Details

analyze2.9s (10.6%)

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%	99.7%	0.3%	13
0%	99.7%	0.3%	14

Compiler

Compiled 44 to 31 computations (29.5% saved)

sample2.6s (9.5%)

Results

1.9s	8256×	body	128	valid
535.0ms	445×	body	8192	exit
99.0ms	460×	body	128	invalid

Compiler

Compiled 87 to 61 computations (29.9% saved)

simplify81.0ms (0.3%)

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

27.3b

Counts

3 → 2

Alt Table

Status	Error	Program
	28.4b	(+.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)))
▶	27.4b	(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

28.4b

(+.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)))

▶

27.4b

(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)

localize21.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(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)
✓	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)
✓	26.6b	(/.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))

series1.8s (6.3%)

Counts

4 → 156

Calls

4 calls:

1.2s	(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)
546.0ms	(/.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)
3.0ms	(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:

3.0ms	(/.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 (+.f64 z 15234687407/1000000000) 314690115749/10000000000) 119400905721/10000000000)
0.0ms	(fma.f64 z (fma.f64 z 313060547623/100000000000 55833770631/5000000000) t)

simplify468.0ms (1.7%)

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

prune272.0ms (1%)

Pruning

8 alts after pruning (8 fresh and 0 done)

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

Error

0.0b

Counts

158 → 8

Alt Table

Status	Error	Program
	33.2b	(-.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)))
	47.6b	(*.f64 (sqrt.f64 (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)) (sqrt.f64 (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)))
	28.4b	(+.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)))
	43.3b	(fma.f64 y (*.f64 (sqrt.f64 (/.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))) (sqrt.f64 (/.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)
	31.0b	(fma.f64 y (-.f64 (+.f64 313060547623/100000000000 (+.f64 (/.f64 t (.f64 z z)) (+.f64 (/.f64 45796100221584283915100827016327/100000000000000000000000000000 (.f64 z z)) (/.f64 a (pow.f64 z 3))))) (fma.f64 15234687407/1000000000 (/.f64 t (pow.f64 z 3)) (+.f64 (/.f64 3652704169880641883561/100000000000000000000 z) (/.f64 586480252826990429730394679450703430294089/100000000000000000000000000000000000000 (pow.f64 z 3))))) x)
	30.9b	(+.f64 (+.f64 (.f64 (.f64 1000000000000/607771387771 y) (+.f64 b (.f64 z (+.f64 a (.f64 t z))))) (fma.f64 123439798033292669987862100000000000000/224502278183706222041215714334315011 (.f64 (.f64 z z) (.f64 b y)) x)) (.f64 -11940090572100000000000000/369386059793087248348441 (.f64 y (.f64 z (fma.f64 a z b)))))
	31.1b	(fma.f64 y (+.f64 (.f64 1000000000000/607771387771 (.f64 z (+.f64 a (.f64 t z)))) (-.f64 (+.f64 (fma.f64 1000000000000/607771387771 b (.f64 (pow.f64 z 3) 11166754126200/607771387771)) (.f64 123439798033292669987862100000000000000/224502278183706222041215714334315011 (.f64 z (.f64 z (fma.f64 a z b))))) (+.f64 (.f64 11940090572100000000000000/369386059793087248348441 (.f64 z (fma.f64 a z b))) (.f64 (pow.f64 z 3) (+.f64 (.f64 1251144097444193138232650020820236307000000000000000/136446061169462227850157143060939731682147130481 b) (.f64 11940090572100000000000000/369386059793087248348441 t)))))) x)
▶	24.4b	(fma.f64 1000000000000/607771387771 (*.f64 b y) x)

Compiler

Compiled 7922 to 5079 computations (35.9% saved)

localize4.0ms (0%)

Local error

Found 1 expressions with local error:

New	Error	Program
✓	0.1b	(fma.f64 1000000000000/607771387771 (*.f64 b y) x)

series8.0ms (0%)

Counts

1 → 36

Calls

1 calls:

8.0ms

(fma.f64 1000000000000/607771387771 (*.f64 b y) x)

rewrite1.0ms (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:

0.0ms

(fma.f64 1000000000000/607771387771 (*.f64 b y) x)

simplify42.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

948×	`distribute-rgt-in_binary64`
932×	`distribute-lft-in_binary64`
726×	`fma-def_binary64`
634×	`distribute-rgt-out_binary64`
519×	`associate-l_binary64`

Counts

46 → 21

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	20	382
1	26	365
2	55	365
3	158	365
4	559	365
5	2181	365
6	5213	365

prune34.0ms (0.1%)

Pruning

8 alts after pruning (7 fresh and 1 done)

	Pruned	Kept	Total
New	21	0	21
Fresh	0	7	7
Picked	0	1	1
Done	0	0	0
Total	21	8	29

Error

0.0b

Counts

29 → 8

Alt Table

Status	Error	Program
	33.2b	(-.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)))
	47.6b	(*.f64 (sqrt.f64 (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)) (sqrt.f64 (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)))
▶	28.4b	(+.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)))
	43.3b	(fma.f64 y (*.f64 (sqrt.f64 (/.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))) (sqrt.f64 (/.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)
	31.0b	(fma.f64 y (-.f64 (+.f64 313060547623/100000000000 (+.f64 (/.f64 t (.f64 z z)) (+.f64 (/.f64 45796100221584283915100827016327/100000000000000000000000000000 (.f64 z z)) (/.f64 a (pow.f64 z 3))))) (fma.f64 15234687407/1000000000 (/.f64 t (pow.f64 z 3)) (+.f64 (/.f64 3652704169880641883561/100000000000000000000 z) (/.f64 586480252826990429730394679450703430294089/100000000000000000000000000000000000000 (pow.f64 z 3))))) x)
	30.9b	(+.f64 (+.f64 (.f64 (.f64 1000000000000/607771387771 y) (+.f64 b (.f64 z (+.f64 a (.f64 t z))))) (fma.f64 123439798033292669987862100000000000000/224502278183706222041215714334315011 (.f64 (.f64 z z) (.f64 b y)) x)) (.f64 -11940090572100000000000000/369386059793087248348441 (.f64 y (.f64 z (fma.f64 a z b)))))
	31.1b	(fma.f64 y (+.f64 (.f64 1000000000000/607771387771 (.f64 z (+.f64 a (.f64 t z)))) (-.f64 (+.f64 (fma.f64 1000000000000/607771387771 b (.f64 (pow.f64 z 3) 11166754126200/607771387771)) (.f64 123439798033292669987862100000000000000/224502278183706222041215714334315011 (.f64 z (.f64 z (fma.f64 a z b))))) (+.f64 (.f64 11940090572100000000000000/369386059793087248348441 (.f64 z (fma.f64 a z b))) (.f64 (pow.f64 z 3) (+.f64 (.f64 1251144097444193138232650020820236307000000000000000/136446061169462227850157143060939731682147130481 b) (.f64 11940090572100000000000000/369386059793087248348441 t)))))) x)
✓	24.4b	(fma.f64 1000000000000/607771387771 (*.f64 b y) x)

Compiler

Compiled 934 to 573 computations (38.7% saved)

localize26.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.3b	(.f64 (+.f64 (.f64 (+.f64 (*.f64 (+.f64 z 15234687407/1000000000) z) 314690115749/10000000000) z) 119400905721/10000000000) z)
✓	0.3b	(.f64 (+.f64 (.f64 z 313060547623/100000000000) 55833770631/5000000000) z)
✓	2.6b	(.f64 y (+.f64 (.f64 (+.f64 (.f64 (+.f64 (.f64 (+.f64 (*.f64 z 313060547623/100000000000) 55833770631/5000000000) z) t) z) a) z) b))
✓	27.4b	(/.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))

series1.1s (3.9%)

Counts

4 → 144

Calls

4 calls:

884.0ms	(/.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))
182.0ms	(.f64 y (+.f64 (.f64 (+.f64 (.f64 (+.f64 (.f64 (+.f64 (*.f64 z 313060547623/100000000000) 55833770631/5000000000) z) t) z) a) z) b))
3.0ms	(.f64 (+.f64 (.f64 (+.f64 (*.f64 (+.f64 z 15234687407/1000000000) z) 314690115749/10000000000) z) 119400905721/10000000000) z)
3.0ms	(.f64 (+.f64 (.f64 z 313060547623/100000000000) 55833770631/5000000000) z)

rewrite65.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

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

Counts

4 → 95

Calls

4 calls:

26.0ms	(/.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))
15.0ms	(.f64 y (+.f64 (.f64 (+.f64 (.f64 (+.f64 (.f64 (+.f64 (*.f64 z 313060547623/100000000000) 55833770631/5000000000) z) t) z) a) z) b))
11.0ms	(.f64 (+.f64 (.f64 (+.f64 (*.f64 (+.f64 z 15234687407/1000000000) z) 314690115749/10000000000) z) 119400905721/10000000000) z)
5.0ms	(.f64 (+.f64 (.f64 z 313060547623/100000000000) 55833770631/5000000000) z)

simplify242.0ms (0.9%)

Algorithm

1×	egg-herbie

Rules

685×	`times-frac_binary64`
359×	`associate-r_binary64`
349×	`fma-def_binary64`
341×	`associate-l_binary64`
197×	`*-commutative_binary64`

Counts

239 → 246

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	369	11586
1	1013	11140
2	3950	11134
3	5124	11134

prune373.0ms (1.3%)

Pruning

6 alts after pruning (5 fresh and 1 done)

	Pruned	Kept	Total
New	245	1	246
Fresh	2	4	6
Picked	0	1	1
Done	1	0	1
Total	248	6	254

Error

0.0b

Counts

254 → 6

Alt Table

Status	Error	Program
	33.2b	(-.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)))
	47.6b	(*.f64 (sqrt.f64 (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)) (sqrt.f64 (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)))
✓	28.4b	(+.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)))
▶	28.6b	(+.f64 x (.f64 (/.f64 (.f64 y (fma.f64 z (fma.f64 z (fma.f64 z (fma.f64 z 313060547623/100000000000 55833770631/5000000000) t) a) b)) (fma.f64 z (.f64 z (.f64 (fma.f64 z (fma.f64 z (+.f64 z 15234687407/1000000000) 314690115749/10000000000) 119400905721/10000000000) (fma.f64 z (fma.f64 z (+.f64 z 15234687407/1000000000) 314690115749/10000000000) 119400905721/10000000000))) -369386059793087248348441/1000000000000000000000000)) (-.f64 (.f64 (+.f64 (.f64 (+.f64 (*.f64 (+.f64 z 15234687407/1000000000) z) 314690115749/10000000000) z) 119400905721/10000000000) z) 607771387771/1000000000000)))
	31.0b	(fma.f64 y (-.f64 (+.f64 313060547623/100000000000 (+.f64 (/.f64 t (.f64 z z)) (+.f64 (/.f64 45796100221584283915100827016327/100000000000000000000000000000 (.f64 z z)) (/.f64 a (pow.f64 z 3))))) (fma.f64 15234687407/1000000000 (/.f64 t (pow.f64 z 3)) (+.f64 (/.f64 3652704169880641883561/100000000000000000000 z) (/.f64 586480252826990429730394679450703430294089/100000000000000000000000000000000000000 (pow.f64 z 3))))) x)
	31.1b	(fma.f64 y (+.f64 (.f64 1000000000000/607771387771 (.f64 z (+.f64 a (.f64 t z)))) (-.f64 (+.f64 (fma.f64 1000000000000/607771387771 b (.f64 (pow.f64 z 3) 11166754126200/607771387771)) (.f64 123439798033292669987862100000000000000/224502278183706222041215714334315011 (.f64 z (.f64 z (fma.f64 a z b))))) (+.f64 (.f64 11940090572100000000000000/369386059793087248348441 (.f64 z (fma.f64 a z b))) (.f64 (pow.f64 z 3) (+.f64 (.f64 1251144097444193138232650020820236307000000000000000/136446061169462227850157143060939731682147130481 b) (.f64 11940090572100000000000000/369386059793087248348441 t)))))) x)

