Details

analyze2.8s (12.1%)

Algorithm

1×

Search

True	Other	False	Iter
0%	99.7%	0.3%	0
0%	99.7%	0.3%	1
0%	99.7%	0.3%	2
0%	99.7%	0.3%	3
0%	99.7%	0.3%	4
0%	99.7%	0.3%	5
0%	99.7%	0.3%	6
0%	99.7%	0.3%	7
0%	99.7%	0.3%	8
0%	99.7%	0.3%	9
0%	99.7%	0.3%	10
0%	99.7%	0.3%	11
0%	99.7%	0.3%	12
0.8%	98.9%	0.3%	13
1.2%	98.5%	0.3%	14

Compiler

Compiled 44 to 31 computations (29.5% saved)

sample2.1s (8.8%)

Results

1.7s	8256×	body	128	valid
185.0ms	916×	body	128	invalid

Compiler

Compiled 131 to 92 computations (29.8% saved)

simplify94.0ms (0.4%)

Algorithm

1×	egg-herbie

Rules

918×	`distribute-rgt-in_binary64`
850×	`distribute-lft-in_binary64`
677×	`associate-/l*_binary64`
676×	`fma-def_binary64`
633×	`associate-+l+_binary64`

Counts

1 → 2

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	31	41
1	63	41
2	131	39
3	274	39
4	720	39
5	1843	39
6	2430	39
7	2851	39
8	3466	39
9	4132	39
10	4596	39
11	5138	39

prune6.0ms (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

29.1b

Counts

3 → 2

Alt Table

Status	Error	Program
	31.4b	(+.f64 x (/.f64 (.f64 y (+.f64 (.f64 (+.f64 (.f64 (+.f64 (.f64 (+.f64 (.f64 z 313060547623/100000000000) 55833770631/5000000000) z) t) z) a) z) b)) (+.f64 (.f64 (+.f64 (.f64 (+.f64 (.f64 (+.f64 z 15234687407/1000000000) z) 314690115749/10000000000) z) 119400905721/10000000000) z) 607771387771/1000000000000)))
▶	29.2b	(fma.f64 y (/.f64 (fma.f64 z (fma.f64 z (fma.f64 z (fma.f64 z 313060547623/100000000000 55833770631/5000000000) t) a) b) (fma.f64 z (fma.f64 z (fma.f64 z (+.f64 z 15234687407/1000000000) 314690115749/10000000000) 119400905721/10000000000) 607771387771/1000000000000)) x)

Status

Error

Program

31.4b

(+.f64 x (/.f64 (*.f64 y (+.f64 (*.f64 (+.f64 (*.f64 (+.f64 (*.f64 (+.f64 (*.f64 z 313060547623/100000000000) 55833770631/5000000000) z) t) z) a) z) b)) (+.f64 (*.f64 (+.f64 (*.f64 (+.f64 (*.f64 (+.f64 z 15234687407/1000000000) z) 314690115749/10000000000) z) 119400905721/10000000000) z) 607771387771/1000000000000)))

▶

29.2b

(fma.f64 y (/.f64 (fma.f64 z (fma.f64 z (fma.f64 z (fma.f64 z 313060547623/100000000000 55833770631/5000000000) t) a) b) (fma.f64 z (fma.f64 z (fma.f64 z (+.f64 z 15234687407/1000000000) 314690115749/10000000000) 119400905721/10000000000) 607771387771/1000000000000)) x)

Compiler

Compiled 228 to 150 computations (34.2% saved)

localize23.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.1b	(fma.f64 y (/.f64 (fma.f64 z (fma.f64 z (fma.f64 z (fma.f64 z 313060547623/100000000000 55833770631/5000000000) t) a) b) (fma.f64 z (fma.f64 z (fma.f64 z (+.f64 z 15234687407/1000000000) 314690115749/10000000000) 119400905721/10000000000) 607771387771/1000000000000)) x)
✓	0.1b	(fma.f64 z (fma.f64 z (+.f64 z 15234687407/1000000000) 314690115749/10000000000) 119400905721/10000000000)
✓	0.1b	(fma.f64 z (fma.f64 z 313060547623/100000000000 55833770631/5000000000) t)
✓	28.3b	(/.f64 (fma.f64 z (fma.f64 z (fma.f64 z (fma.f64 z 313060547623/100000000000 55833770631/5000000000) t) a) b) (fma.f64 z (fma.f64 z (fma.f64 z (+.f64 z 15234687407/1000000000) 314690115749/10000000000) 119400905721/10000000000) 607771387771/1000000000000))

series1.6s (6.7%)

Counts

4 → 156

Calls

4 calls:

1.0s	(fma.f64 y (/.f64 (fma.f64 z (fma.f64 z (fma.f64 z (fma.f64 z 313060547623/100000000000 55833770631/5000000000) t) a) b) (fma.f64 z (fma.f64 z (fma.f64 z (+.f64 z 15234687407/1000000000) 314690115749/10000000000) 119400905721/10000000000) 607771387771/1000000000000)) x)
530.0ms	(/.f64 (fma.f64 z (fma.f64 z (fma.f64 z (fma.f64 z 313060547623/100000000000 55833770631/5000000000) t) a) b) (fma.f64 z (fma.f64 z (fma.f64 z (+.f64 z 15234687407/1000000000) 314690115749/10000000000) 119400905721/10000000000) 607771387771/1000000000000))
6.0ms	(fma.f64 z (fma.f64 z 313060547623/100000000000 55833770631/5000000000) t)
2.0ms	(fma.f64 z (fma.f64 z (+.f64 z 15234687407/1000000000) 314690115749/10000000000) 119400905721/10000000000)

rewrite8.0ms (0%)

Algorithm

1×	rewrite-expression-head

Rules

12×	`*-un-lft-identity_binary64`
12×	`add-sqr-sqrt_binary64`
12×	`add-cube-cbrt_binary64`
9×	`times-frac_binary64`
6×	`add-cbrt-cube_binary64`

Counts

4 → 59

Calls

4 calls:

2.0ms	(/.f64 (fma.f64 z (fma.f64 z (fma.f64 z (fma.f64 z 313060547623/100000000000 55833770631/5000000000) t) a) b) (fma.f64 z (fma.f64 z (fma.f64 z (+.f64 z 15234687407/1000000000) 314690115749/10000000000) 119400905721/10000000000) 607771387771/1000000000000))
0.0ms	(fma.f64 y (/.f64 (fma.f64 z (fma.f64 z (fma.f64 z (fma.f64 z 313060547623/100000000000 55833770631/5000000000) t) a) b) (fma.f64 z (fma.f64 z (fma.f64 z (+.f64 z 15234687407/1000000000) 314690115749/10000000000) 119400905721/10000000000) 607771387771/1000000000000)) x)
0.0ms	(fma.f64 z (fma.f64 z 313060547623/100000000000 55833770631/5000000000) t)
0.0ms	(fma.f64 z (fma.f64 z (+.f64 z 15234687407/1000000000) 314690115749/10000000000) 119400905721/10000000000)

simplify358.0ms (1.5%)

Algorithm

1×	egg-herbie

Rules

467×	`cancel-sign-sub-inv_binary64`
316×	`fma-def_binary64`
302×	`fma-neg_binary64`
258×	`associate-+r+_binary64`
231×	`+-commutative_binary64`

Counts

215 → 156

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	334	18719
1	870	18272
2	2858	15157
3	4757	15157
4	4955	15157

prune292.0ms (1.2%)

Pruning

8 alts after pruning (7 fresh and 1 done)

	Pruned	Kept	Total
New	149	7	156
Fresh	1	0	1
Picked	0	1	1
Done	0	0	0
Total	150	8	158

Error

0.0b

Counts

158 → 8

Alt Table

Status	Error	Program
▶	27.3b	(-.f64 (+.f64 (+.f64 (.f64 (/.f64 y (.f64 z z)) (+.f64 45796100221584283915100827016327/100000000000000000000000000000 (/.f64 a z))) (fma.f64 313060547623/100000000000 y x)) (.f64 (/.f64 y z) (-.f64 (/.f64 t z) (/.f64 586480252826990429730394679450703430294089/100000000000000000000000000000000000000 (.f64 z z))))) (fma.f64 3652704169880641883561/100000000000000000000 (/.f64 y z) (.f64 15234687407/1000000000 (.f64 (/.f64 y (pow.f64 z 3)) t))))
✓	29.2b	(fma.f64 y (/.f64 (fma.f64 z (fma.f64 z (fma.f64 z (fma.f64 z 313060547623/100000000000 55833770631/5000000000) t) a) b) (fma.f64 z (fma.f64 z (fma.f64 z (+.f64 z 15234687407/1000000000) 314690115749/10000000000) 119400905721/10000000000) 607771387771/1000000000000)) x)
	31.2b	(fma.f64 y (fma.f64 1000000000000/607771387771 (fma.f64 a z b) (.f64 b (.f64 z -11940090572100000000000000/369386059793087248348441))) x)
	29.1b	(fma.f64 y (/.f64 (/.f64 (fma.f64 z (fma.f64 z (fma.f64 z (fma.f64 z 313060547623/100000000000 55833770631/5000000000) t) a) b) (sqrt.f64 (fma.f64 z (fma.f64 z (fma.f64 z (+.f64 z 15234687407/1000000000) 314690115749/10000000000) 119400905721/10000000000) 607771387771/1000000000000))) (sqrt.f64 (fma.f64 z (fma.f64 z (fma.f64 z (+.f64 z 15234687407/1000000000) 314690115749/10000000000) 119400905721/10000000000) 607771387771/1000000000000))) x)
	30.6b	(+.f64 (fma.f64 1000000000000/607771387771 (.f64 (.f64 a z) y) x) (.f64 (.f64 b y) (+.f64 1000000000000/607771387771 (*.f64 z -11940090572100000000000000/369386059793087248348441))))
	29.4b	(fma.f64 y (+.f64 (/.f64 b (+.f64 607771387771/1000000000000 (+.f64 (.f64 314690115749/10000000000 (pow.f64 z 2)) (+.f64 (pow.f64 z 4) (+.f64 (.f64 15234687407/1000000000 (pow.f64 z 3)) (.f64 119400905721/10000000000 z)))))) (+.f64 (/.f64 (.f64 t (pow.f64 z 2)) (+.f64 607771387771/1000000000000 (+.f64 (.f64 314690115749/10000000000 (pow.f64 z 2)) (+.f64 (pow.f64 z 4) (+.f64 (.f64 15234687407/1000000000 (pow.f64 z 3)) (.f64 119400905721/10000000000 z)))))) (+.f64 (.f64 55833770631/5000000000 (/.f64 (pow.f64 z 3) (+.f64 607771387771/1000000000000 (+.f64 (.f64 314690115749/10000000000 (pow.f64 z 2)) (+.f64 (pow.f64 z 4) (+.f64 (.f64 15234687407/1000000000 (pow.f64 z 3)) (.f64 119400905721/10000000000 z))))))) (+.f64 (/.f64 (.f64 a z) (+.f64 607771387771/1000000000000 (+.f64 (.f64 314690115749/10000000000 (pow.f64 z 2)) (+.f64 (pow.f64 z 4) (+.f64 (.f64 15234687407/1000000000 (pow.f64 z 3)) (.f64 119400905721/10000000000 z)))))) (.f64 313060547623/100000000000 (/.f64 (pow.f64 z 4) (+.f64 607771387771/1000000000000 (+.f64 (.f64 314690115749/10000000000 (pow.f64 z 2)) (+.f64 (pow.f64 z 4) (+.f64 (.f64 15234687407/1000000000 (pow.f64 z 3)) (*.f64 119400905721/10000000000 z))))))))))) x)
	30.6b	(-.f64 (+.f64 (/.f64 (.f64 y t) (pow.f64 z 2)) (+.f64 (.f64 313060547623/100000000000 y) (+.f64 (.f64 45796100221584283915100827016327/100000000000000000000000000000 (/.f64 y (pow.f64 z 2))) x))) (.f64 3652704169880641883561/100000000000000000000 (/.f64 y z)))
	29.1b	(fma.f64 y (/.f64 (fma.f64 z (fma.f64 z (fma.f64 z (fma.f64 z 313060547623/100000000000 55833770631/5000000000) t) a) b) (fma.f64 z (+.f64 (fma.f64 (*.f64 z z) 15234687407/1000000000 (fma.f64 z 314690115749/10000000000 (pow.f64 z 3))) 119400905721/10000000000) 607771387771/1000000000000)) x)

