Details

analyze3.0ms (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)

sample3.7s (16.1%)

Infinites

47.6% of outputs are infinite.

Results

3.1s	7733×	body	128	valid
210.0ms	194×	body	512	valid
204.0ms	168×	body	1024	valid
101.0ms	161×	body	256	valid

Compiler

Compiled 389 to 242 computations (37.8% saved)

simplify30.0ms (0.1%)

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

prune10.0ms (0%)

Pruning

3 alts after pruning (3 fresh and 0 done)

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

Error

17.4b

Counts

3 → 2

Alt Table

Status	Error	Program
	20.5b	(+.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)))))
▶	17.4b	(+.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

20.5b

(+.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)))))

▶

17.4b

(+.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)

localize43.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	1.4b	(-.f64 (/.f64 (-.f64 (fma.f64 x1 (.f64 x1 3) (.f64 2 x2)) x1) (fma.f64 x1 x1 1)) 3)
✓	16.8b	(/.f64 (-.f64 (.f64 x1 (.f64 x1 3)) (fma.f64 2 x2 x1)) (fma.f64 x1 x1 1))
✓	16.8b	(/.f64 (-.f64 (fma.f64 x1 (.f64 x1 3) (.f64 2 x2)) x1) (fma.f64 x1 x1 1))
✓	16.8b	(+.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))

series378.0ms (1.6%)

Counts

4 → 96

Calls

4 calls:

226.0ms	(+.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))
71.0ms	(/.f64 (-.f64 (.f64 x1 (.f64 x1 3)) (fma.f64 2 x2 x1)) (fma.f64 x1 x1 1))
47.0ms	(-.f64 (/.f64 (-.f64 (fma.f64 x1 (.f64 x1 3) (.f64 2 x2)) x1) (fma.f64 x1 x1 1)) 3)
33.0ms	(/.f64 (-.f64 (fma.f64 x1 (.f64 x1 3) (.f64 2 x2)) x1) (fma.f64 x1 x1 1))

rewrite64.0ms (0.3%)

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:

20.0ms	(+.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))
10.0ms	(-.f64 (/.f64 (-.f64 (fma.f64 x1 (.f64 x1 3) (.f64 2 x2)) x1) (fma.f64 x1 x1 1)) 3)
7.0ms	(/.f64 (-.f64 (.f64 x1 (.f64 x1 3)) (fma.f64 2 x2 x1)) (fma.f64 x1 x1 1))
5.0ms	(/.f64 (-.f64 (fma.f64 x1 (.f64 x1 3) (.f64 2 x2)) x1) (fma.f64 x1 x1 1))

simplify203.0ms (0.9%)

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 → 350

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	445	12228
1	1193	9890
2	4060	9709
3	5000	9709

prune2.8s (12%)

Pruning

9 alts after pruning (9 fresh and 0 done)

	Pruned	Kept	Total
New	511	9	520
Fresh	1	0	1
Picked	1	0	1
Done	0	0	0
Total	513	9	522

