Details

analyze5.0ms (0%)

Algorithm

1×

Search

True	Other	False	Iter
0%	99.9%	0.1%	0
0%	99.9%	0.1%	1
99.9%	0%	0.1%	2

Compiler

Compiled 130 to 81 computations (37.7% saved)

sample7.1s (24.8%)

Results

5.7s	7704×	body	128	valid
506.0ms	222×	body	512	valid
437.0ms	177×	body	1024	valid
176.0ms	153×	body	256	valid

Compiler

Compiled 389 to 242 computations (37.8% saved)

simplify47.0ms (0.2%)

Algorithm

1×	egg-herbie

Rules

797×	`distribute-rgt-in_binary64`
779×	`distribute-lft-in_binary64`
203×	`fma-def_binary64`
172×	`associate-+l+_binary64`
168×	`distribute-lft-out_binary64`

Counts

1 → 2

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	36	164
1	118	155
2	404	150
3	1778	138
4	5017	138

prune21.0ms (0.1%)

Pruning

3 alts after pruning (3 fresh and 0 done)

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

Error

19.4b

Counts

3 → 2

Alt Table

Status	Error	Program
	22.0b	(+.f64 x1 (+.f64 (+.f64 (+.f64 (+.f64 (.f64 (+.f64 (.f64 (.f64 (.f64 2 x1) (/.f64 (-.f64 (+.f64 (.f64 (.f64 3 x1) x1) (.f64 2 x2)) x1) (+.f64 (.f64 x1 x1) 1))) (-.f64 (/.f64 (-.f64 (+.f64 (.f64 (.f64 3 x1) x1) (.f64 2 x2)) x1) (+.f64 (.f64 x1 x1) 1)) 3)) (.f64 (.f64 x1 x1) (-.f64 (.f64 4 (/.f64 (-.f64 (+.f64 (.f64 (.f64 3 x1) x1) (.f64 2 x2)) x1) (+.f64 (.f64 x1 x1) 1))) 6))) (+.f64 (.f64 x1 x1) 1)) (.f64 (.f64 (.f64 3 x1) x1) (/.f64 (-.f64 (+.f64 (.f64 (.f64 3 x1) x1) (.f64 2 x2)) x1) (+.f64 (.f64 x1 x1) 1)))) (.f64 (.f64 x1 x1) x1)) x1) (.f64 3 (/.f64 (-.f64 (-.f64 (.f64 (.f64 3 x1) x1) (.f64 2 x2)) x1) (+.f64 (.f64 x1 x1) 1)))))
▶	19.4b	(+.f64 x1 (fma.f64 3 (/.f64 (-.f64 (.f64 x1 (.f64 x1 3)) (fma.f64 2 x2 x1)) (fma.f64 x1 x1 1)) (fma.f64 x1 (.f64 3 (.f64 x1 (/.f64 (-.f64 (fma.f64 x1 (.f64 x1 3) (.f64 2 x2)) x1) (fma.f64 x1 x1 1)))) (.f64 (fma.f64 x1 x1 1) (+.f64 (+.f64 (.f64 (/.f64 (-.f64 (fma.f64 x1 (.f64 x1 3) (.f64 2 x2)) x1) (fma.f64 x1 x1 1)) (+.f64 (.f64 (+.f64 x1 x1) (-.f64 (/.f64 (-.f64 (fma.f64 x1 (.f64 x1 3) (.f64 2 x2)) x1) (fma.f64 x1 x1 1)) 3)) (.f64 (.f64 x1 x1) 4))) (.f64 (*.f64 x1 x1) -6)) x1)))))

Status

Error

Program

22.0b

(+.f64 x1 (+.f64 (+.f64 (+.f64 (+.f64 (*.f64 (+.f64 (*.f64 (*.f64 (*.f64 2 x1) (/.f64 (-.f64 (+.f64 (*.f64 (*.f64 3 x1) x1) (*.f64 2 x2)) x1) (+.f64 (*.f64 x1 x1) 1))) (-.f64 (/.f64 (-.f64 (+.f64 (*.f64 (*.f64 3 x1) x1) (*.f64 2 x2)) x1) (+.f64 (*.f64 x1 x1) 1)) 3)) (*.f64 (*.f64 x1 x1) (-.f64 (*.f64 4 (/.f64 (-.f64 (+.f64 (*.f64 (*.f64 3 x1) x1) (*.f64 2 x2)) x1) (+.f64 (*.f64 x1 x1) 1))) 6))) (+.f64 (*.f64 x1 x1) 1)) (*.f64 (*.f64 (*.f64 3 x1) x1) (/.f64 (-.f64 (+.f64 (*.f64 (*.f64 3 x1) x1) (*.f64 2 x2)) x1) (+.f64 (*.f64 x1 x1) 1)))) (*.f64 (*.f64 x1 x1) x1)) x1) (*.f64 3 (/.f64 (-.f64 (-.f64 (*.f64 (*.f64 3 x1) x1) (*.f64 2 x2)) x1) (+.f64 (*.f64 x1 x1) 1)))))

▶

19.4b

(+.f64 x1 (fma.f64 3 (/.f64 (-.f64 (*.f64 x1 (*.f64 x1 3)) (fma.f64 2 x2 x1)) (fma.f64 x1 x1 1)) (fma.f64 x1 (*.f64 3 (*.f64 x1 (/.f64 (-.f64 (fma.f64 x1 (*.f64 x1 3) (*.f64 2 x2)) x1) (fma.f64 x1 x1 1)))) (*.f64 (fma.f64 x1 x1 1) (+.f64 (+.f64 (*.f64 (/.f64 (-.f64 (fma.f64 x1 (*.f64 x1 3) (*.f64 2 x2)) x1) (fma.f64 x1 x1 1)) (+.f64 (*.f64 (+.f64 x1 x1) (-.f64 (/.f64 (-.f64 (fma.f64 x1 (*.f64 x1 3) (*.f64 2 x2)) x1) (fma.f64 x1 x1 1)) 3)) (*.f64 (*.f64 x1 x1) 4))) (*.f64 (*.f64 x1 x1) -6)) x1)))))