Compiler

Compiled 12091 to 7833 computations (35.2% saved)

localize34.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.5b	(*.f64 (fma.f64 z (fma.f64 z (+.f64 z 15234687407/1000000000) 314690115749/10000000000) 119400905721/10000000000) (fma.f64 z (fma.f64 z (+.f64 z 15234687407/1000000000) 314690115749/10000000000) 119400905721/10000000000))
✓	2.6b	(*.f64 y (fma.f64 z (fma.f64 z (fma.f64 z (fma.f64 z 313060547623/100000000000 55833770631/5000000000) t) a) b))
✓	26.0b	(/.f64 (.f64 y (fma.f64 z (fma.f64 z (fma.f64 z (fma.f64 z 313060547623/100000000000 55833770631/5000000000) t) a) b)) (fma.f64 z (.f64 z (*.f64 (fma.f64 z (fma.f64 z (+.f64 z 15234687407/1000000000) 314690115749/10000000000) 119400905721/10000000000) (fma.f64 z (fma.f64 z (+.f64 z 15234687407/1000000000) 314690115749/10000000000) 119400905721/10000000000))) -369386059793087248348441/1000000000000000000000000))
✓	26.4b	(.f64 (/.f64 (.f64 y (fma.f64 z (fma.f64 z (fma.f64 z (fma.f64 z 313060547623/100000000000 55833770631/5000000000) t) a) b)) (fma.f64 z (.f64 z (.f64 (fma.f64 z (fma.f64 z (+.f64 z 15234687407/1000000000) 314690115749/10000000000) 119400905721/10000000000) (fma.f64 z (fma.f64 z (+.f64 z 15234687407/1000000000) 314690115749/10000000000) 119400905721/10000000000))) -369386059793087248348441/1000000000000000000000000)) (-.f64 (.f64 (+.f64 (.f64 (+.f64 (*.f64 (+.f64 z 15234687407/1000000000) z) 314690115749/10000000000) z) 119400905721/10000000000) z) 607771387771/1000000000000))

series7.1s (25.5%)

Counts

4 → 192

Calls

4 calls:

4.7s	(.f64 (/.f64 (.f64 y (fma.f64 z (fma.f64 z (fma.f64 z (fma.f64 z 313060547623/100000000000 55833770631/5000000000) t) a) b)) (fma.f64 z (.f64 z (.f64 (fma.f64 z (fma.f64 z (+.f64 z 15234687407/1000000000) 314690115749/10000000000) 119400905721/10000000000) (fma.f64 z (fma.f64 z (+.f64 z 15234687407/1000000000) 314690115749/10000000000) 119400905721/10000000000))) -369386059793087248348441/1000000000000000000000000)) (-.f64 (.f64 (+.f64 (.f64 (+.f64 (*.f64 (+.f64 z 15234687407/1000000000) z) 314690115749/10000000000) z) 119400905721/10000000000) z) 607771387771/1000000000000))
2.2s	(/.f64 (.f64 y (fma.f64 z (fma.f64 z (fma.f64 z (fma.f64 z 313060547623/100000000000 55833770631/5000000000) t) a) b)) (fma.f64 z (.f64 z (*.f64 (fma.f64 z (fma.f64 z (+.f64 z 15234687407/1000000000) 314690115749/10000000000) 119400905721/10000000000) (fma.f64 z (fma.f64 z (+.f64 z 15234687407/1000000000) 314690115749/10000000000) 119400905721/10000000000))) -369386059793087248348441/1000000000000000000000000))
150.0ms	(*.f64 y (fma.f64 z (fma.f64 z (fma.f64 z (fma.f64 z 313060547623/100000000000 55833770631/5000000000) t) a) b))
5.0ms	(*.f64 (fma.f64 z (fma.f64 z (+.f64 z 15234687407/1000000000) 314690115749/10000000000) 119400905721/10000000000) (fma.f64 z (fma.f64 z (+.f64 z 15234687407/1000000000) 314690115749/10000000000) 119400905721/10000000000))

rewrite40.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

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

Counts

4 → 121

Calls

4 calls:

15.0ms	(.f64 (/.f64 (.f64 y (fma.f64 z (fma.f64 z (fma.f64 z (fma.f64 z 313060547623/100000000000 55833770631/5000000000) t) a) b)) (fma.f64 z (.f64 z (.f64 (fma.f64 z (fma.f64 z (+.f64 z 15234687407/1000000000) 314690115749/10000000000) 119400905721/10000000000) (fma.f64 z (fma.f64 z (+.f64 z 15234687407/1000000000) 314690115749/10000000000) 119400905721/10000000000))) -369386059793087248348441/1000000000000000000000000)) (-.f64 (.f64 (+.f64 (.f64 (+.f64 (*.f64 (+.f64 z 15234687407/1000000000) z) 314690115749/10000000000) z) 119400905721/10000000000) z) 607771387771/1000000000000))
5.0ms	(/.f64 (.f64 y (fma.f64 z (fma.f64 z (fma.f64 z (fma.f64 z 313060547623/100000000000 55833770631/5000000000) t) a) b)) (fma.f64 z (.f64 z (*.f64 (fma.f64 z (fma.f64 z (+.f64 z 15234687407/1000000000) 314690115749/10000000000) 119400905721/10000000000) (fma.f64 z (fma.f64 z (+.f64 z 15234687407/1000000000) 314690115749/10000000000) 119400905721/10000000000))) -369386059793087248348441/1000000000000000000000000))
3.0ms	(*.f64 (fma.f64 z (fma.f64 z (+.f64 z 15234687407/1000000000) 314690115749/10000000000) 119400905721/10000000000) (fma.f64 z (fma.f64 z (+.f64 z 15234687407/1000000000) 314690115749/10000000000) 119400905721/10000000000))
3.0ms	(*.f64 y (fma.f64 z (fma.f64 z (fma.f64 z (fma.f64 z 313060547623/100000000000 55833770631/5000000000) t) a) b))

simplify952.0ms (3.4%)

Algorithm

1×	egg-herbie

Rules

746×	`fma-def_binary64`
335×	`associate-/l*_binary64`
237×	`+-commutative_binary64`
221×	`*-commutative_binary64`
198×	`associate-*l/_binary64`

Counts

313 → 286

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	750	60354
1	2053	58764
2	4945	58764

prune876.0ms (3.1%)

Pruning

6 alts after pruning (4 fresh and 2 done)

	Pruned	Kept	Total
New	284	2	286
Fresh	2	2	4
Picked	0	1	1
Done	0	1	1
Total	286	6	292

