))
(*.f64 2 (pow.f64 x 2))
(.f64 2 (.f64 x x))
(*.f64 2 (pow.f64 x 2))
(.f64 2 (.f64 x x))
(*.f64 2 (pow.f64 x 2))
(.f64 2 (.f64 x x))
(*.f64 2 (pow.f64 x 2))
(.f64 2 (.f64 x x))
(*.f64 2 (pow.f64 x 2))
(.f64 2 (.f64 x x))
(*.f64 2 (pow.f64 x 2))
(.f64 2 (.f64 x x))
(*.f64 2 (pow.f64 x 2))
(.f64 2 (.f64 x x))
(*.f64 2 (pow.f64 x 2))
(.f64 2 (.f64 x x))
(*.f64 2 (pow.f64 x 2))
(.f64 2 (.f64 x x))
(*.f64 2 (pow.f64 x 2))
(.f64 2 (.f64 x x))
(*.f64 2 (pow.f64 x 2))
(.f64 2 (.f64 x x))
(*.f64 2 (pow.f64 x 2))
(.f64 2 (.f64 x x))

eval8.0ms (0.1%)

Compiler: Compiled 313 to 236 computations (24.6% saved)

prune11.0ms (0.2%)

Pruning

7 alts after pruning (6 fresh and 1 done)

	Pruned	Kept	Total
New	34	6	40
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	34	7	41

Error

0.2b

Counts

41 → 7

Alt Table

Click to see full alt table

Status	Error	Program
▶	45.7b	(sqrt.f64 (sqrt.f64 (*.f64 4 (pow.f64 x 4))))
▶	32.0b	(*.f64 x (neg.f64 (sqrt.f64 2)))
▶	31.0b	(*.f64 (sqrt.f64 2) x)
✓	34.1b	(sqrt.f64 (.f64 2 (.f64 x x)))
▶	31.7b	(.f64 (sqrt.f64 (.f64 2 x)) (sqrt.f64 x))
	31.8b	(pow.f64 (sqrt.f64 (*.f64 x (sqrt.f64 2))) 2)
▶	31.4b	(pow.f64 (cbrt.f64 (*.f64 x (sqrt.f64 2))) 3)

Compiler

Compiled 93 to 77 computations (17.2% saved)

localize5.0ms (0.1%)

Local error

Found 1 expressions with local error:

New	Error	Program
✓	0.5b	(*.f64 (sqrt.f64 2) x)

Compiler

Compiled 9 to 7 computations (22.2% saved)

series1.0ms (0%)

Counts

1 → 0

Calls

3 calls:

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

rewrite43.0ms (0.7%)

Algorithm

1×	batch-egg-rewrite

Rules

417×	`pow1_binary64`
403×	`add-sqr-sqrt_binary64`
395×	`*-un-lft-identity_binary64`
386×	`add-log-exp_binary64`
386×	`log1p-expm1-u_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	5	6
1	100	6
2	1075	6

Stop Event

1×	node limit

Counts

1 → 15

Calls

Call 1

Inputs
(*.f64 (sqrt.f64 2) x)

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

Outputs

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

simplify6.0ms (0.1%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	0	0

Stop Event

1×

saturated

Counts

15 → 15

Calls

Call 1

Inputs

Outputs

localize7.0ms (0.1%)

Local error

Found 1 expressions with local error:

New	Error	Program
✓	0.5b	(*.f64 x (neg.f64 (sqrt.f64 2)))

Compiler

Compiled 13 to 11 computations (15.4% saved)

series1.0ms (0%)

Counts

1 → 12

Calls

3 calls:

Time	Variable		Point	Expression
1.0ms	x	@	0	(*.f64 x (neg.f64 (sqrt.f64 2)))
0.0ms	x	@	inf	(*.f64 x (neg.f64 (sqrt.f64 2)))
0.0ms	x	@	-inf	(*.f64 x (neg.f64 (sqrt.f64 2)))

rewrite28.0ms (0.5%)

Algorithm

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

Rules

61×	`add-sqr-sqrt_binary64`
57×	`add-exp-log_binary64`
57×	`add-log-exp_binary64`
57×	`log1p-expm1-u_binary64`
57×	`expm1-log1p-u_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	6	8
1	125	8
2	1470	8
0	6	8

Stop Event

1×	iter limit
1×	unsound

Counts

1 → 7

Calls

Call 1

Inputs
(*.f64 x (neg.f64 (sqrt.f64 2)))

Outputs

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

simplify13.0ms (0.2%)

Algorithm

1×	egg-herbie

Rules

38×	`fma-def_binary64`
9×	`sub-neg_binary64`
6×	`+-commutative_binary64`
4×	`*-commutative_binary64`
4×	`distribute-lft-in_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	7	96
1	12	96
2	25	96
3	29	96
4	33	96
5	51	96
6	73	96
7	84	96
8	96	96
9	121	96

Stop Event

1×

saturated

Counts

19 → 9

Calls

Call 1

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

Outputs
(.f64 -1 (.f64 (sqrt.f64 2) x))
(neg.f64 (*.f64 (sqrt.f64 2) x))
(*.f64 (sqrt.f64 2) (neg.f64 x))
(.f64 -1 (.f64 (sqrt.f64 2) x))
(neg.f64 (*.f64 (sqrt.f64 2) x))
(*.f64 (sqrt.f64 2) (neg.f64 x))
(.f64 -1 (.f64 (sqrt.f64 2) x))
(neg.f64 (*.f64 (sqrt.f64 2) x))
(*.f64 (sqrt.f64 2) (neg.f64 x))
(.f64 -1 (.f64 (sqrt.f64 2) x))
(neg.f64 (*.f64 (sqrt.f64 2) x))
(*.f64 (sqrt.f64 2) (neg.f64 x))
(.f64 -1 (.f64 (sqrt.f64 2) x))
(neg.f64 (*.f64 (sqrt.f64 2) x))
(*.f64 (sqrt.f64 2) (neg.f64 x))
(.f64 -1 (.f64 (sqrt.f64 2) x))
(neg.f64 (*.f64 (sqrt.f64 2) x))
(*.f64 (sqrt.f64 2) (neg.f64 x))
(.f64 -1 (.f64 (sqrt.f64 2) x))
(neg.f64 (*.f64 (sqrt.f64 2) x))
(*.f64 (sqrt.f64 2) (neg.f64 x))
(.f64 -1 (.f64 (sqrt.f64 2) x))
(neg.f64 (*.f64 (sqrt.f64 2) x))
(*.f64 (sqrt.f64 2) (neg.f64 x))
(.f64 -1 (.f64 (sqrt.f64 2) x))
(neg.f64 (*.f64 (sqrt.f64 2) x))
(*.f64 (sqrt.f64 2) (neg.f64 x))
(.f64 -1 (.f64 (sqrt.f64 2) x))
(neg.f64 (*.f64 (sqrt.f64 2) x))
(*.f64 (sqrt.f64 2) (neg.f64 x))
(.f64 -1 (.f64 (sqrt.f64 2) x))
(neg.f64 (*.f64 (sqrt.f64 2) x))
(*.f64 (sqrt.f64 2) (neg.f64 x))
(.f64 -1 (.f64 (sqrt.f64 2) x))
(neg.f64 (*.f64 (sqrt.f64 2) x))
(*.f64 (sqrt.f64 2) (neg.f64 x))

localize9.0ms (0.2%)

Local error

Found 1 expressions with local error:

New	Error	Program
✓	0.2b	(.f64 (sqrt.f64 (.f64 2 x)) (sqrt.f64 x))

Compiler

Compiled 19 to 12 computations (36.8% saved)

series2.0ms (0%)

Counts

1 → 12

Calls

3 calls:

Time	Variable		Point	Expression
1.0ms	x	@	-inf	(.f64 (sqrt.f64 (.f64 2 x)) (sqrt.f64 x))
0.0ms	x	@	0	(.f64 (sqrt.f64 (.f64 2 x)) (sqrt.f64 x))
0.0ms	x	@	inf	(.f64 (sqrt.f64 (.f64 2 x)) (sqrt.f64 x))

rewrite44.0ms (0.8%)

Algorithm

1×	batch-egg-rewrite

Rules

597×	`pow1_binary64`
552×	`add-log-exp_binary64`
552×	`log1p-expm1-u_binary64`
552×	`expm1-log1p-u_binary64`
537×	`add-exp-log_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	7	9
1	142	6
2	1593	6

Stop Event

1×	node limit

Counts

1 → 12

Calls

Call 1

Inputs
(.f64 (sqrt.f64 (.f64 2 x)) (sqrt.f64 x))

Outputs

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

simplify18.0ms (0.3%)

Algorithm

1×	egg-herbie

Rules

248×	`fma-def_binary64`
22×	`distribute-rgt-in_binary64`
21×	`associate-l_binary64`
21×	`sub-neg_binary64`
19×	`distribute-lft-in_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	12	100
1	21	100
2	53	100
3	104	100
4	119	100
5	167	100
6	239	100
7	276	100
8	322	100
9	499	100
10	527	100

Stop Event

1×

saturated

Counts

24 → 15

Calls

Call 1

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

Outputs
(*.f64 (sqrt.f64 2) x)
(*.f64 (sqrt.f64 2) x)
(*.f64 (sqrt.f64 2) x)
(*.f64 (sqrt.f64 2) x)
(*.f64 (sqrt.f64 2) x)
(*.f64 (sqrt.f64 2) x)
(*.f64 (sqrt.f64 2) x)
(*.f64 (sqrt.f64 2) x)
(.f64 -1 (.f64 (sqrt.f64 -1) (*.f64 (sqrt.f64 -2) x)))
(neg.f64 (.f64 (.f64 (sqrt.f64 -1) (sqrt.f64 -2)) x))
(.f64 (.f64 (sqrt.f64 -1) (sqrt.f64 -2)) (neg.f64 x))
(.f64 -1 (.f64 (sqrt.f64 -1) (*.f64 (sqrt.f64 -2) x)))
(neg.f64 (.f64 (.f64 (sqrt.f64 -1) (sqrt.f64 -2)) x))
(.f64 (.f64 (sqrt.f64 -1) (sqrt.f64 -2)) (neg.f64 x))
(.f64 -1 (.f64 (sqrt.f64 -1) (*.f64 (sqrt.f64 -2) x)))
(neg.f64 (.f64 (.f64 (sqrt.f64 -1) (sqrt.f64 -2)) x))
(.f64 (.f64 (sqrt.f64 -1) (sqrt.f64 -2)) (neg.f64 x))
(.f64 -1 (.f64 (sqrt.f64 -1) (*.f64 (sqrt.f64 -2) x)))
(neg.f64 (.f64 (.f64 (sqrt.f64 -1) (sqrt.f64 -2)) x))
(.f64 (.f64 (sqrt.f64 -1) (sqrt.f64 -2)) (neg.f64 x))

localize12.0ms (0.2%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.0b	(*.f64 4 (pow.f64 x 4))
✓	11.0b	(sqrt.f64 (*.f64 4 (pow.f64 x 4)))
✓	32.7b	(sqrt.f64 (sqrt.f64 (*.f64 4 (pow.f64 x 4))))

Compiler

Compiled 24 to 19 computations (20.8% saved)

series127.0ms (2.2%)

Counts

3 → 24

Calls

9 calls:

Time	Variable		Point	Expression
124.0ms	x	@	inf	(*.f64 4 (pow.f64 x 4))
1.0ms	x	@	0	(*.f64 4 (pow.f64 x 4))
0.0ms	x	@	0	(sqrt.f64 (sqrt.f64 (*.f64 4 (pow.f64 x 4))))
0.0ms	x	@	inf	(sqrt.f64 (sqrt.f64 (*.f64 4 (pow.f64 x 4))))
0.0ms	x	@	-inf	(*.f64 4 (pow.f64 x 4))

rewrite66.0ms (1.1%)

Algorithm

1×	batch-egg-rewrite

Rules

572×	`pow1_binary64`
531×	`add-log-exp_binary64`
531×	`log1p-expm1-u_binary64`
531×	`expm1-log1p-u_binary64`
515×	`add-exp-log_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	7	27
1	145	20
2	1583	20

Stop Event

1×	node limit

Counts

3 → 63

Calls

Call 1

Inputs
(sqrt.f64 (sqrt.f64 (*.f64 4 (pow.f64 x 4))))
(sqrt.f64 (*.f64 4 (pow.f64 x 4)))
(*.f64 4 (pow.f64 x 4))

Outputs

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

((#(struct:change #<rule egg-rr> (2) ((x -.f64 (+.f64 1 (*.f64 (*.f64 x x) 2)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (*.f64 (*.f64 x x) 2) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (*.f64 (sqrt.f64 2) x) (*.f64 (sqrt.f64 2) x))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 1 (*.f64 (*.f64 x x) 2))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (*.f64 x x) 2)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (*.f64 x x) (pow.f64 4 1/2))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 (*.f64 (*.f64 x x) 2)) (cbrt.f64 (*.f64 4 (pow.f64 x 4))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 (*.f64 (*.f64 x x) 2)) (*.f64 (cbrt.f64 (*.f64 (sqrt.f64 2) x)) (*.f64 (sqrt.f64 2) x)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 (*.f64 4 (pow.f64 x 4))) (cbrt.f64 (*.f64 (*.f64 x x) 2)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 2 (*.f64 x x))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (sqrt.f64 (*.f64 (sqrt.f64 2) x)) (*.f64 (sqrt.f64 (*.f64 (sqrt.f64 2) x)) (*.f64 (sqrt.f64 2) x)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (*.f64 (*.f64 (sqrt.f64 2) x) (sqrt.f64 (*.f64 (sqrt.f64 2) x))) (sqrt.f64 (*.f64 (sqrt.f64 2) x)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (sqrt.f64 (cbrt.f64 (*.f64 16 (pow.f64 x 8)))) (sqrt.f64 (cbrt.f64 (*.f64 4 (pow.f64 x 4)))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 4 1/2) (*.f64 x x))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 1 1/2) (*.f64 (*.f64 x x) 2))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (cbrt.f64 (*.f64 16 (pow.f64 x 8))) 1/2) (pow.f64 (cbrt.f64 (*.f64 4 (pow.f64 x 4))) 1/2))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (*.f64 (*.f64 (sqrt.f64 2) x) (cbrt.f64 (*.f64 (*.f64 x x) 2))) (cbrt.f64 (*.f64 (sqrt.f64 2) x)))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (*.f64 4 (pow.f64 x 4)) 1/2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (*.f64 (*.f64 x x) 2) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (*.f64 (sqrt.f64 2) x) 2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (*.f64 4 (pow.f64 x 4)) 3/2) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (cbrt.f64 (*.f64 (*.f64 x x) 2)) 3)))) (#(struct:change #<rule egg-rr> (2) ((x fabs.f64 (*.f64 (*.f64 x x) 2))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (pow.f64 (exp.f64 2) (*.f64 x x)))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (pow.f64 (*.f64 4 (pow.f64 x 4)) 3/2))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (*.f64 (*.f64 x x) 2)))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (*.f64 (*.f64 x x) 2)))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (log.f64 (*.f64 (*.f64 x x) 2)))))))