Compiler

Compiled 679 to 420 computations (38.1% saved)

localize74.0ms (0.3%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	2.8b	(-.f64 (/.f64 (-.f64 (fma.f64 x1 (.f64 x1 3) (.f64 2 x2)) x1) (fma.f64 x1 x1 1)) 3)
✓	16.4b	(+.f64 (.f64 (/.f64 (-.f64 (fma.f64 x1 (.f64 x1 3) (.f64 2 x2)) x1) (fma.f64 x1 x1 1)) (+.f64 (.f64 (+.f64 x1 x1) (-.f64 (/.f64 (-.f64 (fma.f64 x1 (.f64 x1 3) (.f64 2 x2)) x1) (fma.f64 x1 x1 1)) 3)) (.f64 (.f64 x1 x1) 4))) (.f64 (.f64 x1 x1) -6))
✓	18.7b	(/.f64 (-.f64 (fma.f64 x1 (.f64 x1 3) (.f64 2 x2)) x1) (fma.f64 x1 x1 1))
✓	18.7b	(/.f64 (-.f64 (.f64 x1 (.f64 x1 3)) (fma.f64 2 x2 x1)) (fma.f64 x1 x1 1))

series765.0ms (2.7%)

Counts

4 → 96

Calls

4 calls:

448.0ms	(+.f64 (.f64 (/.f64 (-.f64 (fma.f64 x1 (.f64 x1 3) (.f64 2 x2)) x1) (fma.f64 x1 x1 1)) (+.f64 (.f64 (+.f64 x1 x1) (-.f64 (/.f64 (-.f64 (fma.f64 x1 (.f64 x1 3) (.f64 2 x2)) x1) (fma.f64 x1 x1 1)) 3)) (.f64 (.f64 x1 x1) 4))) (.f64 (.f64 x1 x1) -6))
134.0ms	(/.f64 (-.f64 (fma.f64 x1 (.f64 x1 3) (.f64 2 x2)) x1) (fma.f64 x1 x1 1))
124.0ms	(-.f64 (/.f64 (-.f64 (fma.f64 x1 (.f64 x1 3) (.f64 2 x2)) x1) (fma.f64 x1 x1 1)) 3)
58.0ms	(/.f64 (-.f64 (.f64 x1 (.f64 x1 3)) (fma.f64 2 x2 x1)) (fma.f64 x1 x1 1))

rewrite134.0ms (0.5%)

Algorithm

1×	rewrite-expression-head

Rules

115×	`add-sqr-sqrt_binary64`
112×	`*-un-lft-identity_binary64`
85×	`times-frac_binary64`
78×	`add-cube-cbrt_binary64`
57×	`prod-diff_binary64`

Counts

4 → 184

Calls

4 calls:

41.0ms	(+.f64 (.f64 (/.f64 (-.f64 (fma.f64 x1 (.f64 x1 3) (.f64 2 x2)) x1) (fma.f64 x1 x1 1)) (+.f64 (.f64 (+.f64 x1 x1) (-.f64 (/.f64 (-.f64 (fma.f64 x1 (.f64 x1 3) (.f64 2 x2)) x1) (fma.f64 x1 x1 1)) 3)) (.f64 (.f64 x1 x1) 4))) (.f64 (.f64 x1 x1) -6))
20.0ms	(-.f64 (/.f64 (-.f64 (fma.f64 x1 (.f64 x1 3) (.f64 2 x2)) x1) (fma.f64 x1 x1 1)) 3)
13.0ms	(/.f64 (-.f64 (.f64 x1 (.f64 x1 3)) (fma.f64 2 x2 x1)) (fma.f64 x1 x1 1))
12.0ms	(/.f64 (-.f64 (fma.f64 x1 (.f64 x1 3) (.f64 2 x2)) x1) (fma.f64 x1 x1 1))

simplify408.0ms (1.4%)

Algorithm

1×	egg-herbie

Rules

438×	`fma-neg_binary64`
395×	`times-frac_binary64`
354×	`fma-def_binary64`
215×	`+-commutative_binary64`
151×	`associate-r_binary64`

Counts

280 → 349

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	445	12224
1	1193	9890
2	4060	9709
3	5000	9709

prune3.7s (13.1%)

Pruning

6 alts after pruning (6 fresh and 0 done)

	Pruned	Kept	Total
New	506	5	511
Fresh	0	1	1
Picked	1	0	1
Done	0	0	0
Total	507	6	513