Error

0.0b

Counts

292 → 6

Alt Table

Status	Error	Program
	31.0b	(fma.f64 y (-.f64 (+.f64 313060547623/100000000000 (+.f64 (/.f64 t (.f64 z z)) (+.f64 (/.f64 45796100221584283915100827016327/100000000000000000000000000000 (.f64 z z)) (/.f64 a (pow.f64 z 3))))) (fma.f64 15234687407/1000000000 (/.f64 t (pow.f64 z 3)) (+.f64 (/.f64 3652704169880641883561/100000000000000000000 z) (/.f64 586480252826990429730394679450703430294089/100000000000000000000000000000000000000 (pow.f64 z 3))))) x)
	27.6b	(+.f64 x (.f64 (/.f64 y 1) (.f64 (fma.f64 z (fma.f64 z (fma.f64 z (+.f64 z 15234687407/1000000000) 314690115749/10000000000) 119400905721/10000000000) -607771387771/1000000000000) (/.f64 (fma.f64 z (fma.f64 z (fma.f64 z (fma.f64 z 313060547623/100000000000 55833770631/5000000000) t) a) b) (fma.f64 z (.f64 z (.f64 (fma.f64 z (fma.f64 z (+.f64 z 15234687407/1000000000) 314690115749/10000000000) 119400905721/10000000000) (fma.f64 z (fma.f64 z (+.f64 z 15234687407/1000000000) 314690115749/10000000000) 119400905721/10000000000))) -369386059793087248348441/1000000000000000000000000)))))
✓	28.4b	(+.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)))
✓	28.6b	(+.f64 x (.f64 (/.f64 (.f64 y (fma.f64 z (fma.f64 z (fma.f64 z (fma.f64 z 313060547623/100000000000 55833770631/5000000000) t) a) b)) (fma.f64 z (.f64 z (.f64 (fma.f64 z (fma.f64 z (+.f64 z 15234687407/1000000000) 314690115749/10000000000) 119400905721/10000000000) (fma.f64 z (fma.f64 z (+.f64 z 15234687407/1000000000) 314690115749/10000000000) 119400905721/10000000000))) -369386059793087248348441/1000000000000000000000000)) (-.f64 (.f64 (+.f64 (.f64 (+.f64 (*.f64 (+.f64 z 15234687407/1000000000) z) 314690115749/10000000000) z) 119400905721/10000000000) z) 607771387771/1000000000000)))
	47.6b	(*.f64 (sqrt.f64 (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)) (sqrt.f64 (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)))
	33.2b	(+.f64 x (-.f64 (+.f64 (/.f64 (.f64 y t) (.f64 z z)) (fma.f64 y 313060547623/100000000000 (.f64 45796100221584283915100827016327/100000000000000000000000000000 (/.f64 y (.f64 z z))))) (*.f64 3652704169880641883561/100000000000000000000 (/.f64 y z))))

Compiler

Compiled 34592 to 24393 computations (29.5% saved)

regimes8.4s (30.2%)

Accuracy

Total 0.8b remaining (87.3%)

Threshold costs 0.8b (87.3%)

Counts

243 → 3

Compiler

Compiled 78840 to 53692 computations (31.9% saved)

bsearch133.0ms (0.5%)

Steps

Iters	Range		Point
6	2.4325655466513804e+23	1.8696693604042493e+24	4.5472185148746684e+23
11	-2.0724201604115758e+27	-1.6747984842516482e-5	-3.559639319434067e+26

Compiler

Compiled 7 to 6 computations (14.3% saved)

simplify6.0ms (0%)

Algorithm

1×	egg-herbie

Rules

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

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	59	141
1	74	141
2	79	141
3	81	141
4	82	141
5	80	141

end236.0ms (0.8%)

Compiler: Compiled 524 to 339 computations (35.3% saved)

Details

analyze2.9s (10.6%)

sample2.6s (9.5%)

simplify81.0ms (0.3%)

prune6.0ms (0%)

localize21.0ms (0.1%)

series1.8s (6.3%)

rewrite8.0ms (0%)

simplify468.0ms (1.7%)

prune272.0ms (1%)

localize4.0ms (0%)

series8.0ms (0%)

rewrite1.0ms (0%)

simplify42.0ms (0.1%)

prune34.0ms (0.1%)

localize26.0ms (0.1%)

series1.1s (3.9%)

rewrite65.0ms (0.2%)

simplify242.0ms (0.9%)

prune373.0ms (1.3%)

localize34.0ms (0.1%)

series7.1s (25.5%)

rewrite40.0ms (0.1%)

simplify952.0ms (3.4%)

prune876.0ms (3.1%)

regimes8.4s (30.2%)

bsearch133.0ms (0.5%)

simplify6.0ms (0%)

end236.0ms (0.8%)

Profiling