Details

analyze1.3s (5.4%)

Algorithm

1×

Search

True	Other	False	Iter
0%	99.9%	0.1%	0
0%	99.9%	0.1%	1
0%	99.9%	0.1%	2
0%	99.9%	0.1%	3
0%	99.9%	0.1%	4
25%	74.9%	0.1%	5
25%	74.9%	0.1%	6
25%	74.9%	0.1%	7
37.4%	62.4%	0.1%	8
37.4%	62.4%	0.1%	9
37.4%	62.4%	0.1%	10
43.7%	56.2%	0.1%	11
43.7%	56.2%	0.1%	12
43.7%	56.2%	0.1%	13
61.7%	38.2%	0.1%	14

Compiler

Compiled 41 to 30 computations (26.8% saved)

sample1.5s (6%)

Results

1.4s	8256×	body	128	valid
1.0ms	5×	body	128	invalid

Compiler

Compiled 122 to 89 computations (27% saved)

simplify49.0ms (0.2%)

Algorithm

1×	egg-herbie

Rules

753×	`associate-+l+_binary64`
706×	`distribute-rgt-in_binary64`
700×	`distribute-lft-in_binary64`
667×	`associate-+r+_binary64`
226×	`fma-def_binary64`

Counts

1 → 2

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	30	41
1	64	41
2	154	41
3	357	41
4	1157	41
5	4876	41
6	4976	41
7	4992	41

prune4.0ms (0%)

Pruning

1 alts after pruning (1 fresh and 0 done)

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

Error

25.2b

Counts

3 → 1

Alt Table

Status	Error	Program
▶	25.2b	(/.f64 (*.f64 (-.f64 x 2) (fma.f64 x (fma.f64 x (fma.f64 x (fma.f64 x 104109730557/25000000000 393497462077/5000000000) 4297481763/31250000) y) z)) (fma.f64 x (fma.f64 x (fma.f64 x (+.f64 x 216700011257/5000000000) 263505074721/1000000000) 156699607947/500000000) 23533438303/500000000))

Status

Error

Program

▶

25.2b

(/.f64 (*.f64 (-.f64 x 2) (fma.f64 x (fma.f64 x (fma.f64 x (fma.f64 x 104109730557/25000000000 393497462077/5000000000) 4297481763/31250000) y) z)) (fma.f64 x (fma.f64 x (fma.f64 x (+.f64 x 216700011257/5000000000) 263505074721/1000000000) 156699607947/500000000) 23533438303/500000000))

Compiler

Compiled 136 to 92 computations (32.4% saved)

localize22.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.1b	(fma.f64 x (fma.f64 x 104109730557/25000000000 393497462077/5000000000) 4297481763/31250000)
✓	0.1b	(fma.f64 x (fma.f64 x (fma.f64 x 104109730557/25000000000 393497462077/5000000000) 4297481763/31250000) y)
✓	0.2b	(fma.f64 x 104109730557/25000000000 393497462077/5000000000)
✓	24.5b	(/.f64 (*.f64 (-.f64 x 2) (fma.f64 x (fma.f64 x (fma.f64 x (fma.f64 x 104109730557/25000000000 393497462077/5000000000) 4297481763/31250000) y) z)) (fma.f64 x (fma.f64 x (fma.f64 x (+.f64 x 216700011257/5000000000) 263505074721/1000000000) 156699607947/500000000) 23533438303/500000000))

series329.0ms (1.3%)

Counts

4 → 84

Calls

4 calls:

315.0ms	(/.f64 (*.f64 (-.f64 x 2) (fma.f64 x (fma.f64 x (fma.f64 x (fma.f64 x 104109730557/25000000000 393497462077/5000000000) 4297481763/31250000) y) z)) (fma.f64 x (fma.f64 x (fma.f64 x (+.f64 x 216700011257/5000000000) 263505074721/1000000000) 156699607947/500000000) 23533438303/500000000))
9.0ms	(fma.f64 x (fma.f64 x (fma.f64 x 104109730557/25000000000 393497462077/5000000000) 4297481763/31250000) y)
2.0ms	(fma.f64 x (fma.f64 x 104109730557/25000000000 393497462077/5000000000) 4297481763/31250000)
1.0ms	(fma.f64 x 104109730557/25000000000 393497462077/5000000000)

rewrite10.0ms (0%)

Algorithm

1×	rewrite-expression-head

Rules

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

Counts

4 → 55

Calls

4 calls:

5.0ms	(/.f64 (*.f64 (-.f64 x 2) (fma.f64 x (fma.f64 x (fma.f64 x (fma.f64 x 104109730557/25000000000 393497462077/5000000000) 4297481763/31250000) y) z)) (fma.f64 x (fma.f64 x (fma.f64 x (+.f64 x 216700011257/5000000000) 263505074721/1000000000) 156699607947/500000000) 23533438303/500000000))
0.0ms	(fma.f64 x 104109730557/25000000000 393497462077/5000000000)
0.0ms	(fma.f64 x (fma.f64 x (fma.f64 x 104109730557/25000000000 393497462077/5000000000) 4297481763/31250000) y)
0.0ms	(fma.f64 x (fma.f64 x 104109730557/25000000000 393497462077/5000000000) 4297481763/31250000)

simplify189.0ms (0.8%)

Algorithm

1×	egg-herbie

Rules

899×	`fma-def_binary64`
565×	`distribute-rgt-in_binary64`
296×	`times-frac_binary64`
211×	`fma-neg_binary64`
146×	`cancel-sign-sub-inv_binary64`

Counts

139 → 125

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	236	8000
1	613	7637
2	2009	7248
3	4990	7248
4	5032	7248

prune227.0ms (0.9%)

Pruning

7 alts after pruning (7 fresh and 0 done)

	Pruned	Kept	Total
New	118	7	125
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	119	7	126