Error

17.3b

Counts

522 → 9

Alt Table

Status	Error	Program
	28.9b	(+.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 (fma.f64 8 (.f64 x2 x2) (.f64 x2 -12)) x1) x1)))))
	42.0b	(+.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 (fma.f64 (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))) (.f64 (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))) (/.f64 (-.f64 (fma.f64 x2 2 (.f64 3 (.f64 x1 x1))) x1) (/.f64 (pow.f64 (fma.f64 x1 x1 1) 2) (-.f64 (fma.f64 x2 2 (.f64 3 (.f64 x1 x1))) x1)))) (.f64 (pow.f64 x1 4) -36)) (fma.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))) (.f64 6 (*.f64 x1 x1)))) x1)))))
	17.5b	(+.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 -3 (pow.f64 (/.f64 (cbrt.f64 (-.f64 (fma.f64 x2 2 (.f64 3 (.f64 x1 x1))) x1)) (cbrt.f64 (fma.f64 x1 x1 1))) 3)) 0)) (.f64 (.f64 x1 x1) 4))) (.f64 (*.f64 x1 x1) -6)) x1)))))
	37.3b	(+.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 x1 (.f64 x1 6) (*.f64 x1 -4)) x1)))))
	35.6b	(+.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 (sqrt.f64 (-.f64 (fma.f64 x1 (.f64 x1 3) (.f64 2 x2)) x1)) (/.f64 (fma.f64 x1 x1 1) (sqrt.f64 (-.f64 (fma.f64 x1 (.f64 x1 3) (.f64 2 x2)) 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)))))
	20.3b	(+.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 (-.f64 (fma.f64 x2 2 (.f64 3 (.f64 x1 x1))) x1) (/.f64 (pow.f64 (fma.f64 x1 x1 1) 2) (-.f64 (fma.f64 x2 2 (.f64 3 (.f64 x1 x1))) x1))) -9) (+.f64 3 (/.f64 (-.f64 (fma.f64 x2 2 (.f64 3 (.f64 x1 x1))) x1) (fma.f64 x1 x1 1))))) (.f64 (.f64 x1 x1) 4))) (.f64 (*.f64 x1 x1) -6)) x1)))))
▶	17.4b	(+.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 1 (hypot.f64 1 x1)) (/.f64 (-.f64 (fma.f64 x2 2 (.f64 3 (.f64 x1 x1))) x1) (hypot.f64 1 x1))) 3)) (.f64 (.f64 x1 x1) 4))) (.f64 (.f64 x1 x1) -6)) x1)))))
	17.4b	(+.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 x1 x1) (-.f64 (/.f64 (-.f64 (fma.f64 x1 (.f64 x1 3) (.f64 2 x2)) x1) (fma.f64 x1 x1 1)) 3)) (/.f64 (-.f64 (fma.f64 x1 (.f64 x1 3) (.f64 2 x2)) x1) (fma.f64 x1 x1 1))) (+.f64 (.f64 (.f64 (.f64 x1 x1) 4) (/.f64 (-.f64 (fma.f64 x1 (.f64 x1 3) (.f64 2 x2)) x1) (fma.f64 x1 x1 1))) (.f64 (.f64 x1 x1) -6))) x1)))))
	17.5b	(+.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 (cbrt.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)))))) (cbrt.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))))))) (cbrt.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))))))) x1)))))

Compiler

Compiled 59606 to 36383 computations (39% saved)

localize43.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	16.1b	(/.f64 (-.f64 (fma.f64 x2 2 (.f64 3 (.f64 x1 x1))) x1) (hypot.f64 1 x1))
	16.8b	(/.f64 (-.f64 (.f64 x1 (.f64 x1 3)) (fma.f64 2 x2 x1)) (fma.f64 x1 x1 1))
	16.8b	(/.f64 (-.f64 (fma.f64 x1 (.f64 x1 3) (.f64 2 x2)) x1) (fma.f64 x1 x1 1))
✓	16.8b	(+.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 1 (hypot.f64 1 x1)) (/.f64 (-.f64 (fma.f64 x2 2 (.f64 3 (.f64 x1 x1))) x1) (hypot.f64 1 x1))) 3)) (.f64 (.f64 x1 x1) 4))) (.f64 (*.f64 x1 x1) -6))

series308.0ms (1.3%)

Counts

2 → 48

Calls

2 calls:

265.0ms

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

43.0ms

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

rewrite30.0ms (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-/l*_binary64`

Counts

2 → 56

Calls

2 calls:

21.0ms

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

5.0ms

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

simplify146.0ms (0.6%)

Algorithm

1×	egg-herbie

Rules

510×	`cancel-sign-sub-inv_binary64`
501×	`fma-neg_binary64`
293×	`sub-neg_binary64`
290×	`fma-def_binary64`
270×	`times-frac_binary64`

Counts

104 → 126

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	278	5615
1	855	5222
2	2942	5217
3	4987	5216
4	5092	5216

prune2.2s (9.7%)

Pruning

9 alts after pruning (8 fresh and 1 done)

	Pruned	Kept	Total
New	369	1	370
Fresh	1	7	8
Picked	0	1	1
Done	0	0	0
Total	370	9	379