Compiler

Compiled 7947 to 5139 computations (35.3% saved)

localize28.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	7.0b	(-.f64 (+.f64 (+.f64 (.f64 (/.f64 y (.f64 z z)) (+.f64 45796100221584283915100827016327/100000000000000000000000000000 (/.f64 a z))) (fma.f64 313060547623/100000000000 y x)) (.f64 (/.f64 y z) (-.f64 (/.f64 t z) (/.f64 586480252826990429730394679450703430294089/100000000000000000000000000000000000000 (.f64 z z))))) (fma.f64 3652704169880641883561/100000000000000000000 (/.f64 y z) (.f64 15234687407/1000000000 (.f64 (/.f64 y (pow.f64 z 3)) t))))
✓	7.1b	(/.f64 y (*.f64 z z))
✓	7.2b	(*.f64 (/.f64 y (pow.f64 z 3)) t)
✓	7.7b	(+.f64 (+.f64 (.f64 (/.f64 y (.f64 z z)) (+.f64 45796100221584283915100827016327/100000000000000000000000000000 (/.f64 a z))) (fma.f64 313060547623/100000000000 y x)) (.f64 (/.f64 y z) (-.f64 (/.f64 t z) (/.f64 586480252826990429730394679450703430294089/100000000000000000000000000000000000000 (.f64 z z)))))

series747.0ms (3.2%)

Counts

4 → 180

Calls

4 calls:

388.0ms	(-.f64 (+.f64 (+.f64 (.f64 (/.f64 y (.f64 z z)) (+.f64 45796100221584283915100827016327/100000000000000000000000000000 (/.f64 a z))) (fma.f64 313060547623/100000000000 y x)) (.f64 (/.f64 y z) (-.f64 (/.f64 t z) (/.f64 586480252826990429730394679450703430294089/100000000000000000000000000000000000000 (.f64 z z))))) (fma.f64 3652704169880641883561/100000000000000000000 (/.f64 y z) (.f64 15234687407/1000000000 (.f64 (/.f64 y (pow.f64 z 3)) t))))
271.0ms	(+.f64 (+.f64 (.f64 (/.f64 y (.f64 z z)) (+.f64 45796100221584283915100827016327/100000000000000000000000000000 (/.f64 a z))) (fma.f64 313060547623/100000000000 y x)) (.f64 (/.f64 y z) (-.f64 (/.f64 t z) (/.f64 586480252826990429730394679450703430294089/100000000000000000000000000000000000000 (.f64 z z)))))
62.0ms	(*.f64 (/.f64 y (pow.f64 z 3)) t)
26.0ms	(/.f64 y (*.f64 z z))

rewrite137.0ms (0.6%)

Algorithm

1×	rewrite-expression-head

Rules

253×	`times-frac_binary64`
207×	`add-sqr-sqrt_binary64`
198×	`associate-+r+_binary64`
194×	`*-un-lft-identity_binary64`
192×	`add-cube-cbrt_binary64`

Counts

4 → 353

Calls

4 calls:

26.0ms	(+.f64 (+.f64 (.f64 (/.f64 y (.f64 z z)) (+.f64 45796100221584283915100827016327/100000000000000000000000000000 (/.f64 a z))) (fma.f64 313060547623/100000000000 y x)) (.f64 (/.f64 y z) (-.f64 (/.f64 t z) (/.f64 586480252826990429730394679450703430294089/100000000000000000000000000000000000000 (.f64 z z)))))
17.0ms	(-.f64 (+.f64 (+.f64 (.f64 (/.f64 y (.f64 z z)) (+.f64 45796100221584283915100827016327/100000000000000000000000000000 (/.f64 a z))) (fma.f64 313060547623/100000000000 y x)) (.f64 (/.f64 y z) (-.f64 (/.f64 t z) (/.f64 586480252826990429730394679450703430294089/100000000000000000000000000000000000000 (.f64 z z))))) (fma.f64 3652704169880641883561/100000000000000000000 (/.f64 y z) (.f64 15234687407/1000000000 (.f64 (/.f64 y (pow.f64 z 3)) t))))
10.0ms	(*.f64 (/.f64 y (pow.f64 z 3)) t)
3.0ms	(/.f64 y (*.f64 z z))

simplify696.0ms (3%)

Algorithm

1×	egg-herbie

Rules

512×	`fma-def_binary64`
509×	`times-frac_binary64`
384×	`distribute-rgt-in_binary64`
341×	`distribute-lft-in_binary64`
255×	`+-commutative_binary64`

Counts

533 → 653

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	931	26190
1	1941	22302
2	4703	22290
3	4985	22290
4	4945	22290

prune1.2s (5.3%)

Pruning

9 alts after pruning (7 fresh and 2 done)

	Pruned	Kept	Total
New	652	1	653
Fresh	0	6	6
Picked	0	1	1
Done	0	1	1
Total	652	9	661