Error

0.2b

Counts

126 → 7

Alt Table

Status	Error	Program
▶	22.8b	(/.f64 (*.f64 (/.f64 (-.f64 x 2) (sqrt.f64 (fma.f64 x (fma.f64 x (fma.f64 x (+.f64 x 216700011257/5000000000) 263505074721/1000000000) 156699607947/500000000) 23533438303/500000000))) (fma.f64 x (fma.f64 x (fma.f64 x (fma.f64 x 104109730557/25000000000 393497462077/5000000000) 4297481763/31250000) y) z)) (sqrt.f64 (fma.f64 x (fma.f64 x (fma.f64 x (+.f64 x 216700011257/5000000000) 263505074721/1000000000) 156699607947/500000000) 23533438303/500000000)))
	23.4b	(.f64 (.f64 (cbrt.f64 (.f64 (/.f64 (-.f64 x 2) (fma.f64 x (fma.f64 x (fma.f64 x (+.f64 x 216700011257/5000000000) 263505074721/1000000000) 156699607947/500000000) 23533438303/500000000)) (fma.f64 x (fma.f64 x (fma.f64 x (fma.f64 x 104109730557/25000000000 393497462077/5000000000) 4297481763/31250000) y) z))) (cbrt.f64 (.f64 (/.f64 (-.f64 x 2) (fma.f64 x (fma.f64 x (fma.f64 x (+.f64 x 216700011257/5000000000) 263505074721/1000000000) 156699607947/500000000) 23533438303/500000000)) (fma.f64 x (fma.f64 x (fma.f64 x (fma.f64 x 104109730557/25000000000 393497462077/5000000000) 4297481763/31250000) y) z)))) (cbrt.f64 (*.f64 (/.f64 (-.f64 x 2) (fma.f64 x (fma.f64 x (fma.f64 x (+.f64 x 216700011257/5000000000) 263505074721/1000000000) 156699607947/500000000) 23533438303/500000000)) (fma.f64 x (fma.f64 x (fma.f64 x (fma.f64 x 104109730557/25000000000 393497462077/5000000000) 4297481763/31250000) y) z))))
	25.2b	(.f64 (.f64 (-.f64 x 2) (fma.f64 x (fma.f64 x (fma.f64 x (fma.f64 x 104109730557/25000000000 393497462077/5000000000) 4297481763/31250000) y) z)) (/.f64 1 (fma.f64 x (fma.f64 x (fma.f64 x (+.f64 x 216700011257/5000000000) 263505074721/1000000000) 156699607947/500000000) 23533438303/500000000)))
	24.9b	(-.f64 (+.f64 (.f64 1759267849271/25000000000 (/.f64 (pow.f64 x 4) (+.f64 (pow.f64 x 4) (+.f64 23533438303/500000000 (+.f64 (.f64 263505074721/1000000000 (pow.f64 x 2)) (+.f64 (.f64 216700011257/5000000000 (pow.f64 x 3)) (.f64 156699607947/500000000 x))))))) (+.f64 (/.f64 (.f64 y (pow.f64 x 2)) (+.f64 (pow.f64 x 4) (+.f64 23533438303/500000000 (+.f64 (.f64 263505074721/1000000000 (pow.f64 x 2)) (+.f64 (.f64 216700011257/5000000000 (pow.f64 x 3)) (.f64 156699607947/500000000 x)))))) (+.f64 (.f64 104109730557/25000000000 (/.f64 (pow.f64 x 5) (+.f64 (pow.f64 x 4) (+.f64 23533438303/500000000 (+.f64 (.f64 263505074721/1000000000 (pow.f64 x 2)) (+.f64 (.f64 216700011257/5000000000 (pow.f64 x 3)) (.f64 156699607947/500000000 x))))))) (/.f64 (.f64 z x) (+.f64 (pow.f64 x 4) (+.f64 23533438303/500000000 (+.f64 (.f64 263505074721/1000000000 (pow.f64 x 2)) (+.f64 (.f64 216700011257/5000000000 (pow.f64 x 3)) (.f64 156699607947/500000000 x))))))))) (+.f64 (.f64 2 (/.f64 (.f64 y x) (+.f64 (pow.f64 x 4) (+.f64 23533438303/500000000 (+.f64 (.f64 263505074721/1000000000 (pow.f64 x 2)) (+.f64 (.f64 216700011257/5000000000 (pow.f64 x 3)) (.f64 156699607947/500000000 x))))))) (+.f64 (.f64 2 (/.f64 z (+.f64 (pow.f64 x 4) (+.f64 23533438303/500000000 (+.f64 (.f64 263505074721/1000000000 (pow.f64 x 2)) (+.f64 (.f64 216700011257/5000000000 (pow.f64 x 3)) (.f64 156699607947/500000000 x))))))) (+.f64 (.f64 4297481763/15625000 (/.f64 (pow.f64 x 2) (+.f64 (pow.f64 x 4) (+.f64 23533438303/500000000 (+.f64 (.f64 263505074721/1000000000 (pow.f64 x 2)) (+.f64 (.f64 216700011257/5000000000 (pow.f64 x 3)) (.f64 156699607947/500000000 x))))))) (.f64 49698921037/2500000000 (/.f64 (pow.f64 x 3) (+.f64 (pow.f64 x 4) (+.f64 23533438303/500000000 (+.f64 (.f64 263505074721/1000000000 (pow.f64 x 2)) (+.f64 (.f64 216700011257/5000000000 (pow.f64 x 3)) (*.f64 156699607947/500000000 x)))))))))))
	22.8b	(*.f64 (/.f64 (-.f64 x 2) (sqrt.f64 (fma.f64 x (fma.f64 x (fma.f64 x (+.f64 x 216700011257/5000000000) 263505074721/1000000000) 156699607947/500000000) 23533438303/500000000))) (/.f64 (fma.f64 x (fma.f64 x (fma.f64 x (fma.f64 x 104109730557/25000000000 393497462077/5000000000) 4297481763/31250000) y) z) (sqrt.f64 (fma.f64 x (fma.f64 x (fma.f64 x (+.f64 x 216700011257/5000000000) 263505074721/1000000000) 156699607947/500000000) 23533438303/500000000))))
	23.4b	(.f64 (/.f64 (-.f64 x 2) (.f64 (cbrt.f64 (fma.f64 x (fma.f64 x (fma.f64 x (+.f64 x 216700011257/5000000000) 263505074721/1000000000) 156699607947/500000000) 23533438303/500000000)) (cbrt.f64 (fma.f64 x (fma.f64 x (fma.f64 x (+.f64 x 216700011257/5000000000) 263505074721/1000000000) 156699607947/500000000) 23533438303/500000000)))) (/.f64 (fma.f64 x (fma.f64 x (fma.f64 x (fma.f64 x 104109730557/25000000000 393497462077/5000000000) 4297481763/31250000) y) z) (cbrt.f64 (fma.f64 x (fma.f64 x (fma.f64 x (+.f64 x 216700011257/5000000000) 263505074721/1000000000) 156699607947/500000000) 23533438303/500000000))))
	35.2b	(-.f64 (+.f64 (/.f64 y (pow.f64 x 2)) (+.f64 (.f64 2284450290879775841688574159837293/625000000000000000000000000000 (/.f64 1 x)) (.f64 104109730557/25000000000 x))) (+.f64 13764240537310136880149/125000000000000000000 (*.f64 409304707811198655637810418659684985388407301/3125000000000000000000000000000000000000 (/.f64 1 (pow.f64 x 2)))))