Error

17.3b

Counts

379 → 9

Alt Table

Status	Error	Program
▶	17.4b	(+.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 1 (hypot.f64 1 x1)) (/.f64 (/.f64 (-.f64 (fma.f64 x2 2 (.f64 3 (.f64 x1 x1))) x1) (sqrt.f64 (hypot.f64 1 x1))) (sqrt.f64 (hypot.f64 1 x1)))) 3)) (.f64 (.f64 x1 x1) 4))) (.f64 (.f64 x1 x1) -6)) x1)))))
	28.9b	(+.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 (fma.f64 8 (.f64 x2 x2) (.f64 x2 -12)) x1) x1)))))
	42.0b	(+.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 (fma.f64 (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))) (.f64 (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))) (/.f64 (-.f64 (fma.f64 x2 2 (.f64 3 (.f64 x1 x1))) x1) (/.f64 (pow.f64 (fma.f64 x1 x1 1) 2) (-.f64 (fma.f64 x2 2 (.f64 3 (.f64 x1 x1))) x1)))) (.f64 (pow.f64 x1 4) -36)) (fma.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))) (.f64 6 (*.f64 x1 x1)))) x1)))))
	17.5b	(+.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 -3 (pow.f64 (/.f64 (cbrt.f64 (-.f64 (fma.f64 x2 2 (.f64 3 (.f64 x1 x1))) x1)) (cbrt.f64 (fma.f64 x1 x1 1))) 3)) 0)) (.f64 (.f64 x1 x1) 4))) (.f64 (*.f64 x1 x1) -6)) x1)))))
	37.3b	(+.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 x1 (.f64 x1 6) (*.f64 x1 -4)) x1)))))
	35.6b	(+.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 (sqrt.f64 (-.f64 (fma.f64 x1 (.f64 x1 3) (.f64 2 x2)) x1)) (/.f64 (fma.f64 x1 x1 1) (sqrt.f64 (-.f64 (fma.f64 x1 (.f64 x1 3) (.f64 2 x2)) 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)))))
✓	17.4b	(+.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 1 (hypot.f64 1 x1)) (/.f64 (-.f64 (fma.f64 x2 2 (.f64 3 (.f64 x1 x1))) x1) (hypot.f64 1 x1))) 3)) (.f64 (.f64 x1 x1) 4))) (.f64 (.f64 x1 x1) -6)) x1)))))
	17.4b	(+.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 x1 x1) (-.f64 (/.f64 (-.f64 (fma.f64 x1 (.f64 x1 3) (.f64 2 x2)) x1) (fma.f64 x1 x1 1)) 3)) (/.f64 (-.f64 (fma.f64 x1 (.f64 x1 3) (.f64 2 x2)) x1) (fma.f64 x1 x1 1))) (+.f64 (.f64 (.f64 (.f64 x1 x1) 4) (/.f64 (-.f64 (fma.f64 x1 (.f64 x1 3) (.f64 2 x2)) x1) (fma.f64 x1 x1 1))) (.f64 (.f64 x1 x1) -6))) x1)))))
	17.5b	(+.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 (cbrt.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)))))) (cbrt.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))))))) (cbrt.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))))))) x1)))))

Compiler

Compiled 43544 to 26711 computations (38.7% saved)

localize43.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	13.4b	(-.f64 (.f64 (/.f64 1 (hypot.f64 1 x1)) (/.f64 (/.f64 (-.f64 (fma.f64 x2 2 (.f64 3 (*.f64 x1 x1))) x1) (sqrt.f64 (hypot.f64 1 x1))) (sqrt.f64 (hypot.f64 1 x1)))) 3)
	16.8b	(/.f64 (-.f64 (.f64 x1 (.f64 x1 3)) (fma.f64 2 x2 x1)) (fma.f64 x1 x1 1))
	16.8b	(/.f64 (-.f64 (fma.f64 x1 (.f64 x1 3) (.f64 2 x2)) x1) (fma.f64 x1 x1 1))
✓	16.8b	(+.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 1 (hypot.f64 1 x1)) (/.f64 (/.f64 (-.f64 (fma.f64 x2 2 (.f64 3 (.f64 x1 x1))) x1) (sqrt.f64 (hypot.f64 1 x1))) (sqrt.f64 (hypot.f64 1 x1)))) 3)) (.f64 (.f64 x1 x1) 4))) (.f64 (*.f64 x1 x1) -6))

series325.0ms (1.4%)

Counts

2 → 48

Calls

2 calls:

261.0ms

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

64.0ms

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

rewrite52.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

6×	`add-log-exp_binary64`
4×	`*-un-lft-identity_binary64`
4×	`add-sqr-sqrt_binary64`
4×	`add-cube-cbrt_binary64`
3×	`cancel-sign-sub-inv_binary64`

Counts

2 → 36

Calls

2 calls:

32.0ms

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

17.0ms

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

simplify115.0ms (0.5%)

Algorithm

1×	egg-herbie

Rules

524×	`cancel-sign-sub-inv_binary64`
363×	`fma-neg_binary64`
299×	`sub-neg_binary64`
296×	`times-frac_binary64`
289×	`fma-def_binary64`

Counts

84 → 106

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	261	5446
1	800	4720
2	2865	4689
3	4983	4689

prune2.1s (9.2%)

Pruning

9 alts after pruning (7 fresh and 2 done)

	Pruned	Kept	Total
New	350	0	350
Fresh	0	7	7
Picked	0	1	1
Done	0	1	1
Total	350	9	359

Error

17.3b

Counts

359 → 9

Alt Table

Status	Error	Program
✓	17.4b	(+.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 1 (hypot.f64 1 x1)) (/.f64 (/.f64 (-.f64 (fma.f64 x2 2 (.f64 3 (.f64 x1 x1))) x1) (sqrt.f64 (hypot.f64 1 x1))) (sqrt.f64 (hypot.f64 1 x1)))) 3)) (.f64 (.f64 x1 x1) 4))) (.f64 (.f64 x1 x1) -6)) x1)))))
	28.9b	(+.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 (fma.f64 8 (.f64 x2 x2) (.f64 x2 -12)) x1) x1)))))
	42.0b	(+.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 (fma.f64 (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))) (.f64 (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))) (/.f64 (-.f64 (fma.f64 x2 2 (.f64 3 (.f64 x1 x1))) x1) (/.f64 (pow.f64 (fma.f64 x1 x1 1) 2) (-.f64 (fma.f64 x2 2 (.f64 3 (.f64 x1 x1))) x1)))) (.f64 (pow.f64 x1 4) -36)) (fma.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))) (.f64 6 (*.f64 x1 x1)))) x1)))))
	17.5b	(+.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 -3 (pow.f64 (/.f64 (cbrt.f64 (-.f64 (fma.f64 x2 2 (.f64 3 (.f64 x1 x1))) x1)) (cbrt.f64 (fma.f64 x1 x1 1))) 3)) 0)) (.f64 (.f64 x1 x1) 4))) (.f64 (*.f64 x1 x1) -6)) x1)))))
	37.3b	(+.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 x1 (.f64 x1 6) (*.f64 x1 -4)) x1)))))
	35.6b	(+.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 (sqrt.f64 (-.f64 (fma.f64 x1 (.f64 x1 3) (.f64 2 x2)) x1)) (/.f64 (fma.f64 x1 x1 1) (sqrt.f64 (-.f64 (fma.f64 x1 (.f64 x1 3) (.f64 2 x2)) 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)))))
✓	17.4b	(+.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 1 (hypot.f64 1 x1)) (/.f64 (-.f64 (fma.f64 x2 2 (.f64 3 (.f64 x1 x1))) x1) (hypot.f64 1 x1))) 3)) (.f64 (.f64 x1 x1) 4))) (.f64 (.f64 x1 x1) -6)) x1)))))
▶	17.4b	(+.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 x1 x1) (-.f64 (/.f64 (-.f64 (fma.f64 x1 (.f64 x1 3) (.f64 2 x2)) x1) (fma.f64 x1 x1 1)) 3)) (/.f64 (-.f64 (fma.f64 x1 (.f64 x1 3) (.f64 2 x2)) x1) (fma.f64 x1 x1 1))) (+.f64 (.f64 (.f64 (.f64 x1 x1) 4) (/.f64 (-.f64 (fma.f64 x1 (.f64 x1 3) (.f64 2 x2)) x1) (fma.f64 x1 x1 1))) (.f64 (.f64 x1 x1) -6))) x1)))))
	17.5b	(+.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 (cbrt.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)))))) (cbrt.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))))))) (cbrt.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))))))) x1)))))