Error

19.3b

Counts

513 → 6

Alt Table

Status	Error	Program
	33.0b	(+.f64 x1 (fma.f64 3 (/.f64 (-.f64 (.f64 x1 (.f64 x1 3)) (fma.f64 2 x2 x1)) (fma.f64 x1 x1 1)) (fma.f64 x1 (.f64 3 (.f64 x1 (/.f64 (-.f64 (fma.f64 x1 (.f64 x1 3) (.f64 2 x2)) x1) (fma.f64 x1 x1 1)))) (.f64 (fma.f64 x1 x1 1) (+.f64 (.f64 x1 (fma.f64 x2 (.f64 x2 8) (.f64 x2 -12))) x1)))))
	22.0b	(+.f64 x1 (+.f64 (+.f64 (+.f64 (+.f64 (.f64 (+.f64 (.f64 (.f64 (.f64 2 x1) (/.f64 (-.f64 (+.f64 (.f64 (.f64 3 x1) x1) (.f64 2 x2)) x1) (+.f64 (.f64 x1 x1) 1))) (-.f64 (/.f64 (-.f64 (+.f64 (.f64 (.f64 3 x1) x1) (.f64 2 x2)) x1) (+.f64 (.f64 x1 x1) 1)) 3)) (.f64 (.f64 x1 x1) (-.f64 (.f64 4 (/.f64 (-.f64 (+.f64 (.f64 (.f64 3 x1) x1) (.f64 2 x2)) x1) (+.f64 (.f64 x1 x1) 1))) 6))) (+.f64 (.f64 x1 x1) 1)) (.f64 (.f64 (.f64 3 x1) x1) (/.f64 (-.f64 (+.f64 (.f64 (.f64 3 x1) x1) (.f64 2 x2)) x1) (+.f64 (.f64 x1 x1) 1)))) (.f64 (.f64 x1 x1) x1)) x1) (.f64 3 (/.f64 (-.f64 (-.f64 (.f64 (.f64 3 x1) x1) (.f64 2 x2)) x1) (+.f64 (.f64 x1 x1) 1)))))
	35.1b	(+.f64 x1 (fma.f64 3 (/.f64 (-.f64 (.f64 x1 (.f64 x1 3)) (fma.f64 2 x2 x1)) (fma.f64 x1 x1 1)) (fma.f64 x1 (.f64 3 (.f64 x1 (/.f64 (-.f64 (fma.f64 x1 (.f64 x1 3) (.f64 2 x2)) x1) (fma.f64 x1 x1 1)))) (.f64 (fma.f64 x1 x1 1) (+.f64 (-.f64 (.f64 6 (pow.f64 x1 2)) (*.f64 4 x1)) x1)))))
	26.1b	(+.f64 x1 (fma.f64 3 (/.f64 (-.f64 (.f64 x1 (.f64 x1 3)) (fma.f64 2 x2 x1)) (fma.f64 x1 x1 1)) (fma.f64 x1 (.f64 3 (.f64 x1 (/.f64 (-.f64 (fma.f64 x1 (.f64 x1 3) (.f64 2 x2)) x1) (fma.f64 x1 x1 1)))) (.f64 (fma.f64 x1 x1 1) (+.f64 (cbrt.f64 (pow.f64 (fma.f64 (.f64 x1 x1) -6 (.f64 (/.f64 (-.f64 (fma.f64 x2 2 (.f64 3 (.f64 x1 x1))) x1) (fma.f64 x1 x1 1)) (fma.f64 x1 (.f64 x1 4) (.f64 (+.f64 x1 x1) (-.f64 (/.f64 (-.f64 (fma.f64 x2 2 (.f64 3 (*.f64 x1 x1))) x1) (fma.f64 x1 x1 1)) 3))))) 3)) x1)))))
	20.0b	(+.f64 x1 (fma.f64 3 (/.f64 (.f64 (cbrt.f64 (-.f64 (.f64 x1 (.f64 x1 3)) (fma.f64 2 x2 x1))) (cbrt.f64 (-.f64 (.f64 x1 (.f64 x1 3)) (fma.f64 2 x2 x1)))) (/.f64 (fma.f64 x1 x1 1) (cbrt.f64 (-.f64 (.f64 x1 (.f64 x1 3)) (fma.f64 2 x2 x1))))) (fma.f64 x1 (.f64 3 (.f64 x1 (/.f64 (-.f64 (fma.f64 x1 (.f64 x1 3) (.f64 2 x2)) x1) (fma.f64 x1 x1 1)))) (.f64 (fma.f64 x1 x1 1) (+.f64 (+.f64 (.f64 (/.f64 (-.f64 (fma.f64 x1 (.f64 x1 3) (.f64 2 x2)) x1) (fma.f64 x1 x1 1)) (+.f64 (.f64 (+.f64 x1 x1) (-.f64 (/.f64 (-.f64 (fma.f64 x1 (.f64 x1 3) (.f64 2 x2)) x1) (fma.f64 x1 x1 1)) 3)) (.f64 (.f64 x1 x1) 4))) (.f64 (.f64 x1 x1) -6)) x1)))))
▶	19.4b	(+.f64 x1 (fma.f64 3 (/.f64 (-.f64 (.f64 x1 (.f64 x1 3)) (fma.f64 2 x2 x1)) (fma.f64 x1 x1 1)) (fma.f64 x1 (.f64 3 (.f64 x1 (/.f64 (-.f64 (fma.f64 x1 (.f64 x1 3) (.f64 2 x2)) x1) (fma.f64 x1 x1 1)))) (.f64 (fma.f64 x1 x1 1) (+.f64 (fma.f64 (/.f64 (-.f64 (fma.f64 x1 (.f64 x1 3) (.f64 2 x2)) x1) (fma.f64 x1 x1 1)) (+.f64 (.f64 (+.f64 x1 x1) (-.f64 (/.f64 (-.f64 (fma.f64 x1 (.f64 x1 3) (.f64 2 x2)) x1) (fma.f64 x1 x1 1)) 3)) (.f64 (.f64 x1 x1) 4)) (.f64 (.f64 x1 x1) -6)) x1)))))

Compiler

Compiled 57830 to 35331 computations (38.9% saved)

localize116.0ms (0.4%)

Local error

Found 4 expressions with local error:

New	Error	Program
	2.8b	(-.f64 (/.f64 (-.f64 (fma.f64 x1 (.f64 x1 3) (.f64 2 x2)) x1) (fma.f64 x1 x1 1)) 3)
	18.7b	(/.f64 (-.f64 (fma.f64 x1 (.f64 x1 3) (.f64 2 x2)) x1) (fma.f64 x1 x1 1))
	18.7b	(/.f64 (-.f64 (.f64 x1 (.f64 x1 3)) (fma.f64 2 x2 x1)) (fma.f64 x1 x1 1))
✓	18.9b	(fma.f64 (/.f64 (-.f64 (fma.f64 x1 (.f64 x1 3) (.f64 2 x2)) x1) (fma.f64 x1 x1 1)) (+.f64 (.f64 (+.f64 x1 x1) (-.f64 (/.f64 (-.f64 (fma.f64 x1 (.f64 x1 3) (.f64 2 x2)) x1) (fma.f64 x1 x1 1)) 3)) (.f64 (.f64 x1 x1) 4)) (.f64 (*.f64 x1 x1) -6))

series291.0ms (1%)

Counts

1 → 24

Calls

1 calls:

291.0ms

(fma.f64 (/.f64 (-.f64 (fma.f64 x1 (*.f64 x1 3) (*.f64 2 x2)) x1) (fma.f64 x1 x1 1)) (+.f64 (*.f64 (+.f64 x1 x1) (-.f64 (/.f64 (-.f64 (fma.f64 x1 (*.f64 x1 3) (*.f64 2 x2)) x1) (fma.f64 x1 x1 1)) 3)) (*.f64 (*.f64 x1 x1) 4)) (*.f64 (*.f64 x1 x1) -6))

rewrite3.0ms (0%)