Compiler

Compiled 5991 to 4108 computations (31.4% saved)

localize22.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	2.5b	(*.f64 (/.f64 (-.f64 x 2) (sqrt.f64 (fma.f64 x (fma.f64 x (fma.f64 x (+.f64 x 216700011257/5000000000) 263505074721/1000000000) 156699607947/500000000) 23533438303/500000000))) (fma.f64 x (fma.f64 x (fma.f64 x (fma.f64 x 104109730557/25000000000 393497462077/5000000000) 4297481763/31250000) y) z))
✓	5.8b	(sqrt.f64 (fma.f64 x (fma.f64 x (fma.f64 x (+.f64 x 216700011257/5000000000) 263505074721/1000000000) 156699607947/500000000) 23533438303/500000000))
✓	15.0b	(/.f64 (-.f64 x 2) (sqrt.f64 (fma.f64 x (fma.f64 x (fma.f64 x (+.f64 x 216700011257/5000000000) 263505074721/1000000000) 156699607947/500000000) 23533438303/500000000)))
✓	19.7b	(/.f64 (*.f64 (/.f64 (-.f64 x 2) (sqrt.f64 (fma.f64 x (fma.f64 x (fma.f64 x (+.f64 x 216700011257/5000000000) 263505074721/1000000000) 156699607947/500000000) 23533438303/500000000))) (fma.f64 x (fma.f64 x (fma.f64 x (fma.f64 x 104109730557/25000000000 393497462077/5000000000) 4297481763/31250000) y) z)) (sqrt.f64 (fma.f64 x (fma.f64 x (fma.f64 x (+.f64 x 216700011257/5000000000) 263505074721/1000000000) 156699607947/500000000) 23533438303/500000000)))

series576.0ms (2.4%)

Counts

4 → 96

Calls

4 calls:

298.0ms	(/.f64 (*.f64 (/.f64 (-.f64 x 2) (sqrt.f64 (fma.f64 x (fma.f64 x (fma.f64 x (+.f64 x 216700011257/5000000000) 263505074721/1000000000) 156699607947/500000000) 23533438303/500000000))) (fma.f64 x (fma.f64 x (fma.f64 x (fma.f64 x 104109730557/25000000000 393497462077/5000000000) 4297481763/31250000) y) z)) (sqrt.f64 (fma.f64 x (fma.f64 x (fma.f64 x (+.f64 x 216700011257/5000000000) 263505074721/1000000000) 156699607947/500000000) 23533438303/500000000)))
268.0ms	(*.f64 (/.f64 (-.f64 x 2) (sqrt.f64 (fma.f64 x (fma.f64 x (fma.f64 x (+.f64 x 216700011257/5000000000) 263505074721/1000000000) 156699607947/500000000) 23533438303/500000000))) (fma.f64 x (fma.f64 x (fma.f64 x (fma.f64 x 104109730557/25000000000 393497462077/5000000000) 4297481763/31250000) y) z))
5.0ms	(/.f64 (-.f64 x 2) (sqrt.f64 (fma.f64 x (fma.f64 x (fma.f64 x (+.f64 x 216700011257/5000000000) 263505074721/1000000000) 156699607947/500000000) 23533438303/500000000)))
4.0ms	(sqrt.f64 (fma.f64 x (fma.f64 x (fma.f64 x (+.f64 x 216700011257/5000000000) 263505074721/1000000000) 156699607947/500000000) 23533438303/500000000))

rewrite44.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

81×	`add-sqr-sqrt_binary64`
72×	`*-un-lft-identity_binary64`
68×	`times-frac_binary64`
46×	`add-cube-cbrt_binary64`
43×	`sqrt-prod_binary64`

Counts

4 → 163

Calls

4 calls:

10.0ms	(*.f64 (/.f64 (-.f64 x 2) (sqrt.f64 (fma.f64 x (fma.f64 x (fma.f64 x (+.f64 x 216700011257/5000000000) 263505074721/1000000000) 156699607947/500000000) 23533438303/500000000))) (fma.f64 x (fma.f64 x (fma.f64 x (fma.f64 x 104109730557/25000000000 393497462077/5000000000) 4297481763/31250000) y) z))
8.0ms	(/.f64 (*.f64 (/.f64 (-.f64 x 2) (sqrt.f64 (fma.f64 x (fma.f64 x (fma.f64 x (+.f64 x 216700011257/5000000000) 263505074721/1000000000) 156699607947/500000000) 23533438303/500000000))) (fma.f64 x (fma.f64 x (fma.f64 x (fma.f64 x 104109730557/25000000000 393497462077/5000000000) 4297481763/31250000) y) z)) (sqrt.f64 (fma.f64 x (fma.f64 x (fma.f64 x (+.f64 x 216700011257/5000000000) 263505074721/1000000000) 156699607947/500000000) 23533438303/500000000)))
5.0ms	(/.f64 (-.f64 x 2) (sqrt.f64 (fma.f64 x (fma.f64 x (fma.f64 x (+.f64 x 216700011257/5000000000) 263505074721/1000000000) 156699607947/500000000) 23533438303/500000000)))
1.0ms	(sqrt.f64 (fma.f64 x (fma.f64 x (fma.f64 x (+.f64 x 216700011257/5000000000) 263505074721/1000000000) 156699607947/500000000) 23533438303/500000000))

simplify523.0ms (2.1%)

Algorithm

1×	egg-herbie

Rules

402×	`fma-def_binary64`
257×	`fma-neg_binary64`
218×	`associate-r_binary64`
217×	`associate-/l*_binary64`
214×	`associate-+r+_binary64`

Counts

259 → 268

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	492	21251
1	1426	18816
2	4985	18812
3	5162	18812

prune525.0ms (2.1%)

Pruning

8 alts after pruning (8 fresh and 0 done)

	Pruned	Kept	Total
New	297	2	299
Fresh	0	6	6
Picked	1	0	1
Done	0	0	0
Total	298	8	306