Compiler

Compiled 43048 to 26813 computations (37.7% saved)

localize36.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	3.1b	(+.f64 (.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 (fma.f64 x1 (.f64 x1 3) (.f64 2 x2)) x1) (fma.f64 x1 x1 1))) (+.f64 (.f64 (.f64 (.f64 x1 x1) 4) (/.f64 (-.f64 (fma.f64 x1 (.f64 x1 3) (.f64 2 x2)) x1) (fma.f64 x1 x1 1))) (.f64 (*.f64 x1 x1) -6)))
✓	13.8b	(+.f64 (.f64 (.f64 (.f64 x1 x1) 4) (/.f64 (-.f64 (fma.f64 x1 (.f64 x1 3) (.f64 2 x2)) x1) (fma.f64 x1 x1 1))) (.f64 (*.f64 x1 x1) -6))
	16.8b	(/.f64 (-.f64 (.f64 x1 (.f64 x1 3)) (fma.f64 2 x2 x1)) (fma.f64 x1 x1 1))
	16.8b	(/.f64 (-.f64 (fma.f64 x1 (.f64 x1 3) (.f64 2 x2)) x1) (fma.f64 x1 x1 1))

series304.0ms (1.3%)

Counts

2 → 48

Calls

2 calls:

231.0ms

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

73.0ms

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

rewrite67.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

34×	`frac-add_binary64`
32×	`frac-times_binary64`
31×	`flip-+_binary64`
31×	`flip3-+_binary64`
24×	`associate-*l/_binary64`

Counts

2 → 64

Calls

2 calls:

29.0ms

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

10.0ms

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

simplify243.0ms (1.1%)

Algorithm

1×	egg-herbie

Rules

623×	`fma-def_binary64`
446×	`distribute-rgt-in_binary64`
410×	`distribute-lft-in_binary64`
277×	`fma-neg_binary64`
195×	`*-commutative_binary64`

Counts

112 → 150

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	398	19911
1	1624	12037
2	4768	11987
3	4811	11987

prune3.6s (15.7%)

Pruning

8 alts after pruning (6 fresh and 2 done)

	Pruned	Kept	Total
New	561	3	564
Fresh	3	3	6
Picked	1	0	1
Done	0	2	2
Total	565	8	573

Error

17.3b

Counts

573 → 8

Alt Table

Status	Error	Program
	17.5b	(+.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 -3 (pow.f64 (/.f64 (cbrt.f64 (-.f64 (fma.f64 x2 2 (.f64 3 (.f64 x1 x1))) x1)) (cbrt.f64 (fma.f64 x1 x1 1))) 3)) 0)) (.f64 (.f64 x1 x1) 4))) (.f64 (*.f64 x1 x1) -6)) x1)))))
	26.5b	(+.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 x1 x1) (-.f64 (/.f64 (-.f64 (fma.f64 x1 (.f64 x1 3) (.f64 2 x2)) x1) (fma.f64 x1 x1 1)) 3)) (/.f64 (-.f64 (fma.f64 x1 (.f64 x1 3) (.f64 2 x2)) x1) (fma.f64 x1 x1 1))) (fma.f64 6 (.f64 x1 x1) (*.f64 x1 -4))) x1)))))
✓	17.4b	(+.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 1 (hypot.f64 1 x1)) (/.f64 (/.f64 (-.f64 (fma.f64 x2 2 (.f64 3 (.f64 x1 x1))) x1) (sqrt.f64 (hypot.f64 1 x1))) (sqrt.f64 (hypot.f64 1 x1)))) 3)) (.f64 (.f64 x1 x1) 4))) (.f64 (.f64 x1 x1) -6)) x1)))))
	28.9b	(+.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 (fma.f64 8 (.f64 x2 x2) (.f64 x2 -12)) x1) x1)))))
	17.4b	(+.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 x1 x1) (-.f64 (/.f64 (-.f64 (fma.f64 x1 (.f64 x1 3) (.f64 2 x2)) x1) (fma.f64 x1 x1 1)) 3)) (/.f64 (-.f64 (fma.f64 x1 (.f64 x1 3) (.f64 2 x2)) x1) (fma.f64 x1 x1 1))) (+.f64 (.f64 (.f64 (.f64 x1 x1) 4) (.f64 (-.f64 (fma.f64 x1 (.f64 x1 3) (.f64 2 x2)) x1) (/.f64 1 (fma.f64 x1 x1 1)))) (.f64 (*.f64 x1 x1) -6))) x1)))))
	35.6b	(+.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 (sqrt.f64 (-.f64 (fma.f64 x1 (.f64 x1 3) (.f64 2 x2)) x1)) (/.f64 (fma.f64 x1 x1 1) (sqrt.f64 (-.f64 (fma.f64 x1 (.f64 x1 3) (.f64 2 x2)) 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)))))
✓	17.4b	(+.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 1 (hypot.f64 1 x1)) (/.f64 (-.f64 (fma.f64 x2 2 (.f64 3 (.f64 x1 x1))) x1) (hypot.f64 1 x1))) 3)) (.f64 (.f64 x1 x1) 4))) (.f64 (.f64 x1 x1) -6)) x1)))))
	17.4b	(+.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 x1 x1) (-.f64 (/.f64 (-.f64 (fma.f64 x1 (.f64 x1 3) (.f64 2 x2)) x1) (fma.f64 x1 x1 1)) 3)) (/.f64 (-.f64 (fma.f64 x1 (.f64 x1 3) (.f64 2 x2)) x1) (fma.f64 x1 x1 1))) (.f64 (.f64 (cbrt.f64 (+.f64 (.f64 (.f64 (.f64 x1 x1) 4) (/.f64 (-.f64 (fma.f64 x1 (.f64 x1 3) (.f64 2 x2)) x1) (fma.f64 x1 x1 1))) (.f64 (.f64 x1 x1) -6))) (cbrt.f64 (+.f64 (.f64 (.f64 (.f64 x1 x1) 4) (/.f64 (-.f64 (fma.f64 x1 (.f64 x1 3) (.f64 2 x2)) x1) (fma.f64 x1 x1 1))) (.f64 (.f64 x1 x1) -6)))) (cbrt.f64 (+.f64 (.f64 (.f64 (.f64 x1 x1) 4) (/.f64 (-.f64 (fma.f64 x1 (.f64 x1 3) (.f64 2 x2)) x1) (fma.f64 x1 x1 1))) (.f64 (.f64 x1 x1) -6))))) x1)))))