Algorithm

1×	rewrite-expression-head

Rules

1×	`*-un-lft-identity_binary64`
1×	`add-sqr-sqrt_binary64`
1×	`add-cube-cbrt_binary64`
1×	`add-cbrt-cube_binary64`
1×	`add-exp-log_binary64`

Counts

1 → 10

Calls

1 calls:

1.0ms

(fma.f64 (/.f64 (-.f64 (fma.f64 x1 (*.f64 x1 3) (*.f64 2 x2)) x1) (fma.f64 x1 x1 1)) (+.f64 (*.f64 (+.f64 x1 x1) (-.f64 (/.f64 (-.f64 (fma.f64 x1 (*.f64 x1 3) (*.f64 2 x2)) x1) (fma.f64 x1 x1 1)) 3)) (*.f64 (*.f64 x1 x1) 4)) (*.f64 (*.f64 x1 x1) -6))

simplify178.0ms (0.6%)

Algorithm

1×	egg-herbie

Rules

806×	`fma-neg_binary64`
333×	`associate-r_binary64`
330×	`cancel-sign-sub-inv_binary64`
313×	`associate-l_binary64`
208×	`associate-/l*_binary64`

Counts

34 → 44

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	149	2913
1	467	2764
2	1656	2731
3	4785	2711
4	5371	2711

prune4.7s (16.6%)

Pruning

7 alts after pruning (6 fresh and 1 done)

	Pruned	Kept	Total
New	500	2	502
Fresh	1	4	5
Picked	0	1	1
Done	0	0	0
Total	501	7	508

Error

19.3b

Counts

508 → 7

Alt Table

Status	Error	Program
	33.0b	(+.f64 x1 (fma.f64 3 (/.f64 (-.f64 (.f64 x1 (.f64 x1 3)) (fma.f64 2 x2 x1)) (fma.f64 x1 x1 1)) (fma.f64 x1 (.f64 3 (.f64 x1 (/.f64 (-.f64 (fma.f64 x1 (.f64 x1 3) (.f64 2 x2)) x1) (fma.f64 x1 x1 1)))) (.f64 (fma.f64 x1 x1 1) (+.f64 (.f64 (*.f64 x2 (fma.f64 8 x2 -12)) x1) x1)))))
	26.1b	(+.f64 x1 (fma.f64 3 (/.f64 (-.f64 (.f64 x1 (.f64 x1 3)) (fma.f64 2 x2 x1)) (fma.f64 x1 x1 1)) (fma.f64 x1 (.f64 3 (.f64 x1 (/.f64 (-.f64 (fma.f64 x1 (.f64 x1 3) (.f64 2 x2)) x1) (fma.f64 x1 x1 1)))) (.f64 (fma.f64 x1 x1 1) (+.f64 (cbrt.f64 (pow.f64 (fma.f64 (.f64 x1 x1) -6 (.f64 (/.f64 (-.f64 (fma.f64 x2 2 (.f64 3 (.f64 x1 x1))) x1) (fma.f64 x1 x1 1)) (fma.f64 x1 (.f64 x1 4) (.f64 (+.f64 x1 x1) (-.f64 (/.f64 (-.f64 (fma.f64 x2 2 (.f64 3 (*.f64 x1 x1))) x1) (fma.f64 x1 x1 1)) 3))))) 3)) x1)))))
	35.1b	(+.f64 x1 (fma.f64 3 (/.f64 (-.f64 (.f64 x1 (.f64 x1 3)) (fma.f64 2 x2 x1)) (fma.f64 x1 x1 1)) (fma.f64 x1 (.f64 3 (.f64 x1 (/.f64 (-.f64 (fma.f64 x1 (.f64 x1 3) (.f64 2 x2)) x1) (fma.f64 x1 x1 1)))) (.f64 (fma.f64 x1 x1 1) (+.f64 (-.f64 (.f64 6 (pow.f64 x1 2)) (*.f64 4 x1)) x1)))))
	22.0b	(+.f64 x1 (+.f64 (+.f64 (+.f64 (+.f64 (.f64 (+.f64 (.f64 (.f64 (.f64 2 x1) (/.f64 (-.f64 (+.f64 (.f64 (.f64 3 x1) x1) (.f64 2 x2)) x1) (+.f64 (.f64 x1 x1) 1))) (-.f64 (/.f64 (-.f64 (+.f64 (.f64 (.f64 3 x1) x1) (.f64 2 x2)) x1) (+.f64 (.f64 x1 x1) 1)) 3)) (.f64 (.f64 x1 x1) (-.f64 (.f64 4 (/.f64 (-.f64 (+.f64 (.f64 (.f64 3 x1) x1) (.f64 2 x2)) x1) (+.f64 (.f64 x1 x1) 1))) 6))) (+.f64 (.f64 x1 x1) 1)) (.f64 (.f64 (.f64 3 x1) x1) (/.f64 (-.f64 (+.f64 (.f64 (.f64 3 x1) x1) (.f64 2 x2)) x1) (+.f64 (.f64 x1 x1) 1)))) (.f64 (.f64 x1 x1) x1)) x1) (.f64 3 (/.f64 (-.f64 (-.f64 (.f64 (.f64 3 x1) x1) (.f64 2 x2)) x1) (+.f64 (.f64 x1 x1) 1)))))
	20.0b	(+.f64 x1 (fma.f64 3 (/.f64 (.f64 (cbrt.f64 (-.f64 (.f64 x1 (.f64 x1 3)) (fma.f64 2 x2 x1))) (cbrt.f64 (-.f64 (.f64 x1 (.f64 x1 3)) (fma.f64 2 x2 x1)))) (/.f64 (fma.f64 x1 x1 1) (cbrt.f64 (-.f64 (.f64 x1 (.f64 x1 3)) (fma.f64 2 x2 x1))))) (fma.f64 x1 (.f64 3 (.f64 x1 (/.f64 (-.f64 (fma.f64 x1 (.f64 x1 3) (.f64 2 x2)) x1) (fma.f64 x1 x1 1)))) (.f64 (fma.f64 x1 x1 1) (+.f64 (+.f64 (.f64 (/.f64 (-.f64 (fma.f64 x1 (.f64 x1 3) (.f64 2 x2)) x1) (fma.f64 x1 x1 1)) (+.f64 (.f64 (+.f64 x1 x1) (-.f64 (/.f64 (-.f64 (fma.f64 x1 (.f64 x1 3) (.f64 2 x2)) x1) (fma.f64 x1 x1 1)) 3)) (.f64 (.f64 x1 x1) 4))) (.f64 (.f64 x1 x1) -6)) x1)))))
▶	19.4b	(+.f64 x1 (fma.f64 3 (/.f64 (-.f64 (.f64 x1 (.f64 x1 3)) (fma.f64 2 x2 x1)) (fma.f64 x1 x1 1)) (fma.f64 x1 (.f64 3 (.f64 x1 (/.f64 (-.f64 (fma.f64 x1 (.f64 x1 3) (.f64 2 x2)) x1) (fma.f64 x1 x1 1)))) (.f64 (fma.f64 x1 x1 1) (+.f64 (fma.f64 (/.f64 1 (/.f64 (fma.f64 x1 x1 1) (-.f64 (fma.f64 x2 2 (.f64 3 (.f64 x1 x1))) x1))) (+.f64 (.f64 (+.f64 x1 x1) (-.f64 (/.f64 (-.f64 (fma.f64 x1 (.f64 x1 3) (.f64 2 x2)) x1) (fma.f64 x1 x1 1)) 3)) (.f64 (.f64 x1 x1) 4)) (.f64 (.f64 x1 x1) -6)) x1)))))
✓	19.4b	(+.f64 x1 (fma.f64 3 (/.f64 (-.f64 (.f64 x1 (.f64 x1 3)) (fma.f64 2 x2 x1)) (fma.f64 x1 x1 1)) (fma.f64 x1 (.f64 3 (.f64 x1 (/.f64 (-.f64 (fma.f64 x1 (.f64 x1 3) (.f64 2 x2)) x1) (fma.f64 x1 x1 1)))) (.f64 (fma.f64 x1 x1 1) (+.f64 (fma.f64 (/.f64 (-.f64 (fma.f64 x1 (.f64 x1 3) (.f64 2 x2)) x1) (fma.f64 x1 x1 1)) (+.f64 (.f64 (+.f64 x1 x1) (-.f64 (/.f64 (-.f64 (fma.f64 x1 (.f64 x1 3) (.f64 2 x2)) x1) (fma.f64 x1 x1 1)) 3)) (.f64 (.f64 x1 x1) 4)) (.f64 (.f64 x1 x1) -6)) x1)))))