Error

0.2b

Counts

306 → 8

Alt Table

Status	Error	Program
	23.4b	(.f64 (/.f64 (-.f64 x 2) (.f64 (cbrt.f64 (fma.f64 x (fma.f64 x (fma.f64 x (+.f64 x 216700011257/5000000000) 263505074721/1000000000) 156699607947/500000000) 23533438303/500000000)) (cbrt.f64 (fma.f64 x (fma.f64 x (fma.f64 x (+.f64 x 216700011257/5000000000) 263505074721/1000000000) 156699607947/500000000) 23533438303/500000000)))) (/.f64 (fma.f64 x (fma.f64 x (fma.f64 x (fma.f64 x 104109730557/25000000000 393497462077/5000000000) 4297481763/31250000) y) z) (cbrt.f64 (fma.f64 x (fma.f64 x (fma.f64 x (+.f64 x 216700011257/5000000000) 263505074721/1000000000) 156699607947/500000000) 23533438303/500000000))))
	23.3b	(/.f64 (.f64 (.f64 (/.f64 (-.f64 x 2) (sqrt.f64 (fma.f64 x (fma.f64 x (fma.f64 x (+.f64 x 216700011257/5000000000) 263505074721/1000000000) 156699607947/500000000) 23533438303/500000000))) (*.f64 (cbrt.f64 (fma.f64 x (fma.f64 x (fma.f64 x (fma.f64 x 104109730557/25000000000 393497462077/5000000000) 4297481763/31250000) y) z)) (cbrt.f64 (fma.f64 x (fma.f64 x (fma.f64 x (fma.f64 x 104109730557/25000000000 393497462077/5000000000) 4297481763/31250000) y) z)))) (cbrt.f64 (fma.f64 x (fma.f64 x (fma.f64 x (fma.f64 x 104109730557/25000000000 393497462077/5000000000) 4297481763/31250000) y) z))) (sqrt.f64 (fma.f64 x (fma.f64 x (fma.f64 x (+.f64 x 216700011257/5000000000) 263505074721/1000000000) 156699607947/500000000) 23533438303/500000000)))
	23.4b	(.f64 (.f64 (cbrt.f64 (.f64 (/.f64 (-.f64 x 2) (fma.f64 x (fma.f64 x (fma.f64 x (+.f64 x 216700011257/5000000000) 263505074721/1000000000) 156699607947/500000000) 23533438303/500000000)) (fma.f64 x (fma.f64 x (fma.f64 x (fma.f64 x 104109730557/25000000000 393497462077/5000000000) 4297481763/31250000) y) z))) (cbrt.f64 (.f64 (/.f64 (-.f64 x 2) (fma.f64 x (fma.f64 x (fma.f64 x (+.f64 x 216700011257/5000000000) 263505074721/1000000000) 156699607947/500000000) 23533438303/500000000)) (fma.f64 x (fma.f64 x (fma.f64 x (fma.f64 x 104109730557/25000000000 393497462077/5000000000) 4297481763/31250000) y) z)))) (cbrt.f64 (*.f64 (/.f64 (-.f64 x 2) (fma.f64 x (fma.f64 x (fma.f64 x (+.f64 x 216700011257/5000000000) 263505074721/1000000000) 156699607947/500000000) 23533438303/500000000)) (fma.f64 x (fma.f64 x (fma.f64 x (fma.f64 x 104109730557/25000000000 393497462077/5000000000) 4297481763/31250000) y) z))))
	25.2b	(.f64 (.f64 (-.f64 x 2) (fma.f64 x (fma.f64 x (fma.f64 x (fma.f64 x 104109730557/25000000000 393497462077/5000000000) 4297481763/31250000) y) z)) (/.f64 1 (fma.f64 x (fma.f64 x (fma.f64 x (+.f64 x 216700011257/5000000000) 263505074721/1000000000) 156699607947/500000000) 23533438303/500000000)))
	24.9b	(-.f64 (+.f64 (.f64 1759267849271/25000000000 (/.f64 (pow.f64 x 4) (+.f64 (pow.f64 x 4) (+.f64 23533438303/500000000 (+.f64 (.f64 263505074721/1000000000 (pow.f64 x 2)) (+.f64 (.f64 216700011257/5000000000 (pow.f64 x 3)) (.f64 156699607947/500000000 x))))))) (+.f64 (/.f64 (.f64 y (pow.f64 x 2)) (+.f64 (pow.f64 x 4) (+.f64 23533438303/500000000 (+.f64 (.f64 263505074721/1000000000 (pow.f64 x 2)) (+.f64 (.f64 216700011257/5000000000 (pow.f64 x 3)) (.f64 156699607947/500000000 x)))))) (+.f64 (.f64 104109730557/25000000000 (/.f64 (pow.f64 x 5) (+.f64 (pow.f64 x 4) (+.f64 23533438303/500000000 (+.f64 (.f64 263505074721/1000000000 (pow.f64 x 2)) (+.f64 (.f64 216700011257/5000000000 (pow.f64 x 3)) (.f64 156699607947/500000000 x))))))) (/.f64 (.f64 z x) (+.f64 (pow.f64 x 4) (+.f64 23533438303/500000000 (+.f64 (.f64 263505074721/1000000000 (pow.f64 x 2)) (+.f64 (.f64 216700011257/5000000000 (pow.f64 x 3)) (.f64 156699607947/500000000 x))))))))) (+.f64 (.f64 2 (/.f64 (.f64 y x) (+.f64 (pow.f64 x 4) (+.f64 23533438303/500000000 (+.f64 (.f64 263505074721/1000000000 (pow.f64 x 2)) (+.f64 (.f64 216700011257/5000000000 (pow.f64 x 3)) (.f64 156699607947/500000000 x))))))) (+.f64 (.f64 2 (/.f64 z (+.f64 (pow.f64 x 4) (+.f64 23533438303/500000000 (+.f64 (.f64 263505074721/1000000000 (pow.f64 x 2)) (+.f64 (.f64 216700011257/5000000000 (pow.f64 x 3)) (.f64 156699607947/500000000 x))))))) (+.f64 (.f64 4297481763/15625000 (/.f64 (pow.f64 x 2) (+.f64 (pow.f64 x 4) (+.f64 23533438303/500000000 (+.f64 (.f64 263505074721/1000000000 (pow.f64 x 2)) (+.f64 (.f64 216700011257/5000000000 (pow.f64 x 3)) (.f64 156699607947/500000000 x))))))) (.f64 49698921037/2500000000 (/.f64 (pow.f64 x 3) (+.f64 (pow.f64 x 4) (+.f64 23533438303/500000000 (+.f64 (.f64 263505074721/1000000000 (pow.f64 x 2)) (+.f64 (.f64 216700011257/5000000000 (pow.f64 x 3)) (*.f64 156699607947/500000000 x)))))))))))
▶	22.8b	(*.f64 (/.f64 (-.f64 x 2) (sqrt.f64 (fma.f64 x (fma.f64 x (fma.f64 x (+.f64 x 216700011257/5000000000) 263505074721/1000000000) 156699607947/500000000) 23533438303/500000000))) (/.f64 (fma.f64 x (fma.f64 x (fma.f64 x (fma.f64 x 104109730557/25000000000 393497462077/5000000000) 4297481763/31250000) y) z) (sqrt.f64 (fma.f64 x (fma.f64 x (fma.f64 x (+.f64 x 216700011257/5000000000) 263505074721/1000000000) 156699607947/500000000) 23533438303/500000000))))
	35.2b	(-.f64 (+.f64 (/.f64 y (pow.f64 x 2)) (+.f64 (.f64 2284450290879775841688574159837293/625000000000000000000000000000 (/.f64 1 x)) (.f64 104109730557/25000000000 x))) (+.f64 13764240537310136880149/125000000000000000000 (*.f64 409304707811198655637810418659684985388407301/3125000000000000000000000000000000000000 (/.f64 1 (pow.f64 x 2)))))
	22.8b	(/.f64 (.f64 (/.f64 (-.f64 (pow.f64 x 3) (pow.f64 2 3)) (.f64 (sqrt.f64 (fma.f64 x (fma.f64 x (fma.f64 x (+.f64 x 216700011257/5000000000) 263505074721/1000000000) 156699607947/500000000) 23533438303/500000000)) (fma.f64 x x (fma.f64 x 2 4)))) (fma.f64 x (fma.f64 x (fma.f64 x (fma.f64 x 104109730557/25000000000 393497462077/5000000000) 4297481763/31250000) y) z)) (sqrt.f64 (fma.f64 x (fma.f64 x (fma.f64 x (+.f64 x 216700011257/5000000000) 263505074721/1000000000) 156699607947/500000000) 23533438303/500000000)))