((#(struct:change #<rule egg-rr> (2) ((x -.f64 (+.f64 1 (*.f64 4 (pow.f64 x 4))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (*.f64 4 (pow.f64 x 4)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (*.f64 (*.f64 x x) 2) 2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (*.f64 16 (pow.f64 x 8)) 1/2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (*.f64 4 (pow.f64 x 4)) 3) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (cbrt.f64 (*.f64 4 (pow.f64 x 4))) 3)))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f64 (*.f64 16 (pow.f64 x 8)))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (pow.f64 (exp.f64 4) (pow.f64 x 4)))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (pow.f64 (*.f64 4 (pow.f64 x 4)) 3))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (*.f64 4 (pow.f64 x 4))))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (*.f64 4 (pow.f64 x 4))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (log.f64 (*.f64 4 (pow.f64 x 4))))))))

simplify83.0ms (1.4%)

Algorithm

1×	egg-herbie

Rules

964×	`fma-def_binary64`
402×	`distribute-rgt-neg-out_binary64`
365×	`fma-neg_binary64`
337×	`distribute-rgt-neg-in_binary64`
318×	`fabs-mul_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	9	164
1	20	164
2	43	164
3	83	164
4	205	164
5	632	164
6	988	164
7	1635	164
8	2038	164
9	2907	164
10	3744	164
11	4611	164
12	5738	164

Stop Event

1×	node limit

Counts

87 → 66

Calls

Call 1

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

Outputs
(*.f64 (sqrt.f64 2) x)
(*.f64 (sqrt.f64 2) x)
(*.f64 (sqrt.f64 2) x)
(*.f64 (sqrt.f64 2) x)
(*.f64 (sqrt.f64 2) x)
(*.f64 (sqrt.f64 2) x)
(*.f64 (sqrt.f64 2) x)
(*.f64 (sqrt.f64 2) x)
(.f64 -1 (.f64 (sqrt.f64 2) x))
(neg.f64 (*.f64 (sqrt.f64 2) x))
(*.f64 (sqrt.f64 2) (neg.f64 x))
(*.f64 x (neg.f64 (sqrt.f64 2)))
(.f64 -1 (.f64 (sqrt.f64 2) x))
(neg.f64 (*.f64 (sqrt.f64 2) x))
(*.f64 (sqrt.f64 2) (neg.f64 x))
(*.f64 x (neg.f64 (sqrt.f64 2)))
(.f64 -1 (.f64 (sqrt.f64 2) x))
(neg.f64 (*.f64 (sqrt.f64 2) x))
(*.f64 (sqrt.f64 2) (neg.f64 x))
(*.f64 x (neg.f64 (sqrt.f64 2)))
(.f64 -1 (.f64 (sqrt.f64 2) x))
(neg.f64 (*.f64 (sqrt.f64 2) x))
(*.f64 (sqrt.f64 2) (neg.f64 x))
(*.f64 x (neg.f64 (sqrt.f64 2)))
(*.f64 2 (pow.f64 x 2))
(.f64 2 (.f64 x x))
(*.f64 2 (pow.f64 x 2))
(.f64 2 (.f64 x x))
(*.f64 2 (pow.f64 x 2))
(.f64 2 (.f64 x x))
(*.f64 2 (pow.f64 x 2))
(.f64 2 (.f64 x x))
(*.f64 2 (pow.f64 x 2))
(.f64 2 (.f64 x x))
(*.f64 2 (pow.f64 x 2))
(.f64 2 (.f64 x x))
(*.f64 2 (pow.f64 x 2))
(.f64 2 (.f64 x x))
(*.f64 2 (pow.f64 x 2))
(.f64 2 (.f64 x x))
(*.f64 2 (pow.f64 x 2))
(.f64 2 (.f64 x x))
(*.f64 2 (pow.f64 x 2))
(.f64 2 (.f64 x x))
(*.f64 2 (pow.f64 x 2))
(.f64 2 (.f64 x x))
(*.f64 2 (pow.f64 x 2))
(.f64 2 (.f64 x x))

localize13.0ms (0.2%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.5b	(*.f64 x (sqrt.f64 2))
✓	0.6b	(cbrt.f64 (*.f64 x (sqrt.f64 2)))
✓	0.7b	(pow.f64 (cbrt.f64 (*.f64 x (sqrt.f64 2))) 3)

Compiler

Compiled 22 to 18 computations (18.2% saved)

series6.0ms (0.1%)

Counts

3 → 12

Calls

9 calls:

Time	Variable		Point	Expression
2.0ms	x	@	-inf	(pow.f64 (cbrt.f64 (*.f64 x (sqrt.f64 2))) 3)
1.0ms	x	@	0	(pow.f64 (cbrt.f64 (*.f64 x (sqrt.f64 2))) 3)
1.0ms	x	@	inf	(pow.f64 (cbrt.f64 (*.f64 x (sqrt.f64 2))) 3)
1.0ms	x	@	-inf	(cbrt.f64 (*.f64 x (sqrt.f64 2)))
0.0ms	x	@	inf	(cbrt.f64 (*.f64 x (sqrt.f64 2)))

rewrite60.0ms (1%)

Algorithm

1×	batch-egg-rewrite

Rules

575×	`pow1_binary64`
543×	`add-log-exp_binary64`
542×	`log1p-expm1-u_binary64`
542×	`expm1-log1p-u_binary64`
530×	`add-exp-log_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	8	20
1	168	20
2	1578	20

Stop Event

1×	node limit

Counts

3 → 64

Calls

Call 1

Inputs
(pow.f64 (cbrt.f64 (*.f64 x (sqrt.f64 2))) 3)
(cbrt.f64 (*.f64 x (sqrt.f64 2)))
(*.f64 x (sqrt.f64 2))

Outputs

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

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

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

simplify8.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

1×	`*-commutative_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	5	72
1	6	72

Stop Event

1×

saturated

Counts

76 → 57

Calls

Call 1

Inputs
(*.f64 (sqrt.f64 2) x)
(*.f64 (sqrt.f64 2) x)
(*.f64 (sqrt.f64 2) x)
(*.f64 (sqrt.f64 2) x)
(*.f64 (sqrt.f64 2) x)
(*.f64 (sqrt.f64 2) x)
(*.f64 (sqrt.f64 2) x)
(*.f64 (sqrt.f64 2) x)
(*.f64 (sqrt.f64 2) x)
(*.f64 (sqrt.f64 2) x)
(*.f64 (sqrt.f64 2) x)
(*.f64 (sqrt.f64 2) x)

Outputs
(*.f64 (sqrt.f64 2) x)
(*.f64 (sqrt.f64 2) x)
(*.f64 (sqrt.f64 2) x)
(*.f64 (sqrt.f64 2) x)
(*.f64 (sqrt.f64 2) x)
(*.f64 (sqrt.f64 2) x)
(*.f64 (sqrt.f64 2) x)
(*.f64 (sqrt.f64 2) x)
(*.f64 (sqrt.f64 2) x)
(*.f64 (sqrt.f64 2) x)
(*.f64 (sqrt.f64 2) x)
(*.f64 (sqrt.f64 2) x)

eval48.0ms (0.8%)

Compiler: Compiled 1515 to 1197 computations (21% saved)

prune35.0ms (0.6%)

Pruning

7 alts after pruning (3 fresh and 4 done)

	Pruned	Kept	Total
New	159	3	162
Fresh	1	0	1
Picked	1	0	1
Done	1	4	5
Total	162	7	169

Error

0.1b

Counts

169 → 7

Alt Table

Click to see full alt table

Status	Error	Program
✓	32.0b	(*.f64 x (neg.f64 (sqrt.f64 2)))
✓	31.0b	(*.f64 (sqrt.f64 2) x)
✓	34.1b	(sqrt.f64 (.f64 2 (.f64 x x)))
✓	31.7b	(.f64 (sqrt.f64 (.f64 2 x)) (sqrt.f64 x))
▶	30.9b	(.f64 (pow.f64 2 1/4) (.f64 (pow.f64 2 1/4) x))
▶	45.6b	(pow.f64 (*.f64 4 (pow.f64 x 4)) 1/4)
▶	51.7b	(cbrt.f64 (.f64 (.f64 (.f64 x (neg.f64 (sqrt.f64 2))) (.f64 x (neg.f64 (sqrt.f64 2)))) (*.f64 x (neg.f64 (sqrt.f64 2)))))

Compiler

Compiled 63 to 52 computations (17.5% saved)

localize28.0ms (0.5%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.1b	(.f64 (.f64 (.f64 x (neg.f64 (sqrt.f64 2))) (.f64 x (neg.f64 (sqrt.f64 2)))) (*.f64 x (neg.f64 (sqrt.f64 2))))
✓	0.2b	(.f64 (.f64 x (neg.f64 (sqrt.f64 2))) (*.f64 x (neg.f64 (sqrt.f64 2))))
	0.5b	(*.f64 x (neg.f64 (sqrt.f64 2)))
✓	40.6b	(cbrt.f64 (.f64 (.f64 (.f64 x (neg.f64 (sqrt.f64 2))) (.f64 x (neg.f64 (sqrt.f64 2)))) (*.f64 x (neg.f64 (sqrt.f64 2)))))

Compiler

Compiled 59 to 49 computations (16.9% saved)

series8.0ms (0.1%)

Counts

3 → 36

Calls

9 calls:

Time	Variable		Point	Expression
2.0ms	x	@	0	(cbrt.f64 (.f64 (.f64 (.f64 x (neg.f64 (sqrt.f64 2))) (.f64 x (neg.f64 (sqrt.f64 2)))) (*.f64 x (neg.f64 (sqrt.f64 2)))))
2.0ms	x	@	0	(.f64 (.f64 x (neg.f64 (sqrt.f64 2))) (*.f64 x (neg.f64 (sqrt.f64 2))))
1.0ms	x	@	0	(.f64 (.f64 (.f64 x (neg.f64 (sqrt.f64 2))) (.f64 x (neg.f64 (sqrt.f64 2)))) (*.f64 x (neg.f64 (sqrt.f64 2))))
1.0ms	x	@	inf	(cbrt.f64 (.f64 (.f64 (.f64 x (neg.f64 (sqrt.f64 2))) (.f64 x (neg.f64 (sqrt.f64 2)))) (*.f64 x (neg.f64 (sqrt.f64 2)))))
1.0ms	x	@	inf	(.f64 (.f64 (.f64 x (neg.f64 (sqrt.f64 2))) (.f64 x (neg.f64 (sqrt.f64 2)))) (*.f64 x (neg.f64 (sqrt.f64 2))))

rewrite246.0ms (4.2%)

Algorithm

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

Rules

88×	`associate-r_binary64`
87×	`associate-r_binary64`
87×	`associate-r_binary64`
82×	`add-sqr-sqrt_binary64`
82×	`add-sqr-sqrt_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	9	30
1	185	30
2	2148	30
0	9	8
1	185	8
2	2148	8
0	9	8
0	7	11
1	149	11
2	1827	11
0	7	11
0	8	11
1	169	11
2	2095	11
0	8	11

Stop Event

1×	iter limit
1×	unsound
1×	iter limit
1×	unsound
1×	iter limit
1×	unsound
1×	unsound

Counts

3 → 27

Calls

Call 1

Inputs

(cbrt.f64 (*.f64 (*.f64 (*.f64 x (neg.f64 (sqrt.f64 2))) (*.f64 x (neg.f64 (sqrt.f64 2)))) (*.f64 x (neg.f64 (sqrt.f64 2)))))

(*.f64 (*.f64 x (neg.f64 (sqrt.f64 2))) (*.f64 x (neg.f64 (sqrt.f64 2))))

(*.f64 (*.f64 (*.f64 x (neg.f64 (sqrt.f64 2))) (*.f64 x (neg.f64 (sqrt.f64 2)))) (*.f64 x (neg.f64 (sqrt.f64 2))))

Outputs

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

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

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

simplify94.0ms (1.6%)

Algorithm

1×	egg-herbie

Rules

1004×	`fma-def_binary64`
883×	`distribute-rgt-neg-in_binary64`
869×	`distribute-lft-neg-in_binary64`
545×	`fma-neg_binary64`
536×	`unswap-sqr_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	18	432
1	53	348
2	158	348
3	616	348
4	1289	348
5	2875	348
6	4568	348
7	6916	348
8	7881	348

Stop Event

1×	node limit

Counts

63 → 34

Calls

Call 1

Inputs
(.f64 (sqrt.f64 2) (.f64 (cbrt.f64 -1) x))
(.f64 (sqrt.f64 2) (.f64 (cbrt.f64 -1) x))
(.f64 (sqrt.f64 2) (.f64 (cbrt.f64 -1) x))
(.f64 (sqrt.f64 2) (.f64 (cbrt.f64 -1) x))
(.f64 (sqrt.f64 2) (.f64 (cbrt.f64 -1) x))
(.f64 (sqrt.f64 2) (.f64 (cbrt.f64 -1) x))
(.f64 (sqrt.f64 2) (.f64 (cbrt.f64 -1) x))
(.f64 (sqrt.f64 2) (.f64 (cbrt.f64 -1) x))
(.f64 -1 (.f64 (sqrt.f64 2) x))
(.f64 -1 (.f64 (sqrt.f64 2) x))
(.f64 -1 (.f64 (sqrt.f64 2) x))
(.f64 -1 (.f64 (sqrt.f64 2) x))
(*.f64 (pow.f64 (sqrt.f64 2) 2) (pow.f64 x 2))
(*.f64 (pow.f64 (sqrt.f64 2) 2) (pow.f64 x 2))
(*.f64 (pow.f64 (sqrt.f64 2) 2) (pow.f64 x 2))
(*.f64 (pow.f64 (sqrt.f64 2) 2) (pow.f64 x 2))
(*.f64 (pow.f64 (sqrt.f64 2) 2) (pow.f64 x 2))
(*.f64 (pow.f64 (sqrt.f64 2) 2) (pow.f64 x 2))
(*.f64 (pow.f64 (sqrt.f64 2) 2) (pow.f64 x 2))
(*.f64 (pow.f64 (sqrt.f64 2) 2) (pow.f64 x 2))
(*.f64 (pow.f64 (sqrt.f64 2) 2) (pow.f64 x 2))
(*.f64 (pow.f64 (sqrt.f64 2) 2) (pow.f64 x 2))
(*.f64 (pow.f64 (sqrt.f64 2) 2) (pow.f64 x 2))
(*.f64 (pow.f64 (sqrt.f64 2) 2) (pow.f64 x 2))
(.f64 -1 (.f64 (pow.f64 (sqrt.f64 2) 3) (pow.f64 x 3)))
(.f64 -1 (.f64 (pow.f64 (sqrt.f64 2) 3) (pow.f64 x 3)))
(.f64 -1 (.f64 (pow.f64 (sqrt.f64 2) 3) (pow.f64 x 3)))
(.f64 -1 (.f64 (pow.f64 (sqrt.f64 2) 3) (pow.f64 x 3)))
(.f64 -1 (.f64 (pow.f64 (sqrt.f64 2) 3) (pow.f64 x 3)))
(.f64 -1 (.f64 (pow.f64 (sqrt.f64 2) 3) (pow.f64 x 3)))
(.f64 -1 (.f64 (pow.f64 (sqrt.f64 2) 3) (pow.f64 x 3)))
(.f64 -1 (.f64 (pow.f64 (sqrt.f64 2) 3) (pow.f64 x 3)))
(.f64 -1 (.f64 (pow.f64 (sqrt.f64 2) 3) (pow.f64 x 3)))
(.f64 -1 (.f64 (pow.f64 (sqrt.f64 2) 3) (pow.f64 x 3)))
(.f64 -1 (.f64 (pow.f64 (sqrt.f64 2) 3) (pow.f64 x 3)))
(.f64 -1 (.f64 (pow.f64 (sqrt.f64 2) 3) (pow.f64 x 3)))