Compiler

Compiled 56019 to 34116 computations (39.1% saved)

localize54.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
	18.7b	(/.f64 (-.f64 (fma.f64 x1 (.f64 x1 3) (.f64 2 x2)) x1) (fma.f64 x1 x1 1))
	18.7b	(/.f64 (-.f64 (.f64 x1 (.f64 x1 3)) (fma.f64 2 x2 x1)) (fma.f64 x1 x1 1))
✓	18.7b	(/.f64 (fma.f64 x1 x1 1) (-.f64 (fma.f64 x2 2 (.f64 3 (.f64 x1 x1))) x1))
✓	18.9b	(fma.f64 (/.f64 1 (/.f64 (fma.f64 x1 x1 1) (-.f64 (fma.f64 x2 2 (.f64 3 (.f64 x1 x1))) x1))) (+.f64 (.f64 (+.f64 x1 x1) (-.f64 (/.f64 (-.f64 (fma.f64 x1 (.f64 x1 3) (.f64 2 x2)) x1) (fma.f64 x1 x1 1)) 3)) (.f64 (.f64 x1 x1) 4)) (.f64 (*.f64 x1 x1) -6))

series256.0ms (0.9%)

Counts

2 → 48

Calls

2 calls:

181.0ms

(fma.f64 (/.f64 1 (/.f64 (fma.f64 x1 x1 1) (-.f64 (fma.f64 x2 2 (*.f64 3 (*.f64 x1 x1))) x1))) (+.f64 (*.f64 (+.f64 x1 x1) (-.f64 (/.f64 (-.f64 (fma.f64 x1 (*.f64 x1 3) (*.f64 2 x2)) x1) (fma.f64 x1 x1 1)) 3)) (*.f64 (*.f64 x1 x1) 4)) (*.f64 (*.f64 x1 x1) -6))

75.0ms

(/.f64 (fma.f64 x1 x1 1) (-.f64 (fma.f64 x2 2 (*.f64 3 (*.f64 x1 x1))) x1))

rewrite20.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

20×	`*-un-lft-identity_binary64`
20×	`add-sqr-sqrt_binary64`
15×	`times-frac_binary64`
12×	`add-cube-cbrt_binary64`
5×	`associate-/r*_binary64`

Counts

2 → 49

Calls

2 calls:

8.0ms

(/.f64 (fma.f64 x1 x1 1) (-.f64 (fma.f64 x2 2 (*.f64 3 (*.f64 x1 x1))) x1))

1.0ms

(fma.f64 (/.f64 1 (/.f64 (fma.f64 x1 x1 1) (-.f64 (fma.f64 x2 2 (*.f64 3 (*.f64 x1 x1))) x1))) (+.f64 (*.f64 (+.f64 x1 x1) (-.f64 (/.f64 (-.f64 (fma.f64 x1 (*.f64 x1 3) (*.f64 2 x2)) x1) (fma.f64 x1 x1 1)) 3)) (*.f64 (*.f64 x1 x1) 4)) (*.f64 (*.f64 x1 x1) -6))

simplify242.0ms (0.9%)

Algorithm

1×	egg-herbie

Rules

664×	`cancel-sign-sub-inv_binary64`
378×	`fma-def_binary64`
358×	`sub-neg_binary64`
294×	`fma-neg_binary64`
241×	`associate-+r+_binary64`

Counts

97 → 116

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	367	5870
1	1092	5576
2	4020	5539
3	5520	5539

prune2.5s (8.6%)

Pruning

7 alts after pruning (5 fresh and 2 done)

	Pruned	Kept	Total
New	355	0	355
Fresh	0	5	5
Picked	0	1	1
Done	0	1	1
Total	355	7	362