Compiler

Compiled 19221 to 13490 computations (29.8% saved)

localize23.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
	5.8b	(sqrt.f64 (fma.f64 x (fma.f64 x (fma.f64 x (+.f64 x 216700011257/5000000000) 263505074721/1000000000) 156699607947/500000000) 23533438303/500000000))
	15.0b	(/.f64 (-.f64 x 2) (sqrt.f64 (fma.f64 x (fma.f64 x (fma.f64 x (+.f64 x 216700011257/5000000000) 263505074721/1000000000) 156699607947/500000000) 23533438303/500000000)))
✓	15.2b	(*.f64 (/.f64 (-.f64 x 2) (sqrt.f64 (fma.f64 x (fma.f64 x (fma.f64 x (+.f64 x 216700011257/5000000000) 263505074721/1000000000) 156699607947/500000000) 23533438303/500000000))) (/.f64 (fma.f64 x (fma.f64 x (fma.f64 x (fma.f64 x 104109730557/25000000000 393497462077/5000000000) 4297481763/31250000) y) z) (sqrt.f64 (fma.f64 x (fma.f64 x (fma.f64 x (+.f64 x 216700011257/5000000000) 263505074721/1000000000) 156699607947/500000000) 23533438303/500000000))))
✓	19.0b	(/.f64 (fma.f64 x (fma.f64 x (fma.f64 x (fma.f64 x 104109730557/25000000000 393497462077/5000000000) 4297481763/31250000) y) z) (sqrt.f64 (fma.f64 x (fma.f64 x (fma.f64 x (+.f64 x 216700011257/5000000000) 263505074721/1000000000) 156699607947/500000000) 23533438303/500000000)))

series564.0ms (2.3%)

Counts

2 → 72

Calls

2 calls:

335.0ms

(*.f64 (/.f64 (-.f64 x 2) (sqrt.f64 (fma.f64 x (fma.f64 x (fma.f64 x (+.f64 x 216700011257/5000000000) 263505074721/1000000000) 156699607947/500000000) 23533438303/500000000))) (/.f64 (fma.f64 x (fma.f64 x (fma.f64 x (fma.f64 x 104109730557/25000000000 393497462077/5000000000) 4297481763/31250000) y) z) (sqrt.f64 (fma.f64 x (fma.f64 x (fma.f64 x (+.f64 x 216700011257/5000000000) 263505074721/1000000000) 156699607947/500000000) 23533438303/500000000))))

228.0ms

(/.f64 (fma.f64 x (fma.f64 x (fma.f64 x (fma.f64 x 104109730557/25000000000 393497462077/5000000000) 4297481763/31250000) y) z) (sqrt.f64 (fma.f64 x (fma.f64 x (fma.f64 x (+.f64 x 216700011257/5000000000) 263505074721/1000000000) 156699607947/500000000) 23533438303/500000000)))

rewrite45.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

89×	`add-sqr-sqrt_binary64`
78×	`times-frac_binary64`
59×	`*-un-lft-identity_binary64`
47×	`add-cube-cbrt_binary64`
42×	`sqrt-prod_binary64`

Counts

2 → 128

Calls

2 calls:

17.0ms

(*.f64 (/.f64 (-.f64 x 2) (sqrt.f64 (fma.f64 x (fma.f64 x (fma.f64 x (+.f64 x 216700011257/5000000000) 263505074721/1000000000) 156699607947/500000000) 23533438303/500000000))) (/.f64 (fma.f64 x (fma.f64 x (fma.f64 x (fma.f64 x 104109730557/25000000000 393497462077/5000000000) 4297481763/31250000) y) z) (sqrt.f64 (fma.f64 x (fma.f64 x (fma.f64 x (+.f64 x 216700011257/5000000000) 263505074721/1000000000) 156699607947/500000000) 23533438303/500000000))))

3.0ms

(/.f64 (fma.f64 x (fma.f64 x (fma.f64 x (fma.f64 x 104109730557/25000000000 393497462077/5000000000) 4297481763/31250000) y) z) (sqrt.f64 (fma.f64 x (fma.f64 x (fma.f64 x (+.f64 x 216700011257/5000000000) 263505074721/1000000000) 156699607947/500000000) 23533438303/500000000)))

simplify335.0ms (1.4%)

Algorithm

1×	egg-herbie

Rules

524×	`times-frac_binary64`
254×	`fma-def_binary64`
221×	`*-commutative_binary64`
196×	`sub-neg_binary64`
190×	`associate-*r/_binary64`

Counts

200 → 215

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	373	19214
1	1100	17285
2	3693	17285
3	5019	17285

prune653.0ms (2.7%)

Pruning

8 alts after pruning (7 fresh and 1 done)

	Pruned	Kept	Total
New	346	1	347
Fresh	1	6	7
Picked	0	1	1
Done	0	0	0
Total	347	8	355