Outputs
(.f64 (sqrt.f64 2) (.f64 (cbrt.f64 -1) x))
(.f64 (sqrt.f64 2) (.f64 (cbrt.f64 -1) x))
(.f64 (sqrt.f64 2) (.f64 (cbrt.f64 -1) x))
(.f64 (sqrt.f64 2) (.f64 (cbrt.f64 -1) x))
(.f64 (sqrt.f64 2) (.f64 (cbrt.f64 -1) x))
(.f64 (sqrt.f64 2) (.f64 (cbrt.f64 -1) x))
(.f64 (sqrt.f64 2) (.f64 (cbrt.f64 -1) x))
(.f64 (sqrt.f64 2) (.f64 (cbrt.f64 -1) x))
(.f64 -1 (.f64 (sqrt.f64 2) x))
(neg.f64 (*.f64 (sqrt.f64 2) x))
(*.f64 (sqrt.f64 2) (neg.f64 x))
(.f64 -1 (.f64 (sqrt.f64 2) x))
(neg.f64 (*.f64 (sqrt.f64 2) x))
(*.f64 (sqrt.f64 2) (neg.f64 x))
(.f64 -1 (.f64 (sqrt.f64 2) x))
(neg.f64 (*.f64 (sqrt.f64 2) x))
(*.f64 (sqrt.f64 2) (neg.f64 x))
(.f64 -1 (.f64 (sqrt.f64 2) x))
(neg.f64 (*.f64 (sqrt.f64 2) x))
(*.f64 (sqrt.f64 2) (neg.f64 x))
(*.f64 (pow.f64 (sqrt.f64 2) 2) (pow.f64 x 2))
(.f64 (pow.f64 (sqrt.f64 2) 2) (.f64 x x))
(.f64 x (.f64 x 2))
(.f64 2 (.f64 x x))
(.f64 x (.f64 2 x))
(*.f64 (pow.f64 (sqrt.f64 2) 2) (pow.f64 x 2))
(.f64 (pow.f64 (sqrt.f64 2) 2) (.f64 x x))
(.f64 x (.f64 x 2))
(.f64 2 (.f64 x x))
(.f64 x (.f64 2 x))
(*.f64 (pow.f64 (sqrt.f64 2) 2) (pow.f64 x 2))
(.f64 (pow.f64 (sqrt.f64 2) 2) (.f64 x x))
(.f64 x (.f64 x 2))
(.f64 2 (.f64 x x))
(.f64 x (.f64 2 x))
(*.f64 (pow.f64 (sqrt.f64 2) 2) (pow.f64 x 2))
(.f64 (pow.f64 (sqrt.f64 2) 2) (.f64 x x))
(.f64 x (.f64 x 2))
(.f64 2 (.f64 x x))
(.f64 x (.f64 2 x))
(*.f64 (pow.f64 (sqrt.f64 2) 2) (pow.f64 x 2))
(.f64 (pow.f64 (sqrt.f64 2) 2) (.f64 x x))
(.f64 x (.f64 x 2))
(.f64 2 (.f64 x x))
(.f64 x (.f64 2 x))
(*.f64 (pow.f64 (sqrt.f64 2) 2) (pow.f64 x 2))
(.f64 (pow.f64 (sqrt.f64 2) 2) (.f64 x x))
(.f64 x (.f64 x 2))
(.f64 2 (.f64 x x))
(.f64 x (.f64 2 x))
(*.f64 (pow.f64 (sqrt.f64 2) 2) (pow.f64 x 2))
(.f64 (pow.f64 (sqrt.f64 2) 2) (.f64 x x))
(.f64 x (.f64 x 2))
(.f64 2 (.f64 x x))
(.f64 x (.f64 2 x))
(*.f64 (pow.f64 (sqrt.f64 2) 2) (pow.f64 x 2))
(.f64 (pow.f64 (sqrt.f64 2) 2) (.f64 x x))
(.f64 x (.f64 x 2))
(.f64 2 (.f64 x x))
(.f64 x (.f64 2 x))
(*.f64 (pow.f64 (sqrt.f64 2) 2) (pow.f64 x 2))
(.f64 (pow.f64 (sqrt.f64 2) 2) (.f64 x x))
(.f64 x (.f64 x 2))
(.f64 2 (.f64 x x))
(.f64 x (.f64 2 x))
(*.f64 (pow.f64 (sqrt.f64 2) 2) (pow.f64 x 2))
(.f64 (pow.f64 (sqrt.f64 2) 2) (.f64 x x))
(.f64 x (.f64 x 2))
(.f64 2 (.f64 x x))
(.f64 x (.f64 2 x))
(*.f64 (pow.f64 (sqrt.f64 2) 2) (pow.f64 x 2))
(.f64 (pow.f64 (sqrt.f64 2) 2) (.f64 x x))
(.f64 x (.f64 x 2))
(.f64 2 (.f64 x x))
(.f64 x (.f64 2 x))
(*.f64 (pow.f64 (sqrt.f64 2) 2) (pow.f64 x 2))
(.f64 (pow.f64 (sqrt.f64 2) 2) (.f64 x x))
(.f64 x (.f64 x 2))
(.f64 2 (.f64 x x))
(.f64 x (.f64 2 x))
(.f64 -1 (.f64 (pow.f64 (sqrt.f64 2) 3) (pow.f64 x 3)))
(neg.f64 (*.f64 (pow.f64 (sqrt.f64 2) 3) (pow.f64 x 3)))
(.f64 (pow.f64 x 3) (.f64 -2 (sqrt.f64 2)))
(.f64 (pow.f64 x 3) (.f64 (sqrt.f64 2) -2))
(.f64 (sqrt.f64 2) (.f64 (pow.f64 x 3) -2))
(.f64 -1 (.f64 (pow.f64 (sqrt.f64 2) 3) (pow.f64 x 3)))
(neg.f64 (*.f64 (pow.f64 (sqrt.f64 2) 3) (pow.f64 x 3)))
(.f64 (pow.f64 x 3) (.f64 -2 (sqrt.f64 2)))
(.f64 (pow.f64 x 3) (.f64 (sqrt.f64 2) -2))
(.f64 (sqrt.f64 2) (.f64 (pow.f64 x 3) -2))
(.f64 -1 (.f64 (pow.f64 (sqrt.f64 2) 3) (pow.f64 x 3)))
(neg.f64 (*.f64 (pow.f64 (sqrt.f64 2) 3) (pow.f64 x 3)))
(.f64 (pow.f64 x 3) (.f64 -2 (sqrt.f64 2)))
(.f64 (pow.f64 x 3) (.f64 (sqrt.f64 2) -2))
(.f64 (sqrt.f64 2) (.f64 (pow.f64 x 3) -2))
(.f64 -1 (.f64 (pow.f64 (sqrt.f64 2) 3) (pow.f64 x 3)))
(neg.f64 (*.f64 (pow.f64 (sqrt.f64 2) 3) (pow.f64 x 3)))
(.f64 (pow.f64 x 3) (.f64 -2 (sqrt.f64 2)))
(.f64 (pow.f64 x 3) (.f64 (sqrt.f64 2) -2))
(.f64 (sqrt.f64 2) (.f64 (pow.f64 x 3) -2))
(.f64 -1 (.f64 (pow.f64 (sqrt.f64 2) 3) (pow.f64 x 3)))
(neg.f64 (*.f64 (pow.f64 (sqrt.f64 2) 3) (pow.f64 x 3)))
(.f64 (pow.f64 x 3) (.f64 -2 (sqrt.f64 2)))
(.f64 (pow.f64 x 3) (.f64 (sqrt.f64 2) -2))
(.f64 (sqrt.f64 2) (.f64 (pow.f64 x 3) -2))
(.f64 -1 (.f64 (pow.f64 (sqrt.f64 2) 3) (pow.f64 x 3)))
(neg.f64 (*.f64 (pow.f64 (sqrt.f64 2) 3) (pow.f64 x 3)))
(.f64 (pow.f64 x 3) (.f64 -2 (sqrt.f64 2)))
(.f64 (pow.f64 x 3) (.f64 (sqrt.f64 2) -2))
(.f64 (sqrt.f64 2) (.f64 (pow.f64 x 3) -2))
(.f64 -1 (.f64 (pow.f64 (sqrt.f64 2) 3) (pow.f64 x 3)))
(neg.f64 (*.f64 (pow.f64 (sqrt.f64 2) 3) (pow.f64 x 3)))
(.f64 (pow.f64 x 3) (.f64 -2 (sqrt.f64 2)))
(.f64 (pow.f64 x 3) (.f64 (sqrt.f64 2) -2))
(.f64 (sqrt.f64 2) (.f64 (pow.f64 x 3) -2))
(.f64 -1 (.f64 (pow.f64 (sqrt.f64 2) 3) (pow.f64 x 3)))
(neg.f64 (*.f64 (pow.f64 (sqrt.f64 2) 3) (pow.f64 x 3)))
(.f64 (pow.f64 x 3) (.f64 -2 (sqrt.f64 2)))
(.f64 (pow.f64 x 3) (.f64 (sqrt.f64 2) -2))
(.f64 (sqrt.f64 2) (.f64 (pow.f64 x 3) -2))
(.f64 -1 (.f64 (pow.f64 (sqrt.f64 2) 3) (pow.f64 x 3)))
(neg.f64 (*.f64 (pow.f64 (sqrt.f64 2) 3) (pow.f64 x 3)))
(.f64 (pow.f64 x 3) (.f64 -2 (sqrt.f64 2)))
(.f64 (pow.f64 x 3) (.f64 (sqrt.f64 2) -2))
(.f64 (sqrt.f64 2) (.f64 (pow.f64 x 3) -2))
(.f64 -1 (.f64 (pow.f64 (sqrt.f64 2) 3) (pow.f64 x 3)))
(neg.f64 (*.f64 (pow.f64 (sqrt.f64 2) 3) (pow.f64 x 3)))
(.f64 (pow.f64 x 3) (.f64 -2 (sqrt.f64 2)))
(.f64 (pow.f64 x 3) (.f64 (sqrt.f64 2) -2))
(.f64 (sqrt.f64 2) (.f64 (pow.f64 x 3) -2))
(.f64 -1 (.f64 (pow.f64 (sqrt.f64 2) 3) (pow.f64 x 3)))
(neg.f64 (*.f64 (pow.f64 (sqrt.f64 2) 3) (pow.f64 x 3)))
(.f64 (pow.f64 x 3) (.f64 -2 (sqrt.f64 2)))
(.f64 (pow.f64 x 3) (.f64 (sqrt.f64 2) -2))
(.f64 (sqrt.f64 2) (.f64 (pow.f64 x 3) -2))
(.f64 -1 (.f64 (pow.f64 (sqrt.f64 2) 3) (pow.f64 x 3)))
(neg.f64 (*.f64 (pow.f64 (sqrt.f64 2) 3) (pow.f64 x 3)))
(.f64 (pow.f64 x 3) (.f64 -2 (sqrt.f64 2)))
(.f64 (pow.f64 x 3) (.f64 (sqrt.f64 2) -2))
(.f64 (sqrt.f64 2) (.f64 (pow.f64 x 3) -2))

localize12.0ms (0.2%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.2b	(*.f64 (pow.f64 2 1/4) x)
✓	0.3b	(.f64 (pow.f64 2 1/4) (.f64 (pow.f64 2 1/4) x))

Compiler

Compiled 21 to 18 computations (14.3% saved)

series41.0ms (0.7%)

Counts

2 → 12

Calls

6 calls:

Time	Variable		Point	Expression
39.0ms	x	@	0	(*.f64 (pow.f64 2 1/4) x)
1.0ms	x	@	inf	(.f64 (pow.f64 2 1/4) (.f64 (pow.f64 2 1/4) x))
1.0ms	x	@	inf	(*.f64 (pow.f64 2 1/4) x)
0.0ms	x	@	-inf	(*.f64 (pow.f64 2 1/4) x)
0.0ms	x	@	0	(.f64 (pow.f64 2 1/4) (.f64 (pow.f64 2 1/4) x))

rewrite168.0ms (2.9%)

Algorithm

1×	batch-egg-rewrite

Rules

610×	`pow1_binary64`
566×	`add-log-exp_binary64`
566×	`log1p-expm1-u_binary64`
566×	`expm1-log1p-u_binary64`
554×	`add-exp-log_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	7	20
1	148	13
2	1611	13

Stop Event

1×	node limit

Counts

2 → 22

Calls

Call 1

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

Outputs

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

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

simplify7.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

1×	`*-commutative_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	5	72
1	6	72

Stop Event

1×

saturated

Counts

34 → 23

Calls

Call 1

Inputs
(*.f64 (sqrt.f64 2) x)
(*.f64 (sqrt.f64 2) x)
(*.f64 (sqrt.f64 2) x)
(*.f64 (sqrt.f64 2) x)
(*.f64 (sqrt.f64 2) x)
(*.f64 (sqrt.f64 2) x)
(*.f64 (sqrt.f64 2) x)
(*.f64 (sqrt.f64 2) x)
(*.f64 (sqrt.f64 2) x)
(*.f64 (sqrt.f64 2) x)
(*.f64 (sqrt.f64 2) x)
(*.f64 (sqrt.f64 2) x)

Outputs
(*.f64 (sqrt.f64 2) x)
(*.f64 (sqrt.f64 2) x)
(*.f64 (sqrt.f64 2) x)
(*.f64 (sqrt.f64 2) x)
(*.f64 (sqrt.f64 2) x)
(*.f64 (sqrt.f64 2) x)
(*.f64 (sqrt.f64 2) x)
(*.f64 (sqrt.f64 2) x)
(*.f64 (sqrt.f64 2) x)
(*.f64 (sqrt.f64 2) x)
(*.f64 (sqrt.f64 2) x)
(*.f64 (sqrt.f64 2) x)

localize29.0ms (0.5%)

Local error

Found 2 expressions with local error:

New	Error	Program
	0.0b	(*.f64 4 (pow.f64 x 4))
✓	44.0b	(pow.f64 (*.f64 4 (pow.f64 x 4)) 1/4)

Compiler

Compiled 19 to 15 computations (21.1% saved)

series23.0ms (0.4%)

Counts

1 → 12

Calls

3 calls:

Time	Variable		Point	Expression
12.0ms	x	@	0	(pow.f64 (*.f64 4 (pow.f64 x 4)) 1/4)
10.0ms	x	@	inf	(pow.f64 (*.f64 4 (pow.f64 x 4)) 1/4)
0.0ms	x	@	-inf	(pow.f64 (*.f64 4 (pow.f64 x 4)) 1/4)

rewrite77.0ms (1.3%)

Algorithm

1×	batch-egg-rewrite

Rules

611×	`pow1_binary64`
570×	`add-log-exp_binary64`
570×	`log1p-expm1-u_binary64`
570×	`expm1-log1p-u_binary64`
554×	`add-exp-log_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	7	10
1	155	7
2	1685	7

Stop Event

1×	node limit

Counts

1 → 17

Calls

Call 1

Inputs
(pow.f64 (*.f64 4 (pow.f64 x 4)) 1/4)