Error

0.0b

Counts

661 → 9

Alt Table

Status	Error	Program
✓	27.3b	(-.f64 (+.f64 (+.f64 (.f64 (/.f64 y (.f64 z z)) (+.f64 45796100221584283915100827016327/100000000000000000000000000000 (/.f64 a z))) (fma.f64 313060547623/100000000000 y x)) (.f64 (/.f64 y z) (-.f64 (/.f64 t z) (/.f64 586480252826990429730394679450703430294089/100000000000000000000000000000000000000 (.f64 z z))))) (fma.f64 3652704169880641883561/100000000000000000000 (/.f64 y z) (.f64 15234687407/1000000000 (.f64 (/.f64 y (pow.f64 z 3)) t))))
✓	29.2b	(fma.f64 y (/.f64 (fma.f64 z (fma.f64 z (fma.f64 z (fma.f64 z 313060547623/100000000000 55833770631/5000000000) t) a) b) (fma.f64 z (fma.f64 z (fma.f64 z (+.f64 z 15234687407/1000000000) 314690115749/10000000000) 119400905721/10000000000) 607771387771/1000000000000)) x)
	52.8b	(-.f64 (/.f64 (+.f64 (.f64 (-.f64 (.f64 (.f64 (/.f64 y (.f64 z z)) (+.f64 45796100221584283915100827016327/100000000000000000000000000000 (/.f64 a z))) (.f64 (/.f64 y (.f64 z z)) (+.f64 45796100221584283915100827016327/100000000000000000000000000000 (/.f64 a z)))) (.f64 (fma.f64 313060547623/100000000000 y x) (fma.f64 313060547623/100000000000 y x))) (+.f64 (/.f64 t z) (/.f64 586480252826990429730394679450703430294089/100000000000000000000000000000000000000 (.f64 z z)))) (.f64 (-.f64 (.f64 (/.f64 y (.f64 z z)) (+.f64 45796100221584283915100827016327/100000000000000000000000000000 (/.f64 a z))) (fma.f64 313060547623/100000000000 y x)) (.f64 (/.f64 y z) (-.f64 (.f64 (/.f64 t z) (/.f64 t z)) (.f64 (/.f64 586480252826990429730394679450703430294089/100000000000000000000000000000000000000 (.f64 z z)) (/.f64 586480252826990429730394679450703430294089/100000000000000000000000000000000000000 (.f64 z z))))))) (.f64 (-.f64 (.f64 (/.f64 y (.f64 z z)) (+.f64 45796100221584283915100827016327/100000000000000000000000000000 (/.f64 a z))) (fma.f64 313060547623/100000000000 y x)) (+.f64 (/.f64 t z) (/.f64 586480252826990429730394679450703430294089/100000000000000000000000000000000000000 (.f64 z z))))) (fma.f64 3652704169880641883561/100000000000000000000 (/.f64 y z) (.f64 15234687407/1000000000 (.f64 (/.f64 y (pow.f64 z 3)) t))))
	31.2b	(fma.f64 y (fma.f64 1000000000000/607771387771 (fma.f64 a z b) (.f64 b (.f64 z -11940090572100000000000000/369386059793087248348441))) x)
▶	29.1b	(fma.f64 y (/.f64 (/.f64 (fma.f64 z (fma.f64 z (fma.f64 z (fma.f64 z 313060547623/100000000000 55833770631/5000000000) t) a) b) (sqrt.f64 (fma.f64 z (fma.f64 z (fma.f64 z (+.f64 z 15234687407/1000000000) 314690115749/10000000000) 119400905721/10000000000) 607771387771/1000000000000))) (sqrt.f64 (fma.f64 z (fma.f64 z (fma.f64 z (+.f64 z 15234687407/1000000000) 314690115749/10000000000) 119400905721/10000000000) 607771387771/1000000000000))) x)
	30.6b	(+.f64 (fma.f64 1000000000000/607771387771 (.f64 (.f64 a z) y) x) (.f64 (.f64 b y) (+.f64 1000000000000/607771387771 (*.f64 z -11940090572100000000000000/369386059793087248348441))))
	29.4b	(fma.f64 y (+.f64 (/.f64 b (+.f64 607771387771/1000000000000 (+.f64 (.f64 314690115749/10000000000 (pow.f64 z 2)) (+.f64 (pow.f64 z 4) (+.f64 (.f64 15234687407/1000000000 (pow.f64 z 3)) (.f64 119400905721/10000000000 z)))))) (+.f64 (/.f64 (.f64 t (pow.f64 z 2)) (+.f64 607771387771/1000000000000 (+.f64 (.f64 314690115749/10000000000 (pow.f64 z 2)) (+.f64 (pow.f64 z 4) (+.f64 (.f64 15234687407/1000000000 (pow.f64 z 3)) (.f64 119400905721/10000000000 z)))))) (+.f64 (.f64 55833770631/5000000000 (/.f64 (pow.f64 z 3) (+.f64 607771387771/1000000000000 (+.f64 (.f64 314690115749/10000000000 (pow.f64 z 2)) (+.f64 (pow.f64 z 4) (+.f64 (.f64 15234687407/1000000000 (pow.f64 z 3)) (.f64 119400905721/10000000000 z))))))) (+.f64 (/.f64 (.f64 a z) (+.f64 607771387771/1000000000000 (+.f64 (.f64 314690115749/10000000000 (pow.f64 z 2)) (+.f64 (pow.f64 z 4) (+.f64 (.f64 15234687407/1000000000 (pow.f64 z 3)) (.f64 119400905721/10000000000 z)))))) (.f64 313060547623/100000000000 (/.f64 (pow.f64 z 4) (+.f64 607771387771/1000000000000 (+.f64 (.f64 314690115749/10000000000 (pow.f64 z 2)) (+.f64 (pow.f64 z 4) (+.f64 (.f64 15234687407/1000000000 (pow.f64 z 3)) (*.f64 119400905721/10000000000 z))))))))))) x)
	30.6b	(-.f64 (+.f64 (/.f64 (.f64 y t) (pow.f64 z 2)) (+.f64 (.f64 313060547623/100000000000 y) (+.f64 (.f64 45796100221584283915100827016327/100000000000000000000000000000 (/.f64 y (pow.f64 z 2))) x))) (.f64 3652704169880641883561/100000000000000000000 (/.f64 y z)))
	29.1b	(fma.f64 y (/.f64 (fma.f64 z (fma.f64 z (fma.f64 z (fma.f64 z 313060547623/100000000000 55833770631/5000000000) t) a) b) (fma.f64 z (+.f64 (fma.f64 (*.f64 z z) 15234687407/1000000000 (fma.f64 z 314690115749/10000000000 (pow.f64 z 3))) 119400905721/10000000000) 607771387771/1000000000000)) x)