Error

0.2b

Counts

355 → 8

Alt Table

Status	Error	Program
	23.4b	(.f64 (.f64 (cbrt.f64 (.f64 (/.f64 (-.f64 x 2) (fma.f64 x (fma.f64 x (fma.f64 x (+.f64 x 216700011257/5000000000) 263505074721/1000000000) 156699607947/500000000) 23533438303/500000000)) (fma.f64 x (fma.f64 x (fma.f64 x (fma.f64 x 104109730557/25000000000 393497462077/5000000000) 4297481763/31250000) y) z))) (cbrt.f64 (.f64 (/.f64 (-.f64 x 2) (fma.f64 x (fma.f64 x (fma.f64 x (+.f64 x 216700011257/5000000000) 263505074721/1000000000) 156699607947/500000000) 23533438303/500000000)) (fma.f64 x (fma.f64 x (fma.f64 x (fma.f64 x 104109730557/25000000000 393497462077/5000000000) 4297481763/31250000) y) z)))) (cbrt.f64 (*.f64 (/.f64 (-.f64 x 2) (fma.f64 x (fma.f64 x (fma.f64 x (+.f64 x 216700011257/5000000000) 263505074721/1000000000) 156699607947/500000000) 23533438303/500000000)) (fma.f64 x (fma.f64 x (fma.f64 x (fma.f64 x 104109730557/25000000000 393497462077/5000000000) 4297481763/31250000) y) z))))
	30.5b	(-.f64 (.f64 168466327098500000000/553822718361107519809 (fma.f64 z x (.f64 y (.f64 x x)))) (fma.f64 (.f64 y x) 1000000000/23533438303 (fma.f64 (.f64 z (.f64 x x)) 23298017199368982832548000000000/13033352773350869092174451844127 (fma.f64 z 1000000000/23533438303 (.f64 (.f64 x x) 137519416416/23533438303)))))
	25.2b	(.f64 (.f64 (-.f64 x 2) (fma.f64 x (fma.f64 x (fma.f64 x (fma.f64 x 104109730557/25000000000 393497462077/5000000000) 4297481763/31250000) y) z)) (/.f64 1 (fma.f64 x (fma.f64 x (fma.f64 x (+.f64 x 216700011257/5000000000) 263505074721/1000000000) 156699607947/500000000) 23533438303/500000000)))
	24.9b	(-.f64 (+.f64 (.f64 1759267849271/25000000000 (/.f64 (pow.f64 x 4) (+.f64 (pow.f64 x 4) (+.f64 23533438303/500000000 (+.f64 (.f64 263505074721/1000000000 (pow.f64 x 2)) (+.f64 (.f64 216700011257/5000000000 (pow.f64 x 3)) (.f64 156699607947/500000000 x))))))) (+.f64 (/.f64 (.f64 y (pow.f64 x 2)) (+.f64 (pow.f64 x 4) (+.f64 23533438303/500000000 (+.f64 (.f64 263505074721/1000000000 (pow.f64 x 2)) (+.f64 (.f64 216700011257/5000000000 (pow.f64 x 3)) (.f64 156699607947/500000000 x)))))) (+.f64 (.f64 104109730557/25000000000 (/.f64 (pow.f64 x 5) (+.f64 (pow.f64 x 4) (+.f64 23533438303/500000000 (+.f64 (.f64 263505074721/1000000000 (pow.f64 x 2)) (+.f64 (.f64 216700011257/5000000000 (pow.f64 x 3)) (.f64 156699607947/500000000 x))))))) (/.f64 (.f64 z x) (+.f64 (pow.f64 x 4) (+.f64 23533438303/500000000 (+.f64 (.f64 263505074721/1000000000 (pow.f64 x 2)) (+.f64 (.f64 216700011257/5000000000 (pow.f64 x 3)) (.f64 156699607947/500000000 x))))))))) (+.f64 (.f64 2 (/.f64 (.f64 y x) (+.f64 (pow.f64 x 4) (+.f64 23533438303/500000000 (+.f64 (.f64 263505074721/1000000000 (pow.f64 x 2)) (+.f64 (.f64 216700011257/5000000000 (pow.f64 x 3)) (.f64 156699607947/500000000 x))))))) (+.f64 (.f64 2 (/.f64 z (+.f64 (pow.f64 x 4) (+.f64 23533438303/500000000 (+.f64 (.f64 263505074721/1000000000 (pow.f64 x 2)) (+.f64 (.f64 216700011257/5000000000 (pow.f64 x 3)) (.f64 156699607947/500000000 x))))))) (+.f64 (.f64 4297481763/15625000 (/.f64 (pow.f64 x 2) (+.f64 (pow.f64 x 4) (+.f64 23533438303/500000000 (+.f64 (.f64 263505074721/1000000000 (pow.f64 x 2)) (+.f64 (.f64 216700011257/5000000000 (pow.f64 x 3)) (.f64 156699607947/500000000 x))))))) (.f64 49698921037/2500000000 (/.f64 (pow.f64 x 3) (+.f64 (pow.f64 x 4) (+.f64 23533438303/500000000 (+.f64 (.f64 263505074721/1000000000 (pow.f64 x 2)) (+.f64 (.f64 216700011257/5000000000 (pow.f64 x 3)) (*.f64 156699607947/500000000 x)))))))))))
✓	22.8b	(*.f64 (/.f64 (-.f64 x 2) (sqrt.f64 (fma.f64 x (fma.f64 x (fma.f64 x (+.f64 x 216700011257/5000000000) 263505074721/1000000000) 156699607947/500000000) 23533438303/500000000))) (/.f64 (fma.f64 x (fma.f64 x (fma.f64 x (fma.f64 x 104109730557/25000000000 393497462077/5000000000) 4297481763/31250000) y) z) (sqrt.f64 (fma.f64 x (fma.f64 x (fma.f64 x (+.f64 x 216700011257/5000000000) 263505074721/1000000000) 156699607947/500000000) 23533438303/500000000))))
	23.3b	(/.f64 (.f64 (.f64 (/.f64 (-.f64 x 2) (sqrt.f64 (fma.f64 x (fma.f64 x (fma.f64 x (+.f64 x 216700011257/5000000000) 263505074721/1000000000) 156699607947/500000000) 23533438303/500000000))) (*.f64 (cbrt.f64 (fma.f64 x (fma.f64 x (fma.f64 x (fma.f64 x 104109730557/25000000000 393497462077/5000000000) 4297481763/31250000) y) z)) (cbrt.f64 (fma.f64 x (fma.f64 x (fma.f64 x (fma.f64 x 104109730557/25000000000 393497462077/5000000000) 4297481763/31250000) y) z)))) (cbrt.f64 (fma.f64 x (fma.f64 x (fma.f64 x (fma.f64 x 104109730557/25000000000 393497462077/5000000000) 4297481763/31250000) y) z))) (sqrt.f64 (fma.f64 x (fma.f64 x (fma.f64 x (+.f64 x 216700011257/5000000000) 263505074721/1000000000) 156699607947/500000000) 23533438303/500000000)))
	35.2b	(-.f64 (+.f64 (/.f64 y (pow.f64 x 2)) (+.f64 (.f64 2284450290879775841688574159837293/625000000000000000000000000000 (/.f64 1 x)) (.f64 104109730557/25000000000 x))) (+.f64 13764240537310136880149/125000000000000000000 (*.f64 409304707811198655637810418659684985388407301/3125000000000000000000000000000000000000 (/.f64 1 (pow.f64 x 2)))))
▶	22.8b	(/.f64 (.f64 (/.f64 (-.f64 (pow.f64 x 3) (pow.f64 2 3)) (.f64 (sqrt.f64 (fma.f64 x (fma.f64 x (fma.f64 x (+.f64 x 216700011257/5000000000) 263505074721/1000000000) 156699607947/500000000) 23533438303/500000000)) (fma.f64 x x (fma.f64 x 2 4)))) (fma.f64 x (fma.f64 x (fma.f64 x (fma.f64 x 104109730557/25000000000 393497462077/5000000000) 4297481763/31250000) y) z)) (sqrt.f64 (fma.f64 x (fma.f64 x (fma.f64 x (+.f64 x 216700011257/5000000000) 263505074721/1000000000) 156699607947/500000000) 23533438303/500000000)))