Outputs

((#(struct:change #<rule egg-rr> (2) ((x -.f64 (+.f64 1 (*.f64 x (pow.f64 4 1/4))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 x (pow.f64 4 1/4))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (*.f64 x (pow.f64 4 1/4)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 1 (*.f64 x (pow.f64 4 1/4)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 (*.f64 x (pow.f64 4 1/4))) (cbrt.f64 (*.f64 (*.f64 x x) 2)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 (*.f64 (*.f64 x x) 2)) (cbrt.f64 (*.f64 x (pow.f64 4 1/4))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 4 1/4) x)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (sqrt.f64 (*.f64 x (pow.f64 4 1/4))) (sqrt.f64 (*.f64 x (pow.f64 4 1/4))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 1 1/4) (*.f64 x (pow.f64 4 1/4)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (cbrt.f64 (*.f64 16 (pow.f64 x 8))) 1/4) (pow.f64 (cbrt.f64 (*.f64 4 (pow.f64 x 4))) 1/4))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (*.f64 (*.f64 x x) 2) 1/4) (pow.f64 (*.f64 (*.f64 x x) 2) 1/4))))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f64 (*.f64 (*.f64 x x) 2))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (pow.f64 (exp.f64 (pow.f64 4 1/4)) x))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (pow.f64 (*.f64 x (pow.f64 4 1/4)) 3))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (*.f64 x (pow.f64 4 1/4))))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (*.f64 x (pow.f64 4 1/4))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (log.f64 (*.f64 x (pow.f64 4 1/4))))))))

simplify53.0ms (0.9%)

Algorithm

1×	egg-herbie

Rules

786×	`fma-neg_binary64`
552×	`associate-/l*_binary64`
380×	`exp-sum_binary64`
358×	`fma-def_binary64`
294×	`exp-prod_binary64`

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	25	192
1	61	168
2	146	120
3	309	84
4	714	84
5	2131	84
6	6354	84

Stop Event

1×	node limit

Counts

29 → 20

Calls

Call 1

Inputs
(exp.f64 (.f64 1/4 (+.f64 (log.f64 4) (.f64 4 (log.f64 x)))))
(exp.f64 (.f64 1/4 (+.f64 (log.f64 4) (.f64 4 (log.f64 x)))))
(exp.f64 (.f64 1/4 (+.f64 (log.f64 4) (.f64 4 (log.f64 x)))))
(exp.f64 (.f64 1/4 (+.f64 (log.f64 4) (.f64 4 (log.f64 x)))))
(exp.f64 (.f64 1/4 (+.f64 (.f64 -4 (log.f64 (/.f64 1 x))) (log.f64 4))))
(exp.f64 (.f64 1/4 (+.f64 (.f64 -4 (log.f64 (/.f64 1 x))) (log.f64 4))))
(exp.f64 (.f64 1/4 (+.f64 (.f64 -4 (log.f64 (/.f64 1 x))) (log.f64 4))))
(exp.f64 (.f64 1/4 (+.f64 (.f64 -4 (log.f64 (/.f64 1 x))) (log.f64 4))))
(exp.f64 (.f64 1/4 (+.f64 (.f64 -4 (log.f64 (/.f64 -1 x))) (log.f64 4))))
(exp.f64 (.f64 1/4 (+.f64 (.f64 -4 (log.f64 (/.f64 -1 x))) (log.f64 4))))
(exp.f64 (.f64 1/4 (+.f64 (.f64 -4 (log.f64 (/.f64 -1 x))) (log.f64 4))))
(exp.f64 (.f64 1/4 (+.f64 (.f64 -4 (log.f64 (/.f64 -1 x))) (log.f64 4))))

Outputs
(exp.f64 (.f64 1/4 (+.f64 (log.f64 4) (.f64 4 (log.f64 x)))))
(pow.f64 (exp.f64 1/4) (+.f64 (log.f64 4) (*.f64 4 (log.f64 x))))
(pow.f64 (exp.f64 1/4) (fma.f64 4 (log.f64 x) (log.f64 4)))
(*.f64 (pow.f64 4 1/4) (pow.f64 x 1))
(*.f64 (pow.f64 4 1/4) x)
(exp.f64 (.f64 1/4 (+.f64 (log.f64 4) (.f64 4 (log.f64 x)))))
(pow.f64 (exp.f64 1/4) (+.f64 (log.f64 4) (*.f64 4 (log.f64 x))))
(pow.f64 (exp.f64 1/4) (fma.f64 4 (log.f64 x) (log.f64 4)))
(*.f64 (pow.f64 4 1/4) (pow.f64 x 1))
(*.f64 (pow.f64 4 1/4) x)
(exp.f64 (.f64 1/4 (+.f64 (log.f64 4) (.f64 4 (log.f64 x)))))
(pow.f64 (exp.f64 1/4) (+.f64 (log.f64 4) (*.f64 4 (log.f64 x))))
(pow.f64 (exp.f64 1/4) (fma.f64 4 (log.f64 x) (log.f64 4)))
(*.f64 (pow.f64 4 1/4) (pow.f64 x 1))
(*.f64 (pow.f64 4 1/4) x)
(exp.f64 (.f64 1/4 (+.f64 (log.f64 4) (.f64 4 (log.f64 x)))))
(pow.f64 (exp.f64 1/4) (+.f64 (log.f64 4) (*.f64 4 (log.f64 x))))
(pow.f64 (exp.f64 1/4) (fma.f64 4 (log.f64 x) (log.f64 4)))
(*.f64 (pow.f64 4 1/4) (pow.f64 x 1))
(*.f64 (pow.f64 4 1/4) x)
(exp.f64 (.f64 1/4 (+.f64 (.f64 -4 (log.f64 (/.f64 1 x))) (log.f64 4))))
(pow.f64 (exp.f64 1/4) (+.f64 (log.f64 4) (*.f64 4 (log.f64 x))))
(pow.f64 (exp.f64 1/4) (fma.f64 4 (log.f64 x) (log.f64 4)))
(*.f64 (pow.f64 4 1/4) (pow.f64 x 1))
(*.f64 (pow.f64 4 1/4) x)
(exp.f64 (.f64 1/4 (+.f64 (.f64 -4 (log.f64 (/.f64 1 x))) (log.f64 4))))
(pow.f64 (exp.f64 1/4) (+.f64 (log.f64 4) (*.f64 4 (log.f64 x))))
(pow.f64 (exp.f64 1/4) (fma.f64 4 (log.f64 x) (log.f64 4)))
(*.f64 (pow.f64 4 1/4) (pow.f64 x 1))
(*.f64 (pow.f64 4 1/4) x)
(exp.f64 (.f64 1/4 (+.f64 (.f64 -4 (log.f64 (/.f64 1 x))) (log.f64 4))))
(pow.f64 (exp.f64 1/4) (+.f64 (log.f64 4) (*.f64 4 (log.f64 x))))
(pow.f64 (exp.f64 1/4) (fma.f64 4 (log.f64 x) (log.f64 4)))
(*.f64 (pow.f64 4 1/4) (pow.f64 x 1))
(*.f64 (pow.f64 4 1/4) x)
(exp.f64 (.f64 1/4 (+.f64 (.f64 -4 (log.f64 (/.f64 1 x))) (log.f64 4))))
(pow.f64 (exp.f64 1/4) (+.f64 (log.f64 4) (*.f64 4 (log.f64 x))))
(pow.f64 (exp.f64 1/4) (fma.f64 4 (log.f64 x) (log.f64 4)))
(*.f64 (pow.f64 4 1/4) (pow.f64 x 1))
(*.f64 (pow.f64 4 1/4) x)
(exp.f64 (.f64 1/4 (+.f64 (.f64 -4 (log.f64 (/.f64 -1 x))) (log.f64 4))))
(pow.f64 (exp.f64 1/4) (+.f64 (log.f64 4) (*.f64 4 (log.f64 x))))
(pow.f64 (exp.f64 1/4) (fma.f64 4 (log.f64 x) (log.f64 4)))
(*.f64 (pow.f64 4 1/4) (pow.f64 x 1))
(*.f64 (pow.f64 4 1/4) x)
(exp.f64 (.f64 1/4 (+.f64 (.f64 -4 (log.f64 (/.f64 -1 x))) (log.f64 4))))
(pow.f64 (exp.f64 1/4) (+.f64 (log.f64 4) (*.f64 4 (log.f64 x))))
(pow.f64 (exp.f64 1/4) (fma.f64 4 (log.f64 x) (log.f64 4)))
(*.f64 (pow.f64 4 1/4) (pow.f64 x 1))
(*.f64 (pow.f64 4 1/4) x)
(exp.f64 (.f64 1/4 (+.f64 (.f64 -4 (log.f64 (/.f64 -1 x))) (log.f64 4))))
(pow.f64 (exp.f64 1/4) (+.f64 (log.f64 4) (*.f64 4 (log.f64 x))))
(pow.f64 (exp.f64 1/4) (fma.f64 4 (log.f64 x) (log.f64 4)))
(*.f64 (pow.f64 4 1/4) (pow.f64 x 1))
(*.f64 (pow.f64 4 1/4) x)
(exp.f64 (.f64 1/4 (+.f64 (.f64 -4 (log.f64 (/.f64 -1 x))) (log.f64 4))))
(pow.f64 (exp.f64 1/4) (+.f64 (log.f64 4) (*.f64 4 (log.f64 x))))
(pow.f64 (exp.f64 1/4) (fma.f64 4 (log.f64 x) (log.f64 4)))
(*.f64 (pow.f64 4 1/4) (pow.f64 x 1))
(*.f64 (pow.f64 4 1/4) x)

eval59.0ms (1%)

Compiler: Compiled 1453 to 1236 computations (14.9% saved)

prune25.0ms (0.4%)

Pruning

11 alts after pruning (5 fresh and 6 done)

	Pruned	Kept	Total
New	111	5	116
Fresh	0	0	0
Picked	0	1	1
Done	1	5	6
Total	112	11	123

Error

0.1b

Counts

123 → 11

Alt Table

Click to see full alt table

Status	Error	Program
✓	31.7b	(.f64 (sqrt.f64 (.f64 2 x)) (sqrt.f64 x))
▶	32.5b	(.f64 (.f64 (cbrt.f64 (.f64 x (neg.f64 (sqrt.f64 2)))) (cbrt.f64 (.f64 x (neg.f64 (sqrt.f64 2))))) (cbrt.f64 (*.f64 x (neg.f64 (sqrt.f64 2)))))
▶	34.2b	(.f64 (pow.f64 (.f64 (.f64 x x) 2) 1/4) (pow.f64 (.f64 (*.f64 x x) 2) 1/4))
✓	45.6b	(pow.f64 (*.f64 4 (pow.f64 x 4)) 1/4)
▶	51.7b	(cbrt.f64 (.f64 (.f64 x (.f64 2 x)) (.f64 x (neg.f64 (sqrt.f64 2)))))
▶	34.1b	(.f64 (pow.f64 2 1/4) (sqrt.f64 (.f64 (*.f64 x x) (sqrt.f64 2))))
✓	32.0b	(*.f64 x (neg.f64 (sqrt.f64 2)))
✓	31.0b	(*.f64 (sqrt.f64 2) x)
✓	34.1b	(sqrt.f64 (.f64 2 (.f64 x x)))
▶	32.8b	(.f64 (sqrt.f64 (.f64 x (neg.f64 (sqrt.f64 2)))) (sqrt.f64 (*.f64 x (neg.f64 (sqrt.f64 2)))))
✓	30.9b	(.f64 (pow.f64 2 1/4) (.f64 (pow.f64 2 1/4) x))

Compiler

Compiled 196 to 158 computations (19.4% saved)

localize97.0ms (1.7%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.3b	(.f64 (.f64 (cbrt.f64 (.f64 x (neg.f64 (sqrt.f64 2)))) (cbrt.f64 (.f64 x (neg.f64 (sqrt.f64 2))))) (cbrt.f64 (*.f64 x (neg.f64 (sqrt.f64 2)))))
	0.5b	(*.f64 x (neg.f64 (sqrt.f64 2)))
✓	0.5b	(.f64 (cbrt.f64 (.f64 x (neg.f64 (sqrt.f64 2)))) (cbrt.f64 (*.f64 x (neg.f64 (sqrt.f64 2)))))
✓	0.6b	(cbrt.f64 (*.f64 x (neg.f64 (sqrt.f64 2))))

Compiler

Compiled 52 to 44 computations (15.4% saved)

series8.0ms (0.1%)

Counts

3 → 12

Calls

9 calls:

Time	Variable		Point	Expression
3.0ms	x	@	0	(.f64 (.f64 (cbrt.f64 (.f64 x (neg.f64 (sqrt.f64 2)))) (cbrt.f64 (.f64 x (neg.f64 (sqrt.f64 2))))) (cbrt.f64 (*.f64 x (neg.f64 (sqrt.f64 2)))))
1.0ms	x	@	inf	(.f64 (.f64 (cbrt.f64 (.f64 x (neg.f64 (sqrt.f64 2)))) (cbrt.f64 (.f64 x (neg.f64 (sqrt.f64 2))))) (cbrt.f64 (*.f64 x (neg.f64 (sqrt.f64 2)))))
1.0ms	x	@	0	(.f64 (cbrt.f64 (.f64 x (neg.f64 (sqrt.f64 2)))) (cbrt.f64 (*.f64 x (neg.f64 (sqrt.f64 2)))))
1.0ms	x	@	0	(cbrt.f64 (*.f64 x (neg.f64 (sqrt.f64 2))))
1.0ms	x	@	inf	(.f64 (cbrt.f64 (.f64 x (neg.f64 (sqrt.f64 2)))) (cbrt.f64 (*.f64 x (neg.f64 (sqrt.f64 2)))))

rewrite241.0ms (4.2%)

Algorithm

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

Rules

78×	`add-sqr-sqrt_binary64`
78×	`add-sqr-sqrt_binary64`
77×	`add-sqr-sqrt_binary64`
74×	`add-cbrt-cube_binary64`
74×	`add-exp-log_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	9	31
1	180	31
2	1942	31
0	7	10
1	144	10
2	1675	10
0	7	10
0	8	13
1	164	13
2	1875	13
0	8	13
0	9	8
1	180	8
2	1942	8
0	9	8

Stop Event

1×	iter limit
1×	unsound
1×	iter limit
1×	unsound
1×	iter limit
1×	unsound
1×	unsound

Counts

3 → 26

Calls

Call 1

Inputs

(cbrt.f64 (*.f64 x (neg.f64 (sqrt.f64 2))))

(*.f64 (cbrt.f64 (*.f64 x (neg.f64 (sqrt.f64 2)))) (cbrt.f64 (*.f64 x (neg.f64 (sqrt.f64 2)))))

(*.f64 (*.f64 (cbrt.f64 (*.f64 x (neg.f64 (sqrt.f64 2)))) (cbrt.f64 (*.f64 x (neg.f64 (sqrt.f64 2))))) (cbrt.f64 (*.f64 x (neg.f64 (sqrt.f64 2)))))

Outputs

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

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

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

simplify76.0ms (1.3%)

Algorithm

1×	egg-herbie

Rules

38×	`fma-def_binary64`
9×	`sub-neg_binary64`
6×	`+-commutative_binary64`
4×	`*-commutative_binary64`
4×	`distribute-lft-in_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	7	96
1	12	96
2	25	96
3	29	96
4	33	96
5	51	96
6	73	96
7	84	96
8	96	96
9	121	96