Compiler

Compiled 80137 to 48598 computations (39.4% saved)

regimes5.6s (24.6%)

Accuracy

Total 0.1b remaining (0.5%)

Threshold costs 0.1b (0.5%)

Counts

485 → 1

Compiler

Compiled 208292 to 131408 computations (36.9% saved)

simplify21.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

120×	`distribute-rgt-neg-in_binary64`
103×	`cancel-sign-sub-inv_binary64`
82×	`distribute-lft-neg-out_binary64`
76×	`distribute-lft-neg-in_binary64`
74×	`neg-sub0_binary64`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	45	150
1	79	150
2	101	148
3	123	148
4	163	148
5	233	148
6	315	148
7	415	148
8	506	148
9	560	148
10	608	148
11	637	148
12	645	148
13	648	148
14	638	148

end425.0ms (1.9%)

Compiler: Compiled 1078 to 675 computations (37.4% saved)

Iter	Nodes	Cost
0	45	150
1	79	150
2	101	148
3	123	148
4	163	148
5	233	148
6	315	148
7	415	148
8	506	148
9	560	148
10	608	148
11	637	148
12	645	148
13	648	148
14	638	148

Iter	Nodes	Cost
0	45	150
1	79	150
2	101	148
3	123	148
4	163	148
5	233	148
6	315	148
7	415	148
8	506	148
9	560	148
10	608	148
11	637	148
12	645	148
13	648	148
14	638	148

Details

analyze3.0ms (0%)

sample3.7s (16.1%)

simplify30.0ms (0.1%)

prune10.0ms (0%)

localize43.0ms (0.2%)

series378.0ms (1.6%)

rewrite64.0ms (0.3%)

simplify203.0ms (0.9%)

prune2.8s (12%)

localize43.0ms (0.2%)

series308.0ms (1.3%)

rewrite30.0ms (0.1%)

simplify146.0ms (0.6%)

prune2.2s (9.7%)

localize43.0ms (0.2%)

series325.0ms (1.4%)

rewrite52.0ms (0.2%)

simplify115.0ms (0.5%)

prune2.1s (9.2%)

localize36.0ms (0.2%)

series304.0ms (1.3%)

rewrite67.0ms (0.3%)

simplify243.0ms (1.1%)

prune3.6s (15.7%)

regimes5.6s (24.6%)

simplify21.0ms (0.1%)

end425.0ms (1.9%)

Profiling

Iter	Nodes	Cost
0	45	150
1	79	150
2	101	148
3	123	148
4	163	148
5	233	148
6	315	148
7	415	148
8	506	148
9	560	148
10	608	148
11	637	148
12	645	148
13	648	148
14	638	148