Compiler

Compiled 22629 to 15722 computations (30.5% saved)

localize32.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	2.5b	(.f64 (/.f64 (-.f64 (pow.f64 x 3) (pow.f64 2 3)) (.f64 (sqrt.f64 (fma.f64 x (fma.f64 x (fma.f64 x (+.f64 x 216700011257/5000000000) 263505074721/1000000000) 156699607947/500000000) 23533438303/500000000)) (fma.f64 x x (fma.f64 x 2 4)))) (fma.f64 x (fma.f64 x (fma.f64 x (fma.f64 x 104109730557/25000000000 393497462077/5000000000) 4297481763/31250000) y) z))
	5.8b	(sqrt.f64 (fma.f64 x (fma.f64 x (fma.f64 x (+.f64 x 216700011257/5000000000) 263505074721/1000000000) 156699607947/500000000) 23533438303/500000000))
✓	19.7b	(/.f64 (.f64 (/.f64 (-.f64 (pow.f64 x 3) (pow.f64 2 3)) (.f64 (sqrt.f64 (fma.f64 x (fma.f64 x (fma.f64 x (+.f64 x 216700011257/5000000000) 263505074721/1000000000) 156699607947/500000000) 23533438303/500000000)) (fma.f64 x x (fma.f64 x 2 4)))) (fma.f64 x (fma.f64 x (fma.f64 x (fma.f64 x 104109730557/25000000000 393497462077/5000000000) 4297481763/31250000) y) z)) (sqrt.f64 (fma.f64 x (fma.f64 x (fma.f64 x (+.f64 x 216700011257/5000000000) 263505074721/1000000000) 156699607947/500000000) 23533438303/500000000)))
✓	21.9b	(/.f64 (-.f64 (pow.f64 x 3) (pow.f64 2 3)) (*.f64 (sqrt.f64 (fma.f64 x (fma.f64 x (fma.f64 x (+.f64 x 216700011257/5000000000) 263505074721/1000000000) 156699607947/500000000) 23533438303/500000000)) (fma.f64 x x (fma.f64 x 2 4))))

series951.0ms (3.9%)

Counts

3 → 84

Calls

3 calls:

473.0ms

(*.f64 (/.f64 (-.f64 (pow.f64 x 3) (pow.f64 2 3)) (*.f64 (sqrt.f64 (fma.f64 x (fma.f64 x (fma.f64 x (+.f64 x 216700011257/5000000000) 263505074721/1000000000) 156699607947/500000000) 23533438303/500000000)) (fma.f64 x x (fma.f64 x 2 4)))) (fma.f64 x (fma.f64 x (fma.f64 x (fma.f64 x 104109730557/25000000000 393497462077/5000000000) 4297481763/31250000) y) z))

472.0ms

(/.f64 (*.f64 (/.f64 (-.f64 (pow.f64 x 3) (pow.f64 2 3)) (*.f64 (sqrt.f64 (fma.f64 x (fma.f64 x (fma.f64 x (+.f64 x 216700011257/5000000000) 263505074721/1000000000) 156699607947/500000000) 23533438303/500000000)) (fma.f64 x x (fma.f64 x 2 4)))) (fma.f64 x (fma.f64 x (fma.f64 x (fma.f64 x 104109730557/25000000000 393497462077/5000000000) 4297481763/31250000) y) z)) (sqrt.f64 (fma.f64 x (fma.f64 x (fma.f64 x (+.f64 x 216700011257/5000000000) 263505074721/1000000000) 156699607947/500000000) 23533438303/500000000)))

6.0ms

(/.f64 (-.f64 (pow.f64 x 3) (pow.f64 2 3)) (*.f64 (sqrt.f64 (fma.f64 x (fma.f64 x (fma.f64 x (+.f64 x 216700011257/5000000000) 263505074721/1000000000) 156699607947/500000000) 23533438303/500000000)) (fma.f64 x x (fma.f64 x 2 4))))

rewrite75.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

86×	`add-sqr-sqrt_binary64`
56×	`times-frac_binary64`
48×	`difference-of-squares_binary64`
42×	`*-un-lft-identity_binary64`
36×	`cube-prod_binary64`

Counts

3 → 157

Calls

3 calls:

17.0ms

(/.f64 (-.f64 (pow.f64 x 3) (pow.f64 2 3)) (*.f64 (sqrt.f64 (fma.f64 x (fma.f64 x (fma.f64 x (+.f64 x 216700011257/5000000000) 263505074721/1000000000) 156699607947/500000000) 23533438303/500000000)) (fma.f64 x x (fma.f64 x 2 4))))

17.0ms

(/.f64 (*.f64 (/.f64 (-.f64 (pow.f64 x 3) (pow.f64 2 3)) (*.f64 (sqrt.f64 (fma.f64 x (fma.f64 x (fma.f64 x (+.f64 x 216700011257/5000000000) 263505074721/1000000000) 156699607947/500000000) 23533438303/500000000)) (fma.f64 x x (fma.f64 x 2 4)))) (fma.f64 x (fma.f64 x (fma.f64 x (fma.f64 x 104109730557/25000000000 393497462077/5000000000) 4297481763/31250000) y) z)) (sqrt.f64 (fma.f64 x (fma.f64 x (fma.f64 x (+.f64 x 216700011257/5000000000) 263505074721/1000000000) 156699607947/500000000) 23533438303/500000000)))