Compiler

Compiled 48860 to 23885 computations (51.1% saved)

localize22.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.1b	(fma.f64 z (fma.f64 z 313060547623/100000000000 55833770631/5000000000) t)
✓	10.9b	(sqrt.f64 (fma.f64 z (fma.f64 z (fma.f64 z (+.f64 z 15234687407/1000000000) 314690115749/10000000000) 119400905721/10000000000) 607771387771/1000000000000))
✓	15.0b	(/.f64 (/.f64 (fma.f64 z (fma.f64 z (fma.f64 z (fma.f64 z 313060547623/100000000000 55833770631/5000000000) t) a) b) (sqrt.f64 (fma.f64 z (fma.f64 z (fma.f64 z (+.f64 z 15234687407/1000000000) 314690115749/10000000000) 119400905721/10000000000) 607771387771/1000000000000))) (sqrt.f64 (fma.f64 z (fma.f64 z (fma.f64 z (+.f64 z 15234687407/1000000000) 314690115749/10000000000) 119400905721/10000000000) 607771387771/1000000000000)))
✓	25.0b	(/.f64 (fma.f64 z (fma.f64 z (fma.f64 z (fma.f64 z 313060547623/100000000000 55833770631/5000000000) t) a) b) (sqrt.f64 (fma.f64 z (fma.f64 z (fma.f64 z (+.f64 z 15234687407/1000000000) 314690115749/10000000000) 119400905721/10000000000) 607771387771/1000000000000)))

series968.0ms (4.1%)

Counts

3 → 108

Calls

3 calls:

498.0ms

(/.f64 (/.f64 (fma.f64 z (fma.f64 z (fma.f64 z (fma.f64 z 313060547623/100000000000 55833770631/5000000000) t) a) b) (sqrt.f64 (fma.f64 z (fma.f64 z (fma.f64 z (+.f64 z 15234687407/1000000000) 314690115749/10000000000) 119400905721/10000000000) 607771387771/1000000000000))) (sqrt.f64 (fma.f64 z (fma.f64 z (fma.f64 z (+.f64 z 15234687407/1000000000) 314690115749/10000000000) 119400905721/10000000000) 607771387771/1000000000000)))

463.0ms

(/.f64 (fma.f64 z (fma.f64 z (fma.f64 z (fma.f64 z 313060547623/100000000000 55833770631/5000000000) t) a) b) (sqrt.f64 (fma.f64 z (fma.f64 z (fma.f64 z (+.f64 z 15234687407/1000000000) 314690115749/10000000000) 119400905721/10000000000) 607771387771/1000000000000)))

6.0ms

(sqrt.f64 (fma.f64 z (fma.f64 z (fma.f64 z (+.f64 z 15234687407/1000000000) 314690115749/10000000000) 119400905721/10000000000) 607771387771/1000000000000))

rewrite68.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

276×	`times-frac_binary64`
157×	`add-sqr-sqrt_binary64`
156×	`*-un-lft-identity_binary64`
156×	`add-cube-cbrt_binary64`
147×	`sqrt-prod_binary64`

Counts

3 → 233

Calls

3 calls:

8.0ms

(/.f64 (/.f64 (fma.f64 z (fma.f64 z (fma.f64 z (fma.f64 z 313060547623/100000000000 55833770631/5000000000) t) a) b) (sqrt.f64 (fma.f64 z (fma.f64 z (fma.f64 z (+.f64 z 15234687407/1000000000) 314690115749/10000000000) 119400905721/10000000000) 607771387771/1000000000000))) (sqrt.f64 (fma.f64 z (fma.f64 z (fma.f64 z (+.f64 z 15234687407/1000000000) 314690115749/10000000000) 119400905721/10000000000) 607771387771/1000000000000)))

3.0ms

(/.f64 (fma.f64 z (fma.f64 z (fma.f64 z (fma.f64 z 313060547623/100000000000 55833770631/5000000000) t) a) b) (sqrt.f64 (fma.f64 z (fma.f64 z (fma.f64 z (+.f64 z 15234687407/1000000000) 314690115749/10000000000) 119400905721/10000000000) 607771387771/1000000000000)))

1.0ms

(sqrt.f64 (fma.f64 z (fma.f64 z (fma.f64 z (+.f64 z 15234687407/1000000000) 314690115749/10000000000) 119400905721/10000000000) 607771387771/1000000000000))

simplify537.0ms (2.3%)

Algorithm

1×	egg-herbie

Rules

733×	`times-frac_binary64`
367×	`fma-def_binary64`
250×	`associate-/l/_binary64`
229×	`associate-+r+_binary64`
220×	`+-commutative_binary64`

Counts

341 → 337

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	480	30897
1	1286	29174
2	3770	28106
3	4972	28106

prune881.0ms (3.8%)

Pruning

10 alts after pruning (7 fresh and 3 done)

	Pruned	Kept	Total
New	386	3	389
Fresh	2	4	6
Picked	0	1	1
Done	0	2	2
Total	388	10	398