Stop Event

1×

saturated

Counts

38 → 28

Calls

Call 1

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

Outputs
(.f64 -1 (.f64 (sqrt.f64 2) x))
(neg.f64 (*.f64 (sqrt.f64 2) x))
(*.f64 (sqrt.f64 2) (neg.f64 x))
(.f64 -1 (.f64 (sqrt.f64 2) x))
(neg.f64 (*.f64 (sqrt.f64 2) x))
(*.f64 (sqrt.f64 2) (neg.f64 x))
(.f64 -1 (.f64 (sqrt.f64 2) x))
(neg.f64 (*.f64 (sqrt.f64 2) x))
(*.f64 (sqrt.f64 2) (neg.f64 x))
(.f64 -1 (.f64 (sqrt.f64 2) x))
(neg.f64 (*.f64 (sqrt.f64 2) x))
(*.f64 (sqrt.f64 2) (neg.f64 x))
(.f64 -1 (.f64 (sqrt.f64 2) x))
(neg.f64 (*.f64 (sqrt.f64 2) x))
(*.f64 (sqrt.f64 2) (neg.f64 x))
(.f64 -1 (.f64 (sqrt.f64 2) x))
(neg.f64 (*.f64 (sqrt.f64 2) x))
(*.f64 (sqrt.f64 2) (neg.f64 x))
(.f64 -1 (.f64 (sqrt.f64 2) x))
(neg.f64 (*.f64 (sqrt.f64 2) x))
(*.f64 (sqrt.f64 2) (neg.f64 x))
(.f64 -1 (.f64 (sqrt.f64 2) x))
(neg.f64 (*.f64 (sqrt.f64 2) x))
(*.f64 (sqrt.f64 2) (neg.f64 x))
(.f64 -1 (.f64 (sqrt.f64 2) x))
(neg.f64 (*.f64 (sqrt.f64 2) x))
(*.f64 (sqrt.f64 2) (neg.f64 x))
(.f64 -1 (.f64 (sqrt.f64 2) x))
(neg.f64 (*.f64 (sqrt.f64 2) x))
(*.f64 (sqrt.f64 2) (neg.f64 x))
(.f64 -1 (.f64 (sqrt.f64 2) x))
(neg.f64 (*.f64 (sqrt.f64 2) x))
(*.f64 (sqrt.f64 2) (neg.f64 x))
(.f64 -1 (.f64 (sqrt.f64 2) x))
(neg.f64 (*.f64 (sqrt.f64 2) x))
(*.f64 (sqrt.f64 2) (neg.f64 x))

localize49.0ms (0.9%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.1b	(.f64 (.f64 x (.f64 2 x)) (.f64 x (neg.f64 (sqrt.f64 2))))
	0.5b	(*.f64 x (neg.f64 (sqrt.f64 2)))
✓	40.6b	(cbrt.f64 (.f64 (.f64 x (.f64 2 x)) (.f64 x (neg.f64 (sqrt.f64 2)))))

Compiler

Compiled 44 to 33 computations (25% saved)

series16.0ms (0.3%)

Counts

2 → 24

Calls

6 calls:

Time	Variable		Point	Expression
8.0ms	x	@	0	(cbrt.f64 (.f64 (.f64 x (.f64 2 x)) (.f64 x (neg.f64 (sqrt.f64 2)))))
4.0ms	x	@	-inf	(cbrt.f64 (.f64 (.f64 x (.f64 2 x)) (.f64 x (neg.f64 (sqrt.f64 2)))))
1.0ms	x	@	inf	(cbrt.f64 (.f64 (.f64 x (.f64 2 x)) (.f64 x (neg.f64 (sqrt.f64 2)))))
1.0ms	x	@	0	(.f64 (.f64 x (.f64 2 x)) (.f64 x (neg.f64 (sqrt.f64 2))))
1.0ms	x	@	inf	(.f64 (.f64 x (.f64 2 x)) (.f64 x (neg.f64 (sqrt.f64 2))))

rewrite204.0ms (3.5%)

Algorithm

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

Rules

111×	`associate-r_binary64`
111×	`associate-r_binary64`
104×	`associate-r_binary64`
101×	`add-sqr-sqrt_binary64`
101×	`add-sqr-sqrt_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	10	36
1	209	36
2	2621	36
0	10	19
1	209	19
2	2621	19
0	10	19
0	9	17
1	190	17
2	2401	17
0	9	17

Stop Event

1×	iter limit
1×	unsound
1×	iter limit
1×	unsound
1×	unsound

Counts

2 → 16

Calls

Call 1

Inputs
(cbrt.f64 (.f64 (.f64 x (.f64 2 x)) (.f64 x (neg.f64 (sqrt.f64 2)))))
(.f64 (.f64 x (.f64 2 x)) (.f64 x (neg.f64 (sqrt.f64 2))))

Outputs

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

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

simplify172.0ms (3%)

Algorithm

1×	egg-herbie

Rules

773×	`fma-neg_binary64`
546×	`distribute-lft-neg-in_binary64`
544×	`distribute-rgt-neg-in_binary64`
460×	`unswap-sqr_binary64`
411×	`fma-def_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	21	308
1	55	308
2	149	308
3	434	308
4	1121	308
5	1594	308
6	2059	308
7	2761	308
8	3984	308
9	5106	308
10	5998	308
11	6711	308
12	7865	308

Stop Event

1×	node limit

Counts

40 → 22

Calls

Call 1

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

Outputs
(.f64 (pow.f64 (.f64 (sqrt.f64 2) 1) 1/3) (*.f64 (cbrt.f64 -2) x))
(.f64 (cbrt.f64 (sqrt.f64 2)) (.f64 (cbrt.f64 -2) x))
(.f64 (pow.f64 (.f64 (sqrt.f64 2) 1) 1/3) (*.f64 (cbrt.f64 -2) x))
(.f64 (cbrt.f64 (sqrt.f64 2)) (.f64 (cbrt.f64 -2) x))
(.f64 (pow.f64 (.f64 (sqrt.f64 2) 1) 1/3) (*.f64 (cbrt.f64 -2) x))
(.f64 (cbrt.f64 (sqrt.f64 2)) (.f64 (cbrt.f64 -2) x))
(.f64 (pow.f64 (.f64 (sqrt.f64 2) 1) 1/3) (*.f64 (cbrt.f64 -2) x))
(.f64 (cbrt.f64 (sqrt.f64 2)) (.f64 (cbrt.f64 -2) x))
(.f64 (pow.f64 (.f64 (sqrt.f64 2) 1) 1/3) (*.f64 (cbrt.f64 -2) x))
(.f64 (cbrt.f64 (sqrt.f64 2)) (.f64 (cbrt.f64 -2) x))
(.f64 (pow.f64 (.f64 (sqrt.f64 2) 1) 1/3) (*.f64 (cbrt.f64 -2) x))
(.f64 (cbrt.f64 (sqrt.f64 2)) (.f64 (cbrt.f64 -2) x))
(.f64 (pow.f64 (.f64 (sqrt.f64 2) 1) 1/3) (*.f64 (cbrt.f64 -2) x))
(.f64 (cbrt.f64 (sqrt.f64 2)) (.f64 (cbrt.f64 -2) x))
(.f64 (pow.f64 (.f64 (sqrt.f64 2) 1) 1/3) (*.f64 (cbrt.f64 -2) x))
(.f64 (cbrt.f64 (sqrt.f64 2)) (.f64 (cbrt.f64 -2) x))
(.f64 -1 (.f64 (pow.f64 (.f64 (sqrt.f64 2) 1) 1/3) (.f64 (cbrt.f64 2) x)))
(neg.f64 (.f64 (cbrt.f64 (sqrt.f64 2)) (.f64 x (cbrt.f64 2))))
(.f64 (.f64 (cbrt.f64 (sqrt.f64 2)) (cbrt.f64 2)) (neg.f64 x))
(.f64 x (neg.f64 (.f64 (cbrt.f64 (sqrt.f64 2)) (cbrt.f64 2))))
(.f64 (cbrt.f64 (sqrt.f64 2)) (.f64 (cbrt.f64 2) (neg.f64 x)))
(.f64 (cbrt.f64 (sqrt.f64 2)) (.f64 x (neg.f64 (cbrt.f64 2))))
(.f64 -1 (.f64 (pow.f64 (.f64 (sqrt.f64 2) 1) 1/3) (.f64 (cbrt.f64 2) x)))
(neg.f64 (.f64 (cbrt.f64 (sqrt.f64 2)) (.f64 x (cbrt.f64 2))))
(.f64 (.f64 (cbrt.f64 (sqrt.f64 2)) (cbrt.f64 2)) (neg.f64 x))
(.f64 x (neg.f64 (.f64 (cbrt.f64 (sqrt.f64 2)) (cbrt.f64 2))))
(.f64 (cbrt.f64 (sqrt.f64 2)) (.f64 (cbrt.f64 2) (neg.f64 x)))
(.f64 (cbrt.f64 (sqrt.f64 2)) (.f64 x (neg.f64 (cbrt.f64 2))))
(.f64 -1 (.f64 (pow.f64 (.f64 (sqrt.f64 2) 1) 1/3) (.f64 (cbrt.f64 2) x)))
(neg.f64 (.f64 (cbrt.f64 (sqrt.f64 2)) (.f64 x (cbrt.f64 2))))
(.f64 (.f64 (cbrt.f64 (sqrt.f64 2)) (cbrt.f64 2)) (neg.f64 x))
(.f64 x (neg.f64 (.f64 (cbrt.f64 (sqrt.f64 2)) (cbrt.f64 2))))
(.f64 (cbrt.f64 (sqrt.f64 2)) (.f64 (cbrt.f64 2) (neg.f64 x)))
(.f64 (cbrt.f64 (sqrt.f64 2)) (.f64 x (neg.f64 (cbrt.f64 2))))
(.f64 -1 (.f64 (pow.f64 (.f64 (sqrt.f64 2) 1) 1/3) (.f64 (cbrt.f64 2) x)))
(neg.f64 (.f64 (cbrt.f64 (sqrt.f64 2)) (.f64 x (cbrt.f64 2))))
(.f64 (.f64 (cbrt.f64 (sqrt.f64 2)) (cbrt.f64 2)) (neg.f64 x))
(.f64 x (neg.f64 (.f64 (cbrt.f64 (sqrt.f64 2)) (cbrt.f64 2))))
(.f64 (cbrt.f64 (sqrt.f64 2)) (.f64 (cbrt.f64 2) (neg.f64 x)))
(.f64 (cbrt.f64 (sqrt.f64 2)) (.f64 x (neg.f64 (cbrt.f64 2))))
(.f64 -2 (.f64 (sqrt.f64 2) (pow.f64 x 3)))
(.f64 (sqrt.f64 2) (.f64 -2 (pow.f64 x 3)))
(.f64 -2 (.f64 (sqrt.f64 2) (pow.f64 x 3)))
(.f64 (sqrt.f64 2) (.f64 -2 (pow.f64 x 3)))
(.f64 -2 (.f64 (sqrt.f64 2) (pow.f64 x 3)))
(.f64 (sqrt.f64 2) (.f64 -2 (pow.f64 x 3)))
(.f64 -2 (.f64 (sqrt.f64 2) (pow.f64 x 3)))
(.f64 (sqrt.f64 2) (.f64 -2 (pow.f64 x 3)))
(.f64 -2 (.f64 (sqrt.f64 2) (pow.f64 x 3)))
(.f64 (sqrt.f64 2) (.f64 -2 (pow.f64 x 3)))
(.f64 -2 (.f64 (sqrt.f64 2) (pow.f64 x 3)))
(.f64 (sqrt.f64 2) (.f64 -2 (pow.f64 x 3)))
(.f64 -2 (.f64 (sqrt.f64 2) (pow.f64 x 3)))
(.f64 (sqrt.f64 2) (.f64 -2 (pow.f64 x 3)))
(.f64 -2 (.f64 (sqrt.f64 2) (pow.f64 x 3)))
(.f64 (sqrt.f64 2) (.f64 -2 (pow.f64 x 3)))
(.f64 -2 (.f64 (sqrt.f64 2) (pow.f64 x 3)))
(.f64 (sqrt.f64 2) (.f64 -2 (pow.f64 x 3)))
(.f64 -2 (.f64 (sqrt.f64 2) (pow.f64 x 3)))
(.f64 (sqrt.f64 2) (.f64 -2 (pow.f64 x 3)))
(.f64 -2 (.f64 (sqrt.f64 2) (pow.f64 x 3)))
(.f64 (sqrt.f64 2) (.f64 -2 (pow.f64 x 3)))
(.f64 -2 (.f64 (sqrt.f64 2) (pow.f64 x 3)))
(.f64 (sqrt.f64 2) (.f64 -2 (pow.f64 x 3)))

localize19.0ms (0.3%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.0b	(.f64 (.f64 x x) 2)
✓	0.4b	(.f64 (pow.f64 (.f64 (.f64 x x) 2) 1/4) (pow.f64 (.f64 (*.f64 x x) 2) 1/4))
✓	33.8b	(pow.f64 (.f64 (.f64 x x) 2) 1/4)

Compiler

Compiled 34 to 19 computations (44.1% saved)

series23.0ms (0.4%)

Counts

3 → 36

Calls

9 calls:

Time	Variable		Point	Expression
12.0ms	x	@	inf	(pow.f64 (.f64 (.f64 x x) 2) 1/4)
9.0ms	x	@	0	(pow.f64 (.f64 (.f64 x x) 2) 1/4)
0.0ms	x	@	-inf	(pow.f64 (.f64 (.f64 x x) 2) 1/4)
0.0ms	x	@	0	(.f64 (pow.f64 (.f64 (.f64 x x) 2) 1/4) (pow.f64 (.f64 (*.f64 x x) 2) 1/4))
0.0ms	x	@	inf	(.f64 (pow.f64 (.f64 (.f64 x x) 2) 1/4) (pow.f64 (.f64 (*.f64 x x) 2) 1/4))

rewrite61.0ms (1.1%)

Algorithm

1×	batch-egg-rewrite

Rules

665×	`pow1_binary64`
619×	`add-log-exp_binary64`
619×	`log1p-expm1-u_binary64`
619×	`expm1-log1p-u_binary64`
600×	`add-exp-log_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	8	27
1	174	21
2	1936	21

Stop Event

1×	node limit

Counts

3 → 48

Calls

Call 1

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

Outputs

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

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

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

simplify55.0ms (0.9%)

Algorithm

1×	egg-herbie

Rules

412×	`associate-l_binary64`
372×	`fma-neg_binary64`
362×	`associate-r_binary64`
357×	`distribute-rgt-in_binary64`
322×	`log-prod_binary64`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	30	356
1	74	332
2	182	272
3	386	272
4	891	272
5	3814	272