Error

19.3b

Counts

362 → 7

Alt Table

Status	Error	Program
	33.0b	(+.f64 x1 (fma.f64 3 (/.f64 (-.f64 (.f64 x1 (.f64 x1 3)) (fma.f64 2 x2 x1)) (fma.f64 x1 x1 1)) (fma.f64 x1 (.f64 3 (.f64 x1 (/.f64 (-.f64 (fma.f64 x1 (.f64 x1 3) (.f64 2 x2)) x1) (fma.f64 x1 x1 1)))) (.f64 (fma.f64 x1 x1 1) (+.f64 (.f64 (*.f64 x2 (fma.f64 8 x2 -12)) x1) x1)))))
	26.1b	(+.f64 x1 (fma.f64 3 (/.f64 (-.f64 (.f64 x1 (.f64 x1 3)) (fma.f64 2 x2 x1)) (fma.f64 x1 x1 1)) (fma.f64 x1 (.f64 3 (.f64 x1 (/.f64 (-.f64 (fma.f64 x1 (.f64 x1 3) (.f64 2 x2)) x1) (fma.f64 x1 x1 1)))) (.f64 (fma.f64 x1 x1 1) (+.f64 (cbrt.f64 (pow.f64 (fma.f64 (.f64 x1 x1) -6 (.f64 (/.f64 (-.f64 (fma.f64 x2 2 (.f64 3 (.f64 x1 x1))) x1) (fma.f64 x1 x1 1)) (fma.f64 x1 (.f64 x1 4) (.f64 (+.f64 x1 x1) (-.f64 (/.f64 (-.f64 (fma.f64 x2 2 (.f64 3 (*.f64 x1 x1))) x1) (fma.f64 x1 x1 1)) 3))))) 3)) x1)))))
	35.1b	(+.f64 x1 (fma.f64 3 (/.f64 (-.f64 (.f64 x1 (.f64 x1 3)) (fma.f64 2 x2 x1)) (fma.f64 x1 x1 1)) (fma.f64 x1 (.f64 3 (.f64 x1 (/.f64 (-.f64 (fma.f64 x1 (.f64 x1 3) (.f64 2 x2)) x1) (fma.f64 x1 x1 1)))) (.f64 (fma.f64 x1 x1 1) (+.f64 (-.f64 (.f64 6 (pow.f64 x1 2)) (*.f64 4 x1)) x1)))))
	22.0b	(+.f64 x1 (+.f64 (+.f64 (+.f64 (+.f64 (.f64 (+.f64 (.f64 (.f64 (.f64 2 x1) (/.f64 (-.f64 (+.f64 (.f64 (.f64 3 x1) x1) (.f64 2 x2)) x1) (+.f64 (.f64 x1 x1) 1))) (-.f64 (/.f64 (-.f64 (+.f64 (.f64 (.f64 3 x1) x1) (.f64 2 x2)) x1) (+.f64 (.f64 x1 x1) 1)) 3)) (.f64 (.f64 x1 x1) (-.f64 (.f64 4 (/.f64 (-.f64 (+.f64 (.f64 (.f64 3 x1) x1) (.f64 2 x2)) x1) (+.f64 (.f64 x1 x1) 1))) 6))) (+.f64 (.f64 x1 x1) 1)) (.f64 (.f64 (.f64 3 x1) x1) (/.f64 (-.f64 (+.f64 (.f64 (.f64 3 x1) x1) (.f64 2 x2)) x1) (+.f64 (.f64 x1 x1) 1)))) (.f64 (.f64 x1 x1) x1)) x1) (.f64 3 (/.f64 (-.f64 (-.f64 (.f64 (.f64 3 x1) x1) (.f64 2 x2)) x1) (+.f64 (.f64 x1 x1) 1)))))
▶	20.0b	(+.f64 x1 (fma.f64 3 (/.f64 (.f64 (cbrt.f64 (-.f64 (.f64 x1 (.f64 x1 3)) (fma.f64 2 x2 x1))) (cbrt.f64 (-.f64 (.f64 x1 (.f64 x1 3)) (fma.f64 2 x2 x1)))) (/.f64 (fma.f64 x1 x1 1) (cbrt.f64 (-.f64 (.f64 x1 (.f64 x1 3)) (fma.f64 2 x2 x1))))) (fma.f64 x1 (.f64 3 (.f64 x1 (/.f64 (-.f64 (fma.f64 x1 (.f64 x1 3) (.f64 2 x2)) x1) (fma.f64 x1 x1 1)))) (.f64 (fma.f64 x1 x1 1) (+.f64 (+.f64 (.f64 (/.f64 (-.f64 (fma.f64 x1 (.f64 x1 3) (.f64 2 x2)) x1) (fma.f64 x1 x1 1)) (+.f64 (.f64 (+.f64 x1 x1) (-.f64 (/.f64 (-.f64 (fma.f64 x1 (.f64 x1 3) (.f64 2 x2)) x1) (fma.f64 x1 x1 1)) 3)) (.f64 (.f64 x1 x1) 4))) (.f64 (.f64 x1 x1) -6)) x1)))))
✓	19.4b	(+.f64 x1 (fma.f64 3 (/.f64 (-.f64 (.f64 x1 (.f64 x1 3)) (fma.f64 2 x2 x1)) (fma.f64 x1 x1 1)) (fma.f64 x1 (.f64 3 (.f64 x1 (/.f64 (-.f64 (fma.f64 x1 (.f64 x1 3) (.f64 2 x2)) x1) (fma.f64 x1 x1 1)))) (.f64 (fma.f64 x1 x1 1) (+.f64 (fma.f64 (/.f64 1 (/.f64 (fma.f64 x1 x1 1) (-.f64 (fma.f64 x2 2 (.f64 3 (.f64 x1 x1))) x1))) (+.f64 (.f64 (+.f64 x1 x1) (-.f64 (/.f64 (-.f64 (fma.f64 x1 (.f64 x1 3) (.f64 2 x2)) x1) (fma.f64 x1 x1 1)) 3)) (.f64 (.f64 x1 x1) 4)) (.f64 (.f64 x1 x1) -6)) x1)))))
✓	19.4b	(+.f64 x1 (fma.f64 3 (/.f64 (-.f64 (.f64 x1 (.f64 x1 3)) (fma.f64 2 x2 x1)) (fma.f64 x1 x1 1)) (fma.f64 x1 (.f64 3 (.f64 x1 (/.f64 (-.f64 (fma.f64 x1 (.f64 x1 3) (.f64 2 x2)) x1) (fma.f64 x1 x1 1)))) (.f64 (fma.f64 x1 x1 1) (+.f64 (fma.f64 (/.f64 (-.f64 (fma.f64 x1 (.f64 x1 3) (.f64 2 x2)) x1) (fma.f64 x1 x1 1)) (+.f64 (.f64 (+.f64 x1 x1) (-.f64 (/.f64 (-.f64 (fma.f64 x1 (.f64 x1 3) (.f64 2 x2)) x1) (fma.f64 x1 x1 1)) 3)) (.f64 (.f64 x1 x1) 4)) (.f64 (.f64 x1 x1) -6)) x1)))))