Error

0.0b

Counts

398 → 10

Alt Table

Status	Error	Program
	52.8b	(-.f64 (/.f64 (+.f64 (.f64 (-.f64 (.f64 (.f64 (/.f64 y (.f64 z z)) (+.f64 45796100221584283915100827016327/100000000000000000000000000000 (/.f64 a z))) (.f64 (/.f64 y (.f64 z z)) (+.f64 45796100221584283915100827016327/100000000000000000000000000000 (/.f64 a z)))) (.f64 (fma.f64 313060547623/100000000000 y x) (fma.f64 313060547623/100000000000 y x))) (+.f64 (/.f64 t z) (/.f64 586480252826990429730394679450703430294089/100000000000000000000000000000000000000 (.f64 z z)))) (.f64 (-.f64 (.f64 (/.f64 y (.f64 z z)) (+.f64 45796100221584283915100827016327/100000000000000000000000000000 (/.f64 a z))) (fma.f64 313060547623/100000000000 y x)) (.f64 (/.f64 y z) (-.f64 (.f64 (/.f64 t z) (/.f64 t z)) (.f64 (/.f64 586480252826990429730394679450703430294089/100000000000000000000000000000000000000 (.f64 z z)) (/.f64 586480252826990429730394679450703430294089/100000000000000000000000000000000000000 (.f64 z z))))))) (.f64 (-.f64 (.f64 (/.f64 y (.f64 z z)) (+.f64 45796100221584283915100827016327/100000000000000000000000000000 (/.f64 a z))) (fma.f64 313060547623/100000000000 y x)) (+.f64 (/.f64 t z) (/.f64 586480252826990429730394679450703430294089/100000000000000000000000000000000000000 (.f64 z z))))) (fma.f64 3652704169880641883561/100000000000000000000 (/.f64 y z) (.f64 15234687407/1000000000 (.f64 (/.f64 y (pow.f64 z 3)) t))))
▶	24.2b	(fma.f64 y (/.f64 (*.f64 (sqrt.f64 1000000000000/607771387771) b) (sqrt.f64 (fma.f64 z (fma.f64 z (fma.f64 z (+.f64 z 15234687407/1000000000) 314690115749/10000000000) 119400905721/10000000000) 607771387771/1000000000000))) x)
✓	27.3b	(-.f64 (+.f64 (+.f64 (.f64 (/.f64 y (.f64 z z)) (+.f64 45796100221584283915100827016327/100000000000000000000000000000 (/.f64 a z))) (fma.f64 313060547623/100000000000 y x)) (.f64 (/.f64 y z) (-.f64 (/.f64 t z) (/.f64 586480252826990429730394679450703430294089/100000000000000000000000000000000000000 (.f64 z z))))) (fma.f64 3652704169880641883561/100000000000000000000 (/.f64 y z) (.f64 15234687407/1000000000 (.f64 (/.f64 y (pow.f64 z 3)) t))))
✓	29.2b	(fma.f64 y (/.f64 (fma.f64 z (fma.f64 z (fma.f64 z (fma.f64 z 313060547623/100000000000 55833770631/5000000000) t) a) b) (fma.f64 z (fma.f64 z (fma.f64 z (+.f64 z 15234687407/1000000000) 314690115749/10000000000) 119400905721/10000000000) 607771387771/1000000000000)) x)
	29.4b	(fma.f64 y (+.f64 (/.f64 b (+.f64 607771387771/1000000000000 (fma.f64 (.f64 z z) 314690115749/10000000000 (+.f64 (pow.f64 z 4) (fma.f64 z 119400905721/10000000000 (.f64 (pow.f64 z 3) 15234687407/1000000000)))))) (+.f64 (/.f64 (.f64 t (.f64 z z)) (+.f64 607771387771/1000000000000 (fma.f64 (.f64 z z) 314690115749/10000000000 (+.f64 (pow.f64 z 4) (fma.f64 z 119400905721/10000000000 (.f64 (pow.f64 z 3) 15234687407/1000000000)))))) (fma.f64 55833770631/5000000000 (/.f64 (pow.f64 z 3) (+.f64 607771387771/1000000000000 (fma.f64 (.f64 z z) 314690115749/10000000000 (+.f64 (pow.f64 z 4) (fma.f64 z 119400905721/10000000000 (.f64 (pow.f64 z 3) 15234687407/1000000000)))))) (fma.f64 313060547623/100000000000 (/.f64 (pow.f64 z 4) (+.f64 607771387771/1000000000000 (fma.f64 (.f64 z z) 314690115749/10000000000 (+.f64 (pow.f64 z 4) (fma.f64 z 119400905721/10000000000 (.f64 (pow.f64 z 3) 15234687407/1000000000)))))) (/.f64 (.f64 a z) (+.f64 607771387771/1000000000000 (fma.f64 (.f64 z z) 314690115749/10000000000 (+.f64 (pow.f64 z 4) (fma.f64 z 119400905721/10000000000 (*.f64 (pow.f64 z 3) 15234687407/1000000000)))))))))) x)
✓	29.1b	(fma.f64 y (/.f64 (/.f64 (fma.f64 z (fma.f64 z (fma.f64 z (fma.f64 z 313060547623/100000000000 55833770631/5000000000) t) a) b) (sqrt.f64 (fma.f64 z (fma.f64 z (fma.f64 z (+.f64 z 15234687407/1000000000) 314690115749/10000000000) 119400905721/10000000000) 607771387771/1000000000000))) (sqrt.f64 (fma.f64 z (fma.f64 z (fma.f64 z (+.f64 z 15234687407/1000000000) 314690115749/10000000000) 119400905721/10000000000) 607771387771/1000000000000))) x)
	30.6b	(+.f64 (fma.f64 1000000000000/607771387771 (.f64 (.f64 a z) y) x) (.f64 (.f64 b y) (+.f64 1000000000000/607771387771 (*.f64 z -11940090572100000000000000/369386059793087248348441))))
	30.6b	(-.f64 (+.f64 (/.f64 (.f64 y t) (pow.f64 z 2)) (+.f64 (.f64 313060547623/100000000000 y) (+.f64 (.f64 45796100221584283915100827016327/100000000000000000000000000000 (/.f64 y (pow.f64 z 2))) x))) (.f64 3652704169880641883561/100000000000000000000 (/.f64 y z)))
	27.9b	(fma.f64 y (/.f64 (fma.f64 a (.f64 (sqrt.f64 1000000000000/607771387771) z) (fma.f64 (sqrt.f64 1000000000000/607771387771) b (.f64 (/.f64 (*.f64 b z) (sqrt.f64 1000000000000/607771387771)) -5970045286050000000000000/369386059793087248348441))) (sqrt.f64 (fma.f64 z (fma.f64 z (fma.f64 z (+.f64 z 15234687407/1000000000) 314690115749/10000000000) 119400905721/10000000000) 607771387771/1000000000000))) x)
	29.1b	(fma.f64 y (/.f64 (fma.f64 z (fma.f64 z (fma.f64 z (fma.f64 z 313060547623/100000000000 55833770631/5000000000) t) a) b) (fma.f64 z (+.f64 (fma.f64 (*.f64 z z) 15234687407/1000000000 (fma.f64 z 314690115749/10000000000 (pow.f64 z 3))) 119400905721/10000000000) 607771387771/1000000000000)) x)