Stop Event

1×	node limit

Counts

84 → 57

Calls

Call 1

Inputs
(exp.f64 (.f64 1/4 (+.f64 (log.f64 2) (.f64 2 (log.f64 x)))))
(exp.f64 (.f64 1/4 (+.f64 (log.f64 2) (.f64 2 (log.f64 x)))))
(exp.f64 (.f64 1/4 (+.f64 (log.f64 2) (.f64 2 (log.f64 x)))))
(exp.f64 (.f64 1/4 (+.f64 (log.f64 2) (.f64 2 (log.f64 x)))))
(exp.f64 (.f64 1/4 (+.f64 (log.f64 2) (.f64 -2 (log.f64 (/.f64 1 x))))))
(exp.f64 (.f64 1/4 (+.f64 (log.f64 2) (.f64 -2 (log.f64 (/.f64 1 x))))))
(exp.f64 (.f64 1/4 (+.f64 (log.f64 2) (.f64 -2 (log.f64 (/.f64 1 x))))))
(exp.f64 (.f64 1/4 (+.f64 (log.f64 2) (.f64 -2 (log.f64 (/.f64 1 x))))))
(exp.f64 (.f64 1/4 (+.f64 (log.f64 2) (.f64 -2 (log.f64 (/.f64 -1 x))))))
(exp.f64 (.f64 1/4 (+.f64 (log.f64 2) (.f64 -2 (log.f64 (/.f64 -1 x))))))
(exp.f64 (.f64 1/4 (+.f64 (log.f64 2) (.f64 -2 (log.f64 (/.f64 -1 x))))))
(exp.f64 (.f64 1/4 (+.f64 (log.f64 2) (.f64 -2 (log.f64 (/.f64 -1 x))))))
(*.f64 (sqrt.f64 2) x)
(*.f64 (sqrt.f64 2) x)
(*.f64 (sqrt.f64 2) x)
(*.f64 (sqrt.f64 2) x)
(*.f64 (sqrt.f64 2) x)
(*.f64 (sqrt.f64 2) x)
(*.f64 (sqrt.f64 2) x)
(*.f64 (sqrt.f64 2) x)
(.f64 -1 (.f64 (sqrt.f64 2) x))
(.f64 -1 (.f64 (sqrt.f64 2) x))
(.f64 -1 (.f64 (sqrt.f64 2) x))
(.f64 -1 (.f64 (sqrt.f64 2) x))
(*.f64 2 (pow.f64 x 2))
(*.f64 2 (pow.f64 x 2))
(*.f64 2 (pow.f64 x 2))
(*.f64 2 (pow.f64 x 2))
(*.f64 2 (pow.f64 x 2))
(*.f64 2 (pow.f64 x 2))
(*.f64 2 (pow.f64 x 2))
(*.f64 2 (pow.f64 x 2))
(*.f64 2 (pow.f64 x 2))
(*.f64 2 (pow.f64 x 2))
(*.f64 2 (pow.f64 x 2))
(*.f64 2 (pow.f64 x 2))

Outputs
(exp.f64 (.f64 1/4 (+.f64 (log.f64 2) (.f64 2 (log.f64 x)))))
(pow.f64 (exp.f64 1/4) (+.f64 (log.f64 2) (*.f64 2 (log.f64 x))))
(pow.f64 (exp.f64 1/4) (fma.f64 2 (log.f64 x) (log.f64 2)))
(*.f64 (pow.f64 2 1/4) (sqrt.f64 x))
(exp.f64 (.f64 1/4 (+.f64 (log.f64 2) (.f64 2 (log.f64 x)))))
(pow.f64 (exp.f64 1/4) (+.f64 (log.f64 2) (*.f64 2 (log.f64 x))))
(pow.f64 (exp.f64 1/4) (fma.f64 2 (log.f64 x) (log.f64 2)))
(*.f64 (pow.f64 2 1/4) (sqrt.f64 x))
(exp.f64 (.f64 1/4 (+.f64 (log.f64 2) (.f64 2 (log.f64 x)))))
(pow.f64 (exp.f64 1/4) (+.f64 (log.f64 2) (*.f64 2 (log.f64 x))))
(pow.f64 (exp.f64 1/4) (fma.f64 2 (log.f64 x) (log.f64 2)))
(*.f64 (pow.f64 2 1/4) (sqrt.f64 x))
(exp.f64 (.f64 1/4 (+.f64 (log.f64 2) (.f64 2 (log.f64 x)))))
(pow.f64 (exp.f64 1/4) (+.f64 (log.f64 2) (*.f64 2 (log.f64 x))))
(pow.f64 (exp.f64 1/4) (fma.f64 2 (log.f64 x) (log.f64 2)))
(*.f64 (pow.f64 2 1/4) (sqrt.f64 x))
(exp.f64 (.f64 1/4 (+.f64 (log.f64 2) (.f64 -2 (log.f64 (/.f64 1 x))))))
(pow.f64 (exp.f64 1/4) (+.f64 (log.f64 2) (*.f64 2 (log.f64 x))))
(pow.f64 (exp.f64 1/4) (fma.f64 2 (log.f64 x) (log.f64 2)))
(*.f64 (pow.f64 2 1/4) (sqrt.f64 x))
(exp.f64 (.f64 1/4 (+.f64 (log.f64 2) (.f64 -2 (log.f64 (/.f64 1 x))))))
(pow.f64 (exp.f64 1/4) (+.f64 (log.f64 2) (*.f64 2 (log.f64 x))))
(pow.f64 (exp.f64 1/4) (fma.f64 2 (log.f64 x) (log.f64 2)))
(*.f64 (pow.f64 2 1/4) (sqrt.f64 x))
(exp.f64 (.f64 1/4 (+.f64 (log.f64 2) (.f64 -2 (log.f64 (/.f64 1 x))))))
(pow.f64 (exp.f64 1/4) (+.f64 (log.f64 2) (*.f64 2 (log.f64 x))))
(pow.f64 (exp.f64 1/4) (fma.f64 2 (log.f64 x) (log.f64 2)))
(*.f64 (pow.f64 2 1/4) (sqrt.f64 x))
(exp.f64 (.f64 1/4 (+.f64 (log.f64 2) (.f64 -2 (log.f64 (/.f64 1 x))))))
(pow.f64 (exp.f64 1/4) (+.f64 (log.f64 2) (*.f64 2 (log.f64 x))))
(pow.f64 (exp.f64 1/4) (fma.f64 2 (log.f64 x) (log.f64 2)))
(*.f64 (pow.f64 2 1/4) (sqrt.f64 x))
(exp.f64 (.f64 1/4 (+.f64 (log.f64 2) (.f64 -2 (log.f64 (/.f64 -1 x))))))
(pow.f64 (exp.f64 1/4) (+.f64 (log.f64 2) (*.f64 2 (log.f64 x))))
(pow.f64 (exp.f64 1/4) (fma.f64 2 (log.f64 x) (log.f64 2)))
(*.f64 (pow.f64 2 1/4) (sqrt.f64 x))
(exp.f64 (.f64 1/4 (+.f64 (log.f64 2) (.f64 -2 (log.f64 (/.f64 -1 x))))))
(pow.f64 (exp.f64 1/4) (+.f64 (log.f64 2) (*.f64 2 (log.f64 x))))
(pow.f64 (exp.f64 1/4) (fma.f64 2 (log.f64 x) (log.f64 2)))
(*.f64 (pow.f64 2 1/4) (sqrt.f64 x))
(exp.f64 (.f64 1/4 (+.f64 (log.f64 2) (.f64 -2 (log.f64 (/.f64 -1 x))))))
(pow.f64 (exp.f64 1/4) (+.f64 (log.f64 2) (*.f64 2 (log.f64 x))))
(pow.f64 (exp.f64 1/4) (fma.f64 2 (log.f64 x) (log.f64 2)))
(*.f64 (pow.f64 2 1/4) (sqrt.f64 x))
(exp.f64 (.f64 1/4 (+.f64 (log.f64 2) (.f64 -2 (log.f64 (/.f64 -1 x))))))
(pow.f64 (exp.f64 1/4) (+.f64 (log.f64 2) (*.f64 2 (log.f64 x))))
(pow.f64 (exp.f64 1/4) (fma.f64 2 (log.f64 x) (log.f64 2)))
(*.f64 (pow.f64 2 1/4) (sqrt.f64 x))
(*.f64 (sqrt.f64 2) x)
(*.f64 x (sqrt.f64 2))
(*.f64 (sqrt.f64 2) x)
(*.f64 x (sqrt.f64 2))
(*.f64 (sqrt.f64 2) x)
(*.f64 x (sqrt.f64 2))
(*.f64 (sqrt.f64 2) x)
(*.f64 x (sqrt.f64 2))
(*.f64 (sqrt.f64 2) x)
(*.f64 x (sqrt.f64 2))
(*.f64 (sqrt.f64 2) x)
(*.f64 x (sqrt.f64 2))
(*.f64 (sqrt.f64 2) x)
(*.f64 x (sqrt.f64 2))
(*.f64 (sqrt.f64 2) x)
(*.f64 x (sqrt.f64 2))
(.f64 -1 (.f64 (sqrt.f64 2) x))
(neg.f64 (*.f64 x (sqrt.f64 2)))
(*.f64 x (neg.f64 (sqrt.f64 2)))
(.f64 -1 (.f64 (sqrt.f64 2) x))
(neg.f64 (*.f64 x (sqrt.f64 2)))
(*.f64 x (neg.f64 (sqrt.f64 2)))
(.f64 -1 (.f64 (sqrt.f64 2) x))
(neg.f64 (*.f64 x (sqrt.f64 2)))
(*.f64 x (neg.f64 (sqrt.f64 2)))
(.f64 -1 (.f64 (sqrt.f64 2) x))
(neg.f64 (*.f64 x (sqrt.f64 2)))
(*.f64 x (neg.f64 (sqrt.f64 2)))
(*.f64 2 (pow.f64 x 2))
(.f64 2 (.f64 x x))
(.f64 x (.f64 x 2))
(*.f64 2 (pow.f64 x 2))
(.f64 2 (.f64 x x))
(.f64 x (.f64 x 2))
(*.f64 2 (pow.f64 x 2))
(.f64 2 (.f64 x x))
(.f64 x (.f64 x 2))
(*.f64 2 (pow.f64 x 2))
(.f64 2 (.f64 x x))
(.f64 x (.f64 x 2))
(*.f64 2 (pow.f64 x 2))
(.f64 2 (.f64 x x))
(.f64 x (.f64 x 2))
(*.f64 2 (pow.f64 x 2))
(.f64 2 (.f64 x x))
(.f64 x (.f64 x 2))
(*.f64 2 (pow.f64 x 2))
(.f64 2 (.f64 x x))
(.f64 x (.f64 x 2))
(*.f64 2 (pow.f64 x 2))
(.f64 2 (.f64 x x))
(.f64 x (.f64 x 2))
(*.f64 2 (pow.f64 x 2))
(.f64 2 (.f64 x x))
(.f64 x (.f64 x 2))
(*.f64 2 (pow.f64 x 2))
(.f64 2 (.f64 x x))
(.f64 x (.f64 x 2))
(*.f64 2 (pow.f64 x 2))
(.f64 2 (.f64 x x))
(.f64 x (.f64 x 2))
(*.f64 2 (pow.f64 x 2))
(.f64 2 (.f64 x x))
(.f64 x (.f64 x 2))

localize20.0ms (0.3%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.2b	(.f64 (.f64 x x) (sqrt.f64 2))
✓	0.3b	(.f64 (pow.f64 2 1/4) (sqrt.f64 (.f64 (*.f64 x x) (sqrt.f64 2))))
✓	32.7b	(sqrt.f64 (.f64 (.f64 x x) (sqrt.f64 2)))

Compiler

Compiled 36 to 24 computations (33.3% saved)

series4.0ms (0.1%)

Counts

3 → 36

Calls

9 calls:

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

rewrite54.0ms (0.9%)

Algorithm

1×	batch-egg-rewrite

Rules

795×	`pow1_binary64`
736×	`add-log-exp_binary64`
736×	`log1p-expm1-u_binary64`
736×	`expm1-log1p-u_binary64`
716×	`add-exp-log_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	10	37
1	207	22
2	2269	22

Stop Event

1×	node limit

Counts

3 → 51

Calls

Call 1

Inputs
(sqrt.f64 (.f64 (.f64 x x) (sqrt.f64 2)))
(.f64 (pow.f64 2 1/4) (sqrt.f64 (.f64 (*.f64 x x) (sqrt.f64 2))))
(.f64 (.f64 x x) (sqrt.f64 2))

Outputs

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

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

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

simplify106.0ms (1.8%)

Algorithm

1×	egg-herbie

Rules

706×	`distribute-lft-neg-in_binary64`
688×	`distribute-rgt-neg-in_binary64`
598×	`fma-def_binary64`
454×	`unswap-sqr_binary64`
441×	`fma-neg_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	15	388
1	37	388
2	95	388
3	270	388
4	1142	388
5	2167	388
6	3835	388
7	5287	388
8	6626	388
9	7448	388