Compiler

Compiled 40396 to 24372 computations (39.7% saved)

localize40.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	11.5b	(/.f64 (fma.f64 x1 x1 1) (cbrt.f64 (-.f64 (.f64 x1 (.f64 x1 3)) (fma.f64 2 x2 x1))))
	16.4b	(+.f64 (.f64 (/.f64 (-.f64 (fma.f64 x1 (.f64 x1 3) (.f64 2 x2)) x1) (fma.f64 x1 x1 1)) (+.f64 (.f64 (+.f64 x1 x1) (-.f64 (/.f64 (-.f64 (fma.f64 x1 (.f64 x1 3) (.f64 2 x2)) x1) (fma.f64 x1 x1 1)) 3)) (.f64 (.f64 x1 x1) 4))) (.f64 (.f64 x1 x1) -6))
	18.7b	(/.f64 (-.f64 (fma.f64 x1 (.f64 x1 3) (.f64 2 x2)) x1) (fma.f64 x1 x1 1))
✓	18.7b	(cbrt.f64 (-.f64 (.f64 x1 (.f64 x1 3)) (fma.f64 2 x2 x1)))

series132.0ms (0.5%)

Counts

2 → 48

Calls

2 calls:

93.0ms	(/.f64 (fma.f64 x1 x1 1) (cbrt.f64 (-.f64 (.f64 x1 (.f64 x1 3)) (fma.f64 2 x2 x1))))
38.0ms	(cbrt.f64 (-.f64 (.f64 x1 (.f64 x1 3)) (fma.f64 2 x2 x1)))

rewrite68.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

18×	`times-frac_binary64`
18×	`*-un-lft-identity_binary64`
18×	`add-sqr-sqrt_binary64`
18×	`add-cube-cbrt_binary64`
15×	`cbrt-prod_binary64`

Counts

2 → 58

Calls

2 calls:

57.0ms	(cbrt.f64 (-.f64 (.f64 x1 (.f64 x1 3)) (fma.f64 2 x2 x1)))
7.0ms	(/.f64 (fma.f64 x1 x1 1) (cbrt.f64 (-.f64 (.f64 x1 (.f64 x1 3)) (fma.f64 2 x2 x1))))

simplify184.0ms (0.6%)

Algorithm

1×	egg-herbie

Rules

583×	`fma-def_binary64`
296×	`times-frac_binary64`
285×	`associate-/l*_binary64`
222×	`associate-/r*_binary64`
204×	`associate-l_binary64`

Counts

106 → 197

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	624	7403
1	1858	6937
2	4968	6937
3	4961	6937

prune4.1s (14.6%)

Pruning

7 alts after pruning (5 fresh and 2 done)

	Pruned	Kept	Total
New	636	1	637
Fresh	0	4	4
Picked	1	0	1
Done	0	2	2
Total	637	7	644