Compiler

Compiled 27521 to 17892 computations (35% saved)

localize16.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.1b	(fma.f64 z (fma.f64 z (+.f64 z 15234687407/1000000000) 314690115749/10000000000) 119400905721/10000000000)
✓	0.8b	(fma.f64 y (/.f64 (*.f64 (sqrt.f64 1000000000000/607771387771) b) (sqrt.f64 (fma.f64 z (fma.f64 z (fma.f64 z (+.f64 z 15234687407/1000000000) 314690115749/10000000000) 119400905721/10000000000) 607771387771/1000000000000))) x)
✓	4.2b	(/.f64 (*.f64 (sqrt.f64 1000000000000/607771387771) b) (sqrt.f64 (fma.f64 z (fma.f64 z (fma.f64 z (+.f64 z 15234687407/1000000000) 314690115749/10000000000) 119400905721/10000000000) 607771387771/1000000000000)))
	10.9b	(sqrt.f64 (fma.f64 z (fma.f64 z (fma.f64 z (+.f64 z 15234687407/1000000000) 314690115749/10000000000) 119400905721/10000000000) 607771387771/1000000000000))

series620.0ms (2.7%)

Counts

2 → 72

Calls

2 calls:

403.0ms

(fma.f64 y (/.f64 (*.f64 (sqrt.f64 1000000000000/607771387771) b) (sqrt.f64 (fma.f64 z (fma.f64 z (fma.f64 z (+.f64 z 15234687407/1000000000) 314690115749/10000000000) 119400905721/10000000000) 607771387771/1000000000000))) x)

216.0ms

(/.f64 (*.f64 (sqrt.f64 1000000000000/607771387771) b) (sqrt.f64 (fma.f64 z (fma.f64 z (fma.f64 z (+.f64 z 15234687407/1000000000) 314690115749/10000000000) 119400905721/10000000000) 607771387771/1000000000000)))

rewrite7.0ms (0%)

Algorithm

1×	rewrite-expression-head

Rules

7×	`add-cbrt-cube_binary64`
7×	`add-exp-log_binary64`
6×	`associate-/r*_binary64`
6×	`*-un-lft-identity_binary64`
6×	`sqrt-prod_binary64`

Counts

2 → 39

Calls

2 calls:

4.0ms

(/.f64 (*.f64 (sqrt.f64 1000000000000/607771387771) b) (sqrt.f64 (fma.f64 z (fma.f64 z (fma.f64 z (+.f64 z 15234687407/1000000000) 314690115749/10000000000) 119400905721/10000000000) 607771387771/1000000000000)))

0.0ms

(fma.f64 y (/.f64 (*.f64 (sqrt.f64 1000000000000/607771387771) b) (sqrt.f64 (fma.f64 z (fma.f64 z (fma.f64 z (+.f64 z 15234687407/1000000000) 314690115749/10000000000) 119400905721/10000000000) 607771387771/1000000000000))) x)

simplify122.0ms (0.5%)

Algorithm

1×	egg-herbie

Rules

667×	`times-frac_binary64`
623×	`fma-def_binary64`
331×	`fma-neg_binary64`
286×	`associate-/r/_binary64`
277×	`cancel-sign-sub-inv_binary64`

Counts

111 → 83

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	200	4178
1	540	3946
2	1860	3730
3	4848	3726
4	5022	3726

prune238.0ms (1%)

Pruning

10 alts after pruning (6 fresh and 4 done)

	Pruned	Kept	Total
New	138	0	138
Fresh	0	6	6
Picked	0	1	1
Done	0	3	3
Total	138	10	148