Stop Event

1×	node limit

Counts

87 → 60

Calls

Call 1

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

Outputs
(*.f64 (sqrt.f64 (sqrt.f64 2)) x)
(*.f64 (sqrt.f64 (sqrt.f64 2)) x)
(*.f64 (sqrt.f64 (sqrt.f64 2)) x)
(*.f64 (sqrt.f64 (sqrt.f64 2)) x)
(*.f64 (sqrt.f64 (sqrt.f64 2)) x)
(*.f64 (sqrt.f64 (sqrt.f64 2)) x)
(*.f64 (sqrt.f64 (sqrt.f64 2)) x)
(*.f64 (sqrt.f64 (sqrt.f64 2)) x)
(.f64 -1 (.f64 (sqrt.f64 (sqrt.f64 2)) x))
(neg.f64 (*.f64 (sqrt.f64 (sqrt.f64 2)) x))
(*.f64 (sqrt.f64 (sqrt.f64 2)) (neg.f64 x))
(.f64 -1 (.f64 (sqrt.f64 (sqrt.f64 2)) x))
(neg.f64 (*.f64 (sqrt.f64 (sqrt.f64 2)) x))
(*.f64 (sqrt.f64 (sqrt.f64 2)) (neg.f64 x))
(.f64 -1 (.f64 (sqrt.f64 (sqrt.f64 2)) x))
(neg.f64 (*.f64 (sqrt.f64 (sqrt.f64 2)) x))
(*.f64 (sqrt.f64 (sqrt.f64 2)) (neg.f64 x))
(.f64 -1 (.f64 (sqrt.f64 (sqrt.f64 2)) x))
(neg.f64 (*.f64 (sqrt.f64 (sqrt.f64 2)) x))
(*.f64 (sqrt.f64 (sqrt.f64 2)) (neg.f64 x))
(.f64 (sqrt.f64 (sqrt.f64 2)) (.f64 (pow.f64 2 1/4) x))
(.f64 (sqrt.f64 (sqrt.f64 2)) (.f64 x (pow.f64 2 1/4)))
(.f64 x (.f64 (sqrt.f64 (sqrt.f64 2)) (pow.f64 2 1/4)))
(.f64 (sqrt.f64 (sqrt.f64 2)) (.f64 (pow.f64 2 1/4) x))
(.f64 (sqrt.f64 (sqrt.f64 2)) (.f64 x (pow.f64 2 1/4)))
(.f64 x (.f64 (sqrt.f64 (sqrt.f64 2)) (pow.f64 2 1/4)))
(.f64 (sqrt.f64 (sqrt.f64 2)) (.f64 (pow.f64 2 1/4) x))
(.f64 (sqrt.f64 (sqrt.f64 2)) (.f64 x (pow.f64 2 1/4)))
(.f64 x (.f64 (sqrt.f64 (sqrt.f64 2)) (pow.f64 2 1/4)))
(.f64 (sqrt.f64 (sqrt.f64 2)) (.f64 (pow.f64 2 1/4) x))
(.f64 (sqrt.f64 (sqrt.f64 2)) (.f64 x (pow.f64 2 1/4)))
(.f64 x (.f64 (sqrt.f64 (sqrt.f64 2)) (pow.f64 2 1/4)))
(.f64 (sqrt.f64 (sqrt.f64 2)) (.f64 (pow.f64 2 1/4) x))
(.f64 (sqrt.f64 (sqrt.f64 2)) (.f64 x (pow.f64 2 1/4)))
(.f64 x (.f64 (sqrt.f64 (sqrt.f64 2)) (pow.f64 2 1/4)))
(.f64 (sqrt.f64 (sqrt.f64 2)) (.f64 (pow.f64 2 1/4) x))
(.f64 (sqrt.f64 (sqrt.f64 2)) (.f64 x (pow.f64 2 1/4)))
(.f64 x (.f64 (sqrt.f64 (sqrt.f64 2)) (pow.f64 2 1/4)))
(.f64 (sqrt.f64 (sqrt.f64 2)) (.f64 (pow.f64 2 1/4) x))
(.f64 (sqrt.f64 (sqrt.f64 2)) (.f64 x (pow.f64 2 1/4)))
(.f64 x (.f64 (sqrt.f64 (sqrt.f64 2)) (pow.f64 2 1/4)))
(.f64 (sqrt.f64 (sqrt.f64 2)) (.f64 (pow.f64 2 1/4) x))
(.f64 (sqrt.f64 (sqrt.f64 2)) (.f64 x (pow.f64 2 1/4)))
(.f64 x (.f64 (sqrt.f64 (sqrt.f64 2)) (pow.f64 2 1/4)))
(.f64 -1 (.f64 (sqrt.f64 (sqrt.f64 2)) (*.f64 (pow.f64 2 1/4) x)))
(neg.f64 (.f64 (sqrt.f64 (sqrt.f64 2)) (.f64 x (pow.f64 2 1/4))))
(.f64 (sqrt.f64 (sqrt.f64 2)) (neg.f64 (.f64 x (pow.f64 2 1/4))))
(neg.f64 (.f64 x (.f64 (sqrt.f64 (sqrt.f64 2)) (pow.f64 2 1/4))))
(.f64 (sqrt.f64 (sqrt.f64 2)) (.f64 (pow.f64 2 1/4) (neg.f64 x)))
(.f64 (sqrt.f64 (sqrt.f64 2)) (.f64 x (neg.f64 (pow.f64 2 1/4))))
(.f64 -1 (.f64 (sqrt.f64 (sqrt.f64 2)) (*.f64 (pow.f64 2 1/4) x)))
(neg.f64 (.f64 (sqrt.f64 (sqrt.f64 2)) (.f64 x (pow.f64 2 1/4))))
(.f64 (sqrt.f64 (sqrt.f64 2)) (neg.f64 (.f64 x (pow.f64 2 1/4))))
(neg.f64 (.f64 x (.f64 (sqrt.f64 (sqrt.f64 2)) (pow.f64 2 1/4))))
(.f64 (sqrt.f64 (sqrt.f64 2)) (.f64 (pow.f64 2 1/4) (neg.f64 x)))
(.f64 (sqrt.f64 (sqrt.f64 2)) (.f64 x (neg.f64 (pow.f64 2 1/4))))
(.f64 -1 (.f64 (sqrt.f64 (sqrt.f64 2)) (*.f64 (pow.f64 2 1/4) x)))
(neg.f64 (.f64 (sqrt.f64 (sqrt.f64 2)) (.f64 x (pow.f64 2 1/4))))
(.f64 (sqrt.f64 (sqrt.f64 2)) (neg.f64 (.f64 x (pow.f64 2 1/4))))
(neg.f64 (.f64 x (.f64 (sqrt.f64 (sqrt.f64 2)) (pow.f64 2 1/4))))
(.f64 (sqrt.f64 (sqrt.f64 2)) (.f64 (pow.f64 2 1/4) (neg.f64 x)))
(.f64 (sqrt.f64 (sqrt.f64 2)) (.f64 x (neg.f64 (pow.f64 2 1/4))))
(.f64 -1 (.f64 (sqrt.f64 (sqrt.f64 2)) (*.f64 (pow.f64 2 1/4) x)))
(neg.f64 (.f64 (sqrt.f64 (sqrt.f64 2)) (.f64 x (pow.f64 2 1/4))))
(.f64 (sqrt.f64 (sqrt.f64 2)) (neg.f64 (.f64 x (pow.f64 2 1/4))))
(neg.f64 (.f64 x (.f64 (sqrt.f64 (sqrt.f64 2)) (pow.f64 2 1/4))))
(.f64 (sqrt.f64 (sqrt.f64 2)) (.f64 (pow.f64 2 1/4) (neg.f64 x)))
(.f64 (sqrt.f64 (sqrt.f64 2)) (.f64 x (neg.f64 (pow.f64 2 1/4))))
(*.f64 (sqrt.f64 2) (pow.f64 x 2))
(.f64 (sqrt.f64 2) (.f64 x x))
(*.f64 (sqrt.f64 2) (pow.f64 x 2))
(.f64 (sqrt.f64 2) (.f64 x x))
(*.f64 (sqrt.f64 2) (pow.f64 x 2))
(.f64 (sqrt.f64 2) (.f64 x x))
(*.f64 (sqrt.f64 2) (pow.f64 x 2))
(.f64 (sqrt.f64 2) (.f64 x x))
(*.f64 (sqrt.f64 2) (pow.f64 x 2))
(.f64 (sqrt.f64 2) (.f64 x x))
(*.f64 (sqrt.f64 2) (pow.f64 x 2))
(.f64 (sqrt.f64 2) (.f64 x x))
(*.f64 (sqrt.f64 2) (pow.f64 x 2))
(.f64 (sqrt.f64 2) (.f64 x x))
(*.f64 (sqrt.f64 2) (pow.f64 x 2))
(.f64 (sqrt.f64 2) (.f64 x x))
(*.f64 (sqrt.f64 2) (pow.f64 x 2))
(.f64 (sqrt.f64 2) (.f64 x x))
(*.f64 (sqrt.f64 2) (pow.f64 x 2))
(.f64 (sqrt.f64 2) (.f64 x x))
(*.f64 (sqrt.f64 2) (pow.f64 x 2))
(.f64 (sqrt.f64 2) (.f64 x x))
(*.f64 (sqrt.f64 2) (pow.f64 x 2))
(.f64 (sqrt.f64 2) (.f64 x x))

localize25.0ms (0.4%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.1b	(sqrt.f64 (*.f64 x (neg.f64 (sqrt.f64 2))))
✓	0.2b	(.f64 (sqrt.f64 (.f64 x (neg.f64 (sqrt.f64 2)))) (sqrt.f64 (*.f64 x (neg.f64 (sqrt.f64 2)))))
	0.5b	(*.f64 x (neg.f64 (sqrt.f64 2)))

Compiler

Compiled 32 to 27 computations (15.6% saved)

series5.0ms (0.1%)

Counts

2 → 12

Calls

6 calls:

Time	Variable		Point	Expression
1.0ms	x	@	0	(.f64 (sqrt.f64 (.f64 x (neg.f64 (sqrt.f64 2)))) (sqrt.f64 (*.f64 x (neg.f64 (sqrt.f64 2)))))
1.0ms	x	@	0	(sqrt.f64 (*.f64 x (neg.f64 (sqrt.f64 2))))
1.0ms	x	@	inf	(.f64 (sqrt.f64 (.f64 x (neg.f64 (sqrt.f64 2)))) (sqrt.f64 (*.f64 x (neg.f64 (sqrt.f64 2)))))
1.0ms	x	@	inf	(sqrt.f64 (*.f64 x (neg.f64 (sqrt.f64 2))))
1.0ms	x	@	-inf	(sqrt.f64 (*.f64 x (neg.f64 (sqrt.f64 2))))

rewrite77.0ms (1.3%)

Algorithm

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

Rules

69×	`add-sqr-sqrt_binary64`
69×	`add-sqr-sqrt_binary64`
69×	`add-sqr-sqrt_binary64`
65×	`add-exp-log_binary64`
65×	`add-log-exp_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	8	18
1	165	18
2	1716	18
0	8	8
1	165	8
2	1716	8
0	8	8
0	7	10
1	145	10
2	1684	10
0	7	10

Stop Event

1×	iter limit
1×	unsound
1×	iter limit
1×	unsound
1×	unsound

Counts

2 → 20

Calls

Call 1

Inputs
(.f64 (sqrt.f64 (.f64 x (neg.f64 (sqrt.f64 2)))) (sqrt.f64 (*.f64 x (neg.f64 (sqrt.f64 2)))))
(sqrt.f64 (*.f64 x (neg.f64 (sqrt.f64 2))))

Outputs

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

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

simplify115.0ms (2%)

Algorithm

1×	egg-herbie

Rules

1037×	`fma-def_binary64`
795×	`fabs-mul_binary64`
775×	`cube-prod_binary64`
741×	`sqr-pow_binary64`
409×	`pow-sqr_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	11	168
1	25	96
2	54	96
3	91	96
4	198	96
5	632	96
6	902	96
7	1097	96
8	1918	96
9	2939	96
10	3217	96
11	3476	96
12	3793	96
13	4185	96
14	4666	96
15	5307	96
16	6203	96
17	7388	96

Stop Event

1×	node limit

Counts

32 → 23

Calls

Call 1

Inputs
(.f64 (sqrt.f64 2) (.f64 (pow.f64 (sqrt.f64 -1) 2) x))
(.f64 (sqrt.f64 2) (.f64 (pow.f64 (sqrt.f64 -1) 2) x))
(.f64 (sqrt.f64 2) (.f64 (pow.f64 (sqrt.f64 -1) 2) x))
(.f64 (sqrt.f64 2) (.f64 (pow.f64 (sqrt.f64 -1) 2) x))
(.f64 (sqrt.f64 2) (.f64 (pow.f64 (sqrt.f64 -1) 2) x))
(.f64 (sqrt.f64 2) (.f64 (pow.f64 (sqrt.f64 -1) 2) x))
(.f64 (sqrt.f64 2) (.f64 (pow.f64 (sqrt.f64 -1) 2) x))
(.f64 (sqrt.f64 2) (.f64 (pow.f64 (sqrt.f64 -1) 2) x))
(.f64 -1 (.f64 (sqrt.f64 2) x))
(.f64 -1 (.f64 (sqrt.f64 2) x))
(.f64 -1 (.f64 (sqrt.f64 2) x))
(.f64 -1 (.f64 (sqrt.f64 2) x))

Outputs
(.f64 (sqrt.f64 2) (.f64 (pow.f64 (sqrt.f64 -1) 2) x))
(*.f64 (sqrt.f64 2) (neg.f64 x))
(.f64 (sqrt.f64 2) (.f64 (pow.f64 (sqrt.f64 -1) 2) x))
(*.f64 (sqrt.f64 2) (neg.f64 x))
(.f64 (sqrt.f64 2) (.f64 (pow.f64 (sqrt.f64 -1) 2) x))
(*.f64 (sqrt.f64 2) (neg.f64 x))
(.f64 (sqrt.f64 2) (.f64 (pow.f64 (sqrt.f64 -1) 2) x))
(*.f64 (sqrt.f64 2) (neg.f64 x))
(.f64 (sqrt.f64 2) (.f64 (pow.f64 (sqrt.f64 -1) 2) x))
(*.f64 (sqrt.f64 2) (neg.f64 x))
(.f64 (sqrt.f64 2) (.f64 (pow.f64 (sqrt.f64 -1) 2) x))
(*.f64 (sqrt.f64 2) (neg.f64 x))
(.f64 (sqrt.f64 2) (.f64 (pow.f64 (sqrt.f64 -1) 2) x))
(*.f64 (sqrt.f64 2) (neg.f64 x))
(.f64 (sqrt.f64 2) (.f64 (pow.f64 (sqrt.f64 -1) 2) x))
(*.f64 (sqrt.f64 2) (neg.f64 x))
(.f64 -1 (.f64 (sqrt.f64 2) x))
(.f64 (sqrt.f64 2) (.f64 (pow.f64 (sqrt.f64 -1) 2) x))
(*.f64 (sqrt.f64 2) (neg.f64 x))
(.f64 -1 (.f64 (sqrt.f64 2) x))
(.f64 (sqrt.f64 2) (.f64 (pow.f64 (sqrt.f64 -1) 2) x))
(*.f64 (sqrt.f64 2) (neg.f64 x))
(.f64 -1 (.f64 (sqrt.f64 2) x))
(.f64 (sqrt.f64 2) (.f64 (pow.f64 (sqrt.f64 -1) 2) x))
(*.f64 (sqrt.f64 2) (neg.f64 x))
(.f64 -1 (.f64 (sqrt.f64 2) x))
(.f64 (sqrt.f64 2) (.f64 (pow.f64 (sqrt.f64 -1) 2) x))
(*.f64 (sqrt.f64 2) (neg.f64 x))

eval207.0ms (3.6%)

Compiler: Compiled 4959 to 4035 computations (18.6% saved)

prune56.0ms (1%)

Pruning

16 alts after pruning (8 fresh and 8 done)

	Pruned	Kept	Total
New	306	8	314
Fresh	0	0	0
Picked	1	0	1
Done	2	8	10
Total	309	16	325

Error

0.0b

Counts

325 → 16

Alt Table

Click to see full alt table

Status	Error	Program
✓	31.0b	(*.f64 (sqrt.f64 2) x)
	34.6b	(.f64 (.f64 (cbrt.f64 (.f64 x (neg.f64 (sqrt.f64 2)))) (cbrt.f64 (exp.f64 (log.f64 (.f64 x (neg.f64 (sqrt.f64 2))))))) (cbrt.f64 (*.f64 x (neg.f64 (sqrt.f64 2)))))
	44.7b	(.f64 (sqrt.f64 (.f64 x (neg.f64 (sqrt.f64 2)))) (cbrt.f64 (.f64 (.f64 x (neg.f64 (sqrt.f64 2))) (sqrt.f64 (*.f64 x (neg.f64 (sqrt.f64 2)))))))
✓	34.1b	(sqrt.f64 (.f64 2 (.f64 x x)))
	32.4b	(.f64 (.f64 (.f64 (cbrt.f64 x) (cbrt.f64 (neg.f64 (sqrt.f64 2)))) (cbrt.f64 (.f64 x (neg.f64 (sqrt.f64 2))))) (cbrt.f64 (*.f64 x (neg.f64 (sqrt.f64 2)))))
✓	34.2b	(.f64 (pow.f64 (.f64 (.f64 x x) 2) 1/4) (pow.f64 (.f64 (*.f64 x x) 2) 1/4))
✓	45.6b	(pow.f64 (*.f64 4 (pow.f64 x 4)) 1/4)
✓	51.7b	(cbrt.f64 (.f64 (.f64 x (.f64 2 x)) (.f64 x (neg.f64 (sqrt.f64 2)))))
	32.5b	(pow.f64 (cbrt.f64 (*.f64 x (neg.f64 (sqrt.f64 2)))) 3)
	33.2b	(.f64 (.f64 (.f64 (cbrt.f64 (sqrt.f64 (.f64 x (neg.f64 (sqrt.f64 2))))) (cbrt.f64 (sqrt.f64 (.f64 x (neg.f64 (sqrt.f64 2)))))) (cbrt.f64 (sqrt.f64 (.f64 x (neg.f64 (sqrt.f64 2)))))) (sqrt.f64 (*.f64 x (neg.f64 (sqrt.f64 2)))))
✓	32.0b	(*.f64 x (neg.f64 (sqrt.f64 2)))
	31.0b	(.f64 x (.f64 (sqrt.f64 (sqrt.f64 2)) (pow.f64 2 1/4)))
✓	31.7b	(.f64 (sqrt.f64 (.f64 2 x)) (sqrt.f64 x))
	32.0b	(.f64 (pow.f64 2 1/4) (.f64 (sqrt.f64 (sqrt.f64 2)) (neg.f64 x)))
	32.8b	(pow.f64 (sqrt.f64 (*.f64 x (neg.f64 (sqrt.f64 2)))) 2)
✓	30.9b	(.f64 (pow.f64 2 1/4) (.f64 (pow.f64 2 1/4) x))