Error

19.3b

Counts

644 → 7

Alt Table

Status	Error	Program
	33.0b	(+.f64 x1 (fma.f64 3 (/.f64 (-.f64 (.f64 x1 (.f64 x1 3)) (fma.f64 2 x2 x1)) (fma.f64 x1 x1 1)) (fma.f64 x1 (.f64 3 (.f64 x1 (/.f64 (-.f64 (fma.f64 x1 (.f64 x1 3) (.f64 2 x2)) x1) (fma.f64 x1 x1 1)))) (.f64 (fma.f64 x1 x1 1) (+.f64 (.f64 (*.f64 x2 (fma.f64 8 x2 -12)) x1) x1)))))
	26.1b	(+.f64 x1 (fma.f64 3 (/.f64 (-.f64 (.f64 x1 (.f64 x1 3)) (fma.f64 2 x2 x1)) (fma.f64 x1 x1 1)) (fma.f64 x1 (.f64 3 (.f64 x1 (/.f64 (-.f64 (fma.f64 x1 (.f64 x1 3) (.f64 2 x2)) x1) (fma.f64 x1 x1 1)))) (.f64 (fma.f64 x1 x1 1) (+.f64 (cbrt.f64 (pow.f64 (fma.f64 (.f64 x1 x1) -6 (.f64 (/.f64 (-.f64 (fma.f64 x2 2 (.f64 3 (.f64 x1 x1))) x1) (fma.f64 x1 x1 1)) (fma.f64 x1 (.f64 x1 4) (.f64 (+.f64 x1 x1) (-.f64 (/.f64 (-.f64 (fma.f64 x2 2 (.f64 3 (*.f64 x1 x1))) x1) (fma.f64 x1 x1 1)) 3))))) 3)) x1)))))
	35.1b	(+.f64 x1 (fma.f64 3 (/.f64 (-.f64 (.f64 x1 (.f64 x1 3)) (fma.f64 2 x2 x1)) (fma.f64 x1 x1 1)) (fma.f64 x1 (.f64 3 (.f64 x1 (/.f64 (-.f64 (fma.f64 x1 (.f64 x1 3) (.f64 2 x2)) x1) (fma.f64 x1 x1 1)))) (.f64 (fma.f64 x1 x1 1) (+.f64 (-.f64 (.f64 6 (pow.f64 x1 2)) (*.f64 4 x1)) x1)))))
	22.0b	(+.f64 x1 (+.f64 (+.f64 (+.f64 (+.f64 (.f64 (+.f64 (.f64 (.f64 (.f64 2 x1) (/.f64 (-.f64 (+.f64 (.f64 (.f64 3 x1) x1) (.f64 2 x2)) x1) (+.f64 (.f64 x1 x1) 1))) (-.f64 (/.f64 (-.f64 (+.f64 (.f64 (.f64 3 x1) x1) (.f64 2 x2)) x1) (+.f64 (.f64 x1 x1) 1)) 3)) (.f64 (.f64 x1 x1) (-.f64 (.f64 4 (/.f64 (-.f64 (+.f64 (.f64 (.f64 3 x1) x1) (.f64 2 x2)) x1) (+.f64 (.f64 x1 x1) 1))) 6))) (+.f64 (.f64 x1 x1) 1)) (.f64 (.f64 (.f64 3 x1) x1) (/.f64 (-.f64 (+.f64 (.f64 (.f64 3 x1) x1) (.f64 2 x2)) x1) (+.f64 (.f64 x1 x1) 1)))) (.f64 (.f64 x1 x1) x1)) x1) (.f64 3 (/.f64 (-.f64 (-.f64 (.f64 (.f64 3 x1) x1) (.f64 2 x2)) x1) (+.f64 (.f64 x1 x1) 1)))))
	19.9b	(+.f64 x1 (fma.f64 3 (/.f64 (.f64 (cbrt.f64 (-.f64 (.f64 x1 (.f64 x1 3)) (fma.f64 2 x2 x1))) (cbrt.f64 (-.f64 (.f64 x1 (.f64 x1 3)) (fma.f64 2 x2 x1)))) (cbrt.f64 (/.f64 (pow.f64 (fma.f64 x1 x1 1) 3) (-.f64 (.f64 (.f64 x1 x1) 3) (fma.f64 2 x2 x1))))) (fma.f64 x1 (.f64 3 (.f64 x1 (/.f64 (-.f64 (fma.f64 x1 (.f64 x1 3) (.f64 2 x2)) x1) (fma.f64 x1 x1 1)))) (.f64 (fma.f64 x1 x1 1) (+.f64 (+.f64 (.f64 (/.f64 (-.f64 (fma.f64 x1 (.f64 x1 3) (.f64 2 x2)) x1) (fma.f64 x1 x1 1)) (+.f64 (.f64 (+.f64 x1 x1) (-.f64 (/.f64 (-.f64 (fma.f64 x1 (.f64 x1 3) (.f64 2 x2)) x1) (fma.f64 x1 x1 1)) 3)) (.f64 (.f64 x1 x1) 4))) (.f64 (.f64 x1 x1) -6)) x1)))))
✓	19.4b	(+.f64 x1 (fma.f64 3 (/.f64 (-.f64 (.f64 x1 (.f64 x1 3)) (fma.f64 2 x2 x1)) (fma.f64 x1 x1 1)) (fma.f64 x1 (.f64 3 (.f64 x1 (/.f64 (-.f64 (fma.f64 x1 (.f64 x1 3) (.f64 2 x2)) x1) (fma.f64 x1 x1 1)))) (.f64 (fma.f64 x1 x1 1) (+.f64 (fma.f64 (/.f64 1 (/.f64 (fma.f64 x1 x1 1) (-.f64 (fma.f64 x2 2 (.f64 3 (.f64 x1 x1))) x1))) (+.f64 (.f64 (+.f64 x1 x1) (-.f64 (/.f64 (-.f64 (fma.f64 x1 (.f64 x1 3) (.f64 2 x2)) x1) (fma.f64 x1 x1 1)) 3)) (.f64 (.f64 x1 x1) 4)) (.f64 (.f64 x1 x1) -6)) x1)))))
✓	19.4b	(+.f64 x1 (fma.f64 3 (/.f64 (-.f64 (.f64 x1 (.f64 x1 3)) (fma.f64 2 x2 x1)) (fma.f64 x1 x1 1)) (fma.f64 x1 (.f64 3 (.f64 x1 (/.f64 (-.f64 (fma.f64 x1 (.f64 x1 3) (.f64 2 x2)) x1) (fma.f64 x1 x1 1)))) (.f64 (fma.f64 x1 x1 1) (+.f64 (fma.f64 (/.f64 (-.f64 (fma.f64 x1 (.f64 x1 3) (.f64 2 x2)) x1) (fma.f64 x1 x1 1)) (+.f64 (.f64 (+.f64 x1 x1) (-.f64 (/.f64 (-.f64 (fma.f64 x1 (.f64 x1 3) (.f64 2 x2)) x1) (fma.f64 x1 x1 1)) 3)) (.f64 (.f64 x1 x1) 4)) (.f64 (.f64 x1 x1) -6)) x1)))))

Compiler

Compiled 93821 to 60063 computations (36% saved)

regimes2.8s (9.7%)

Accuracy

Total 0.1b remaining (0.6%)

Threshold costs 0.1b (0.6%)

Counts

206 → 1

Compiler

Compiled 80094 to 50585 computations (36.8% saved)

simplify7.0ms (0%)

Algorithm

1×	egg-herbie

Rules

17×	`*-commutative_binary64`
15×	`+-commutative_binary64`
9×	`sub-neg_binary64`
6×	`neg-sub0_binary64`
6×	`neg-mul-1_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	39	160
1	65	160
2	77	160
3	95	160
4	105	160
5	111	160
6	114	160
7	115	160
8	112	160

end565.0ms (2%)

Compiler: Compiled 888 to 565 computations (36.4% saved)

Details

analyze5.0ms (0%)

sample7.1s (24.8%)

simplify47.0ms (0.2%)

prune21.0ms (0.1%)

localize74.0ms (0.3%)

series765.0ms (2.7%)

rewrite134.0ms (0.5%)

simplify408.0ms (1.4%)

prune3.7s (13.1%)

localize116.0ms (0.4%)

series291.0ms (1%)

rewrite3.0ms (0%)

simplify178.0ms (0.6%)

prune4.7s (16.6%)

localize54.0ms (0.2%)

series256.0ms (0.9%)

rewrite20.0ms (0.1%)

simplify242.0ms (0.9%)

prune2.5s (8.6%)

localize40.0ms (0.1%)

series132.0ms (0.5%)

rewrite68.0ms (0.2%)

simplify184.0ms (0.6%)

prune4.1s (14.6%)

regimes2.8s (9.7%)

simplify7.0ms (0%)

end565.0ms (2%)

Profiling