Error

0.0b

Counts

148 → 10

Alt Table

Status	Error	Program
	52.8b	(-.f64 (/.f64 (+.f64 (.f64 (-.f64 (.f64 (.f64 (/.f64 y (.f64 z z)) (+.f64 45796100221584283915100827016327/100000000000000000000000000000 (/.f64 a z))) (.f64 (/.f64 y (.f64 z z)) (+.f64 45796100221584283915100827016327/100000000000000000000000000000 (/.f64 a z)))) (.f64 (fma.f64 313060547623/100000000000 y x) (fma.f64 313060547623/100000000000 y x))) (+.f64 (/.f64 t z) (/.f64 586480252826990429730394679450703430294089/100000000000000000000000000000000000000 (.f64 z z)))) (.f64 (-.f64 (.f64 (/.f64 y (.f64 z z)) (+.f64 45796100221584283915100827016327/100000000000000000000000000000 (/.f64 a z))) (fma.f64 313060547623/100000000000 y x)) (.f64 (/.f64 y z) (-.f64 (.f64 (/.f64 t z) (/.f64 t z)) (.f64 (/.f64 586480252826990429730394679450703430294089/100000000000000000000000000000000000000 (.f64 z z)) (/.f64 586480252826990429730394679450703430294089/100000000000000000000000000000000000000 (.f64 z z))))))) (.f64 (-.f64 (.f64 (/.f64 y (.f64 z z)) (+.f64 45796100221584283915100827016327/100000000000000000000000000000 (/.f64 a z))) (fma.f64 313060547623/100000000000 y x)) (+.f64 (/.f64 t z) (/.f64 586480252826990429730394679450703430294089/100000000000000000000000000000000000000 (.f64 z z))))) (fma.f64 3652704169880641883561/100000000000000000000 (/.f64 y z) (.f64 15234687407/1000000000 (.f64 (/.f64 y (pow.f64 z 3)) t))))
✓	24.2b	(fma.f64 y (/.f64 (*.f64 (sqrt.f64 1000000000000/607771387771) b) (sqrt.f64 (fma.f64 z (fma.f64 z (fma.f64 z (+.f64 z 15234687407/1000000000) 314690115749/10000000000) 119400905721/10000000000) 607771387771/1000000000000))) x)
✓	27.3b	(-.f64 (+.f64 (+.f64 (.f64 (/.f64 y (.f64 z z)) (+.f64 45796100221584283915100827016327/100000000000000000000000000000 (/.f64 a z))) (fma.f64 313060547623/100000000000 y x)) (.f64 (/.f64 y z) (-.f64 (/.f64 t z) (/.f64 586480252826990429730394679450703430294089/100000000000000000000000000000000000000 (.f64 z z))))) (fma.f64 3652704169880641883561/100000000000000000000 (/.f64 y z) (.f64 15234687407/1000000000 (.f64 (/.f64 y (pow.f64 z 3)) t))))
✓	29.2b	(fma.f64 y (/.f64 (fma.f64 z (fma.f64 z (fma.f64 z (fma.f64 z 313060547623/100000000000 55833770631/5000000000) t) a) b) (fma.f64 z (fma.f64 z (fma.f64 z (+.f64 z 15234687407/1000000000) 314690115749/10000000000) 119400905721/10000000000) 607771387771/1000000000000)) x)
	29.4b	(fma.f64 y (+.f64 (/.f64 b (+.f64 607771387771/1000000000000 (fma.f64 (.f64 z z) 314690115749/10000000000 (+.f64 (pow.f64 z 4) (fma.f64 z 119400905721/10000000000 (.f64 (pow.f64 z 3) 15234687407/1000000000)))))) (+.f64 (/.f64 (.f64 t (.f64 z z)) (+.f64 607771387771/1000000000000 (fma.f64 (.f64 z z) 314690115749/10000000000 (+.f64 (pow.f64 z 4) (fma.f64 z 119400905721/10000000000 (.f64 (pow.f64 z 3) 15234687407/1000000000)))))) (fma.f64 55833770631/5000000000 (/.f64 (pow.f64 z 3) (+.f64 607771387771/1000000000000 (fma.f64 (.f64 z z) 314690115749/10000000000 (+.f64 (pow.f64 z 4) (fma.f64 z 119400905721/10000000000 (.f64 (pow.f64 z 3) 15234687407/1000000000)))))) (fma.f64 313060547623/100000000000 (/.f64 (pow.f64 z 4) (+.f64 607771387771/1000000000000 (fma.f64 (.f64 z z) 314690115749/10000000000 (+.f64 (pow.f64 z 4) (fma.f64 z 119400905721/10000000000 (.f64 (pow.f64 z 3) 15234687407/1000000000)))))) (/.f64 (.f64 a z) (+.f64 607771387771/1000000000000 (fma.f64 (.f64 z z) 314690115749/10000000000 (+.f64 (pow.f64 z 4) (fma.f64 z 119400905721/10000000000 (*.f64 (pow.f64 z 3) 15234687407/1000000000)))))))))) x)
✓	29.1b	(fma.f64 y (/.f64 (/.f64 (fma.f64 z (fma.f64 z (fma.f64 z (fma.f64 z 313060547623/100000000000 55833770631/5000000000) t) a) b) (sqrt.f64 (fma.f64 z (fma.f64 z (fma.f64 z (+.f64 z 15234687407/1000000000) 314690115749/10000000000) 119400905721/10000000000) 607771387771/1000000000000))) (sqrt.f64 (fma.f64 z (fma.f64 z (fma.f64 z (+.f64 z 15234687407/1000000000) 314690115749/10000000000) 119400905721/10000000000) 607771387771/1000000000000))) x)
	30.6b	(+.f64 (fma.f64 1000000000000/607771387771 (.f64 (.f64 a z) y) x) (.f64 (.f64 b y) (+.f64 1000000000000/607771387771 (*.f64 z -11940090572100000000000000/369386059793087248348441))))
	30.6b	(-.f64 (+.f64 (/.f64 (.f64 y t) (pow.f64 z 2)) (+.f64 (.f64 313060547623/100000000000 y) (+.f64 (.f64 45796100221584283915100827016327/100000000000000000000000000000 (/.f64 y (pow.f64 z 2))) x))) (.f64 3652704169880641883561/100000000000000000000 (/.f64 y z)))
	27.9b	(fma.f64 y (/.f64 (fma.f64 a (.f64 (sqrt.f64 1000000000000/607771387771) z) (fma.f64 (sqrt.f64 1000000000000/607771387771) b (.f64 (/.f64 (*.f64 b z) (sqrt.f64 1000000000000/607771387771)) -5970045286050000000000000/369386059793087248348441))) (sqrt.f64 (fma.f64 z (fma.f64 z (fma.f64 z (+.f64 z 15234687407/1000000000) 314690115749/10000000000) 119400905721/10000000000) 607771387771/1000000000000))) x)
	29.1b	(fma.f64 y (/.f64 (fma.f64 z (fma.f64 z (fma.f64 z (fma.f64 z 313060547623/100000000000 55833770631/5000000000) t) a) b) (fma.f64 z (+.f64 (fma.f64 (*.f64 z z) 15234687407/1000000000 (fma.f64 z 314690115749/10000000000 (pow.f64 z 3))) 119400905721/10000000000) 607771387771/1000000000000)) x)

Compiler

Compiled 4543 to 3137 computations (30.9% saved)

regimes9.2s (39.5%)

Accuracy

Total 0.8b remaining (93.2%)

Threshold costs 0.8b (93.2%)

Counts

279 → 3

Compiler

Compiled 121152 to 82900 computations (31.6% saved)

bsearch26.0ms (0.1%)

Compiler: Compiled 41 to 29 computations (29.3% saved)

simplify11.0ms (0%)

Algorithm

1×	egg-herbie

Rules

19×	`+-commutative_binary64`
15×	`*-commutative_binary64`
6×	`sub-neg_binary64`
3×	`neg-sub0_binary64`
3×	`neg-mul-1_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	84	299
1	115	299
2	129	299
3	135	299
4	138	299
5	137	299

end552.0ms (2.4%)

Compiler: Compiled 986 to 622 computations (36.9% saved)

Details

analyze2.8s (12.1%)

sample2.1s (8.8%)

simplify94.0ms (0.4%)

prune6.0ms (0%)

localize23.0ms (0.1%)

series1.6s (6.7%)

rewrite8.0ms (0%)

simplify358.0ms (1.5%)

prune292.0ms (1.2%)

localize28.0ms (0.1%)

series747.0ms (3.2%)

rewrite137.0ms (0.6%)

simplify696.0ms (3%)

prune1.2s (5.3%)

localize22.0ms (0.1%)

series968.0ms (4.1%)

rewrite68.0ms (0.3%)

simplify537.0ms (2.3%)

prune881.0ms (3.8%)

localize16.0ms (0.1%)

series620.0ms (2.7%)

rewrite7.0ms (0%)

simplify122.0ms (0.5%)

prune238.0ms (1%)

regimes9.2s (39.5%)

bsearch26.0ms (0.1%)

simplify11.0ms (0%)

end552.0ms (2.4%)

Profiling