Compiler

Compiled 209 to 176 computations (15.8% saved)

regimes135.0ms (2.3%)

Counts

24 → 2

Calls

Call 1

Inputs
(*.f64 (sqrt.f64 2) x)
(*.f64 x (neg.f64 (sqrt.f64 2)))
(sqrt.f64 (.f64 2 (.f64 x x)))
(sqrt.f64 (*.f64 2 (pow.f64 x 2)))
(pow.f64 (*.f64 4 (pow.f64 x 4)) 1/4)
(.f64 (sqrt.f64 (.f64 2 x)) (sqrt.f64 x))
(.f64 (pow.f64 2 1/4) (.f64 (pow.f64 2 1/4) x))
(cbrt.f64 (.f64 (.f64 x (.f64 2 x)) (.f64 x (neg.f64 (sqrt.f64 2)))))
(.f64 (pow.f64 (.f64 (.f64 x x) 2) 1/4) (pow.f64 (.f64 (*.f64 x x) 2) 1/4))
(sqrt.f64 (sqrt.f64 (*.f64 4 (pow.f64 x 4))))
(pow.f64 (sqrt.f64 (*.f64 x (sqrt.f64 2))) 2)
(pow.f64 (cbrt.f64 (*.f64 x (sqrt.f64 2))) 3)
(pow.f64 (cbrt.f64 (*.f64 x (neg.f64 (sqrt.f64 2)))) 3)
(pow.f64 (sqrt.f64 (*.f64 x (neg.f64 (sqrt.f64 2)))) 2)
(.f64 x (.f64 (sqrt.f64 (sqrt.f64 2)) (pow.f64 2 1/4)))
(.f64 (pow.f64 2 1/4) (.f64 (sqrt.f64 (sqrt.f64 2)) (neg.f64 x)))
(.f64 (pow.f64 2 1/4) (sqrt.f64 (.f64 (*.f64 x x) (sqrt.f64 2))))
(.f64 (sqrt.f64 (.f64 x (neg.f64 (sqrt.f64 2)))) (sqrt.f64 (*.f64 x (neg.f64 (sqrt.f64 2)))))
(cbrt.f64 (.f64 (.f64 (.f64 x (neg.f64 (sqrt.f64 2))) (.f64 x (neg.f64 (sqrt.f64 2)))) (*.f64 x (neg.f64 (sqrt.f64 2)))))
(.f64 (sqrt.f64 (.f64 x (neg.f64 (sqrt.f64 2)))) (cbrt.f64 (.f64 (.f64 x (neg.f64 (sqrt.f64 2))) (sqrt.f64 (*.f64 x (neg.f64 (sqrt.f64 2)))))))
(.f64 (.f64 (cbrt.f64 (.f64 x (neg.f64 (sqrt.f64 2)))) (cbrt.f64 (.f64 x (neg.f64 (sqrt.f64 2))))) (cbrt.f64 (*.f64 x (neg.f64 (sqrt.f64 2)))))
(.f64 (.f64 (.f64 (cbrt.f64 x) (cbrt.f64 (neg.f64 (sqrt.f64 2)))) (cbrt.f64 (.f64 x (neg.f64 (sqrt.f64 2))))) (cbrt.f64 (*.f64 x (neg.f64 (sqrt.f64 2)))))
(.f64 (.f64 (cbrt.f64 (.f64 x (neg.f64 (sqrt.f64 2)))) (cbrt.f64 (exp.f64 (log.f64 (.f64 x (neg.f64 (sqrt.f64 2))))))) (cbrt.f64 (*.f64 x (neg.f64 (sqrt.f64 2)))))
(.f64 (.f64 (.f64 (cbrt.f64 (sqrt.f64 (.f64 x (neg.f64 (sqrt.f64 2))))) (cbrt.f64 (sqrt.f64 (.f64 x (neg.f64 (sqrt.f64 2)))))) (cbrt.f64 (sqrt.f64 (.f64 x (neg.f64 (sqrt.f64 2)))))) (sqrt.f64 (*.f64 x (neg.f64 (sqrt.f64 2)))))

Outputs
(*.f64 x (neg.f64 (sqrt.f64 2)))
(.f64 (sqrt.f64 (.f64 2 x)) (sqrt.f64 x))

Calls

4 calls:

48.0ms	x
37.0ms	(*.f64 2 (pow.f64 x 2))
20.0ms	(pow.f64 x 2)
20.0ms	(sqrt.f64 (*.f64 2 (pow.f64 x 2)))

Results

Error	Segments	Branch
0.4b	2	`x`
16.5b	3	`(sqrt.f64 (*.f64 2 (pow.f64 x 2)))`
16.5b	3	`(*.f64 2 (pow.f64 x 2))`
16.5b	3	`(pow.f64 x 2)`

Compiler

Compiled 302 to 249 computations (17.5% saved)

bsearch24.0ms (0.4%)

Algorithm

1×	binary-search

Steps

Time	Left	Right
24.0ms	-2.713715200157104e-299	5.5881129459418656e-303

Compiler

Compiled 11 to 9 computations (18.2% saved)

regimes99.0ms (1.7%)

Accuracy

Total -62.1b remaining (-13369.3%)

Threshold costs -62.1b (-13369.3%)

Counts

5 → 2

Calls

Call 1

Inputs
(*.f64 (sqrt.f64 2) x)
(*.f64 x (neg.f64 (sqrt.f64 2)))
(sqrt.f64 (.f64 2 (.f64 x x)))
(sqrt.f64 (*.f64 2 (pow.f64 x 2)))
(pow.f64 (*.f64 4 (pow.f64 x 4)) 1/4)

Outputs
(*.f64 x (neg.f64 (sqrt.f64 2)))
(*.f64 (sqrt.f64 2) x)

Calls

4 calls:

72.0ms	(pow.f64 x 2)
9.0ms	x
8.0ms	(*.f64 2 (pow.f64 x 2))
8.0ms	(sqrt.f64 (*.f64 2 (pow.f64 x 2)))

Results

Error	Segments	Branch
0.5b	2	`x`
16.5b	3	`(sqrt.f64 (*.f64 2 (pow.f64 x 2)))`
16.5b	3	`(*.f64 2 (pow.f64 x 2))`
16.5b	3	`(pow.f64 x 2)`

Compiler

Compiled 48 to 38 computations (20.8% saved)

bsearch24.0ms (0.4%)

Algorithm

1×	binary-search

Steps

Time	Left	Right
23.0ms	-2.713715200157104e-299	5.5881129459418656e-303

Compiler

Compiled 11 to 9 computations (18.2% saved)

simplify5.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

7×	`*-commutative_binary64`
3×	`+-commutative_binary64`
3×	`sub-neg_binary64`
3×	`neg-sub0_binary64`
3×	`neg-mul-1_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	16	51
1	26	51
2	33	51
3	38	51
4	41	51
5	42	51

Stop Event

1×	fuel
1×	saturated

Calls

Call 1

Inputs

(if (<=.f64 x -1278850416061695/47125446914534694131579097993419809976955095716785201420286055195012674566357244479460731079205201122720511132925006540350105785156086431086764996857554304860885586653967937772270969055149056096849908977391371752266308172471982589601097478449614615258949356272900190565812730839296826751014759649673012612226351104) (*.f64 x (neg.f64 (sqrt.f64 2))) (*.f64 (sqrt.f64 (*.f64 2 x)) (sqrt.f64 x)))

(if (<=.f64 x -1278850416061695/47125446914534694131579097993419809976955095716785201420286055195012674566357244479460731079205201122720511132925006540350105785156086431086764996857554304860885586653967937772270969055149056096849908977391371752266308172471982589601097478449614615258949356272900190565812730839296826751014759649673012612226351104) (*.f64 x (neg.f64 (sqrt.f64 2))) (*.f64 (sqrt.f64 2) x))

(*.f64 (sqrt.f64 2) x)

Outputs
(if (<=.f64 x -1278850416061695/47125446914534694131579097993419809976955095716785201420286055195012674566357244479460731079205201122720511132925006540350105785156086431086764996857554304860885586653967937772270969055149056096849908977391371752266308172471982589601097478449614615258949356272900190565812730839296826751014759649673012612226351104) (.f64 x (neg.f64 (sqrt.f64 2))) (.f64 (sqrt.f64 (*.f64 2 x)) (sqrt.f64 x)))
(if (<=.f64 x -1278850416061695/47125446914534694131579097993419809976955095716785201420286055195012674566357244479460731079205201122720511132925006540350105785156086431086764996857554304860885586653967937772270969055149056096849908977391371752266308172471982589601097478449614615258949356272900190565812730839296826751014759649673012612226351104) (neg.f64 (.f64 x (sqrt.f64 2))) (.f64 (sqrt.f64 (*.f64 x 2)) (sqrt.f64 x)))
(if (<=.f64 x -1278850416061695/47125446914534694131579097993419809976955095716785201420286055195012674566357244479460731079205201122720511132925006540350105785156086431086764996857554304860885586653967937772270969055149056096849908977391371752266308172471982589601097478449614615258949356272900190565812730839296826751014759649673012612226351104) (.f64 (sqrt.f64 2) (neg.f64 x)) (.f64 (sqrt.f64 (*.f64 x 2)) (sqrt.f64 x)))
(if (<=.f64 x -1278850416061695/47125446914534694131579097993419809976955095716785201420286055195012674566357244479460731079205201122720511132925006540350105785156086431086764996857554304860885586653967937772270969055149056096849908977391371752266308172471982589601097478449614615258949356272900190565812730839296826751014759649673012612226351104) (.f64 x (neg.f64 (sqrt.f64 2))) (.f64 (sqrt.f64 2) x))
(if (<=.f64 x -1278850416061695/47125446914534694131579097993419809976955095716785201420286055195012674566357244479460731079205201122720511132925006540350105785156086431086764996857554304860885586653967937772270969055149056096849908977391371752266308172471982589601097478449614615258949356272900190565812730839296826751014759649673012612226351104) (neg.f64 (.f64 x (sqrt.f64 2))) (.f64 x (sqrt.f64 2)))
(if (<=.f64 x -1278850416061695/47125446914534694131579097993419809976955095716785201420286055195012674566357244479460731079205201122720511132925006540350105785156086431086764996857554304860885586653967937772270969055149056096849908977391371752266308172471982589601097478449614615258949356272900190565812730839296826751014759649673012612226351104) (.f64 (sqrt.f64 2) (neg.f64 x)) (.f64 x (sqrt.f64 2)))
(*.f64 (sqrt.f64 2) x)
(*.f64 x (sqrt.f64 2))

Compiler

Compiled 36 to 28 computations (22.2% saved)

soundness644.0ms (11.1%)

Algorithm

3×	egg-herbie

Rules

1082×	`sqr-pow_binary64`
1082×	`sqr-pow_binary64`
964×	`fma-def_binary64`
617×	`cube-prod_binary64`
617×	`cube-prod_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	6	9
1	12	9
2	23	9
3	44	9
4	108	9
5	330	9
6	1255	9
7	2129	9
8	2293	9
9	2477	9
10	2685	9
11	2984	9
12	3375	9
13	3856	9
14	4422	9
15	5110	9
16	5947	9
17	6337	9
18	6625	9
19	6903	9
20	6977	9
21	7013	9
22	7954	9
0	9	164
1	20	164
2	43	164
3	83	164
4	205	164
5	632	164
6	988	164
7	1635	164
8	2038	164
9	2907	164
10	3744	164
11	4611	164
12	5738	164
0	6	9
1	12	9
2	23	9
3	44	9
4	108	9
5	330	9
6	1255	9
7	2129	9
8	2293	9
9	2477	9
10	2685	9
11	2984	9
12	3375	9
13	3856	9
14	4422	9
15	5110	9
16	5947	9
17	6337	9
18	6625	9
19	6903	9
20	6977	9
21	7013	9
22	7954	9

Stop Event

1×	node limit
1×	node limit
1×	node limit

Compiler

Compiled 53 to 43 computations (18.9% saved)

end29.0ms (0.5%)

Compiler: Compiled 34 to 25 computations (26.5% saved)

Iter	Nodes	Cost
0	12	100
1	21	100
2	53	100
3	104	100
4	119	100
5	167	100
6	239	100
7	276	100
8	322	100
9	499	100
10	527	100

Iter	Nodes	Cost
0	12	100
1	21	100
2	53	100
3	104	100
4	119	100
5	167	100
6	239	100
7	276	100
8	322	100
9	499	100
10	527	100

Details

analyze9.0ms (0.2%)

sample1.1s (18.4%)

preprocess172.0ms (3%)

simplify171.0ms (3%)

eval1.0ms (0%)

prune1.0ms (0%)

localize7.0ms (0.1%)

series3.0ms (0.1%)

rewrite99.0ms (1.7%)

simplify88.0ms (1.5%)

eval8.0ms (0.1%)

prune11.0ms (0.2%)

localize5.0ms (0.1%)

series1.0ms (0%)

rewrite43.0ms (0.7%)

simplify6.0ms (0.1%)

localize7.0ms (0.1%)

series1.0ms (0%)

rewrite28.0ms (0.5%)

simplify13.0ms (0.2%)

localize9.0ms (0.2%)

series2.0ms (0%)

rewrite44.0ms (0.8%)

simplify18.0ms (0.3%)

localize12.0ms (0.2%)

series127.0ms (2.2%)

rewrite66.0ms (1.1%)

simplify83.0ms (1.4%)

localize13.0ms (0.2%)

series6.0ms (0.1%)

rewrite60.0ms (1%)

simplify8.0ms (0.1%)

eval48.0ms (0.8%)

prune35.0ms (0.6%)

localize28.0ms (0.5%)

series8.0ms (0.1%)

rewrite246.0ms (4.2%)

simplify94.0ms (1.6%)

localize12.0ms (0.2%)

series41.0ms (0.7%)

rewrite168.0ms (2.9%)

simplify7.0ms (0.1%)

localize29.0ms (0.5%)

series23.0ms (0.4%)

rewrite77.0ms (1.3%)

simplify53.0ms (0.9%)

eval59.0ms (1%)

prune25.0ms (0.4%)

localize97.0ms (1.7%)

series8.0ms (0.1%)

rewrite241.0ms (4.2%)

simplify76.0ms (1.3%)

localize49.0ms (0.9%)

series16.0ms (0.3%)

rewrite204.0ms (3.5%)

simplify172.0ms (3%)

localize19.0ms (0.3%)

series23.0ms (0.4%)

rewrite61.0ms (1.1%)

simplify55.0ms (0.9%)

localize20.0ms (0.3%)

series4.0ms (0.1%)

rewrite54.0ms (0.9%)

simplify106.0ms (1.8%)

localize25.0ms (0.4%)

series5.0ms (0.1%)

rewrite77.0ms (1.3%)

simplify115.0ms (2%)

eval207.0ms (3.6%)

prune56.0ms (1%)

regimes135.0ms (2.3%)

bsearch24.0ms (0.4%)

regimes99.0ms (1.7%)

bsearch24.0ms (0.4%)

simplify5.0ms (0.1%)

soundness644.0ms (11.1%)

end29.0ms (0.5%)

Profiling

Iter	Nodes	Cost
0	12	100
1	21	100
2	53	100
3	104	100
4	119	100
5	167	100
6	239	100
7	276	100
8	322	100
9	499	100
10	527	100