16.0ms

(*.f64 (/.f64 (-.f64 (pow.f64 x 3) (pow.f64 2 3)) (*.f64 (sqrt.f64 (fma.f64 x (fma.f64 x (fma.f64 x (+.f64 x 216700011257/5000000000) 263505074721/1000000000) 156699607947/500000000) 23533438303/500000000)) (fma.f64 x x (fma.f64 x 2 4)))) (fma.f64 x (fma.f64 x (fma.f64 x (fma.f64 x 104109730557/25000000000 393497462077/5000000000) 4297481763/31250000) y) z))

simplify387.0ms (1.6%)

Algorithm

1×	egg-herbie

Rules

431×	`fma-def_binary64`
319×	`associate-/l*_binary64`
271×	`times-frac_binary64`
223×	`associate-l_binary64`
203×	`associate-/r*_binary64`

Counts

241 → 279

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	540	31115
1	1607	25974
2	5018	25974

prune774.0ms (3.2%)

Pruning

8 alts after pruning (6 fresh and 2 done)

	Pruned	Kept	Total
New	340	1	341
Fresh	1	5	6
Picked	0	1	1
Done	0	1	1
Total	341	8	349

Error

0.2b

Counts

349 → 8

Alt Table

Status	Error	Program
	36.5b	(/.f64 (.f64 (-.f64 (pow.f64 x 3) 8) (fma.f64 (pow.f64 x 4) 104109730557/25000000000 (+.f64 z (fma.f64 (.f64 x x) 4297481763/31250000 (.f64 (pow.f64 x 3) 393497462077/5000000000))))) (.f64 (+.f64 4 (.f64 x (+.f64 x 2))) (+.f64 (pow.f64 x 4) (+.f64 23533438303/500000000 (fma.f64 (.f64 x x) 263505074721/1000000000 (fma.f64 x 156699607947/500000000 (*.f64 (pow.f64 x 3) 216700011257/5000000000)))))))
	35.2b	(-.f64 (+.f64 (/.f64 y (pow.f64 x 2)) (+.f64 (.f64 2284450290879775841688574159837293/625000000000000000000000000000 (/.f64 1 x)) (.f64 104109730557/25000000000 x))) (+.f64 13764240537310136880149/125000000000000000000 (*.f64 409304707811198655637810418659684985388407301/3125000000000000000000000000000000000000 (/.f64 1 (pow.f64 x 2)))))
	23.4b	(.f64 (.f64 (cbrt.f64 (.f64 (/.f64 (-.f64 x 2) (fma.f64 x (fma.f64 x (fma.f64 x (+.f64 x 216700011257/5000000000) 263505074721/1000000000) 156699607947/500000000) 23533438303/500000000)) (fma.f64 x (fma.f64 x (fma.f64 x (fma.f64 x 104109730557/25000000000 393497462077/5000000000) 4297481763/31250000) y) z))) (cbrt.f64 (.f64 (/.f64 (-.f64 x 2) (fma.f64 x (fma.f64 x (fma.f64 x (+.f64 x 216700011257/5000000000) 263505074721/1000000000) 156699607947/500000000) 23533438303/500000000)) (fma.f64 x (fma.f64 x (fma.f64 x (fma.f64 x 104109730557/25000000000 393497462077/5000000000) 4297481763/31250000) y) z)))) (cbrt.f64 (*.f64 (/.f64 (-.f64 x 2) (fma.f64 x (fma.f64 x (fma.f64 x (+.f64 x 216700011257/5000000000) 263505074721/1000000000) 156699607947/500000000) 23533438303/500000000)) (fma.f64 x (fma.f64 x (fma.f64 x (fma.f64 x 104109730557/25000000000 393497462077/5000000000) 4297481763/31250000) y) z))))
	25.2b	(.f64 (.f64 (-.f64 x 2) (fma.f64 x (fma.f64 x (fma.f64 x (fma.f64 x 104109730557/25000000000 393497462077/5000000000) 4297481763/31250000) y) z)) (/.f64 1 (fma.f64 x (fma.f64 x (fma.f64 x (+.f64 x 216700011257/5000000000) 263505074721/1000000000) 156699607947/500000000) 23533438303/500000000)))
	24.9b	(-.f64 (+.f64 (.f64 1759267849271/25000000000 (/.f64 (pow.f64 x 4) (+.f64 (pow.f64 x 4) (+.f64 23533438303/500000000 (+.f64 (.f64 263505074721/1000000000 (pow.f64 x 2)) (+.f64 (.f64 216700011257/5000000000 (pow.f64 x 3)) (.f64 156699607947/500000000 x))))))) (+.f64 (/.f64 (.f64 y (pow.f64 x 2)) (+.f64 (pow.f64 x 4) (+.f64 23533438303/500000000 (+.f64 (.f64 263505074721/1000000000 (pow.f64 x 2)) (+.f64 (.f64 216700011257/5000000000 (pow.f64 x 3)) (.f64 156699607947/500000000 x)))))) (+.f64 (.f64 104109730557/25000000000 (/.f64 (pow.f64 x 5) (+.f64 (pow.f64 x 4) (+.f64 23533438303/500000000 (+.f64 (.f64 263505074721/1000000000 (pow.f64 x 2)) (+.f64 (.f64 216700011257/5000000000 (pow.f64 x 3)) (.f64 156699607947/500000000 x))))))) (/.f64 (.f64 z x) (+.f64 (pow.f64 x 4) (+.f64 23533438303/500000000 (+.f64 (.f64 263505074721/1000000000 (pow.f64 x 2)) (+.f64 (.f64 216700011257/5000000000 (pow.f64 x 3)) (.f64 156699607947/500000000 x))))))))) (+.f64 (.f64 2 (/.f64 (.f64 y x) (+.f64 (pow.f64 x 4) (+.f64 23533438303/500000000 (+.f64 (.f64 263505074721/1000000000 (pow.f64 x 2)) (+.f64 (.f64 216700011257/5000000000 (pow.f64 x 3)) (.f64 156699607947/500000000 x))))))) (+.f64 (.f64 2 (/.f64 z (+.f64 (pow.f64 x 4) (+.f64 23533438303/500000000 (+.f64 (.f64 263505074721/1000000000 (pow.f64 x 2)) (+.f64 (.f64 216700011257/5000000000 (pow.f64 x 3)) (.f64 156699607947/500000000 x))))))) (+.f64 (.f64 4297481763/15625000 (/.f64 (pow.f64 x 2) (+.f64 (pow.f64 x 4) (+.f64 23533438303/500000000 (+.f64 (.f64 263505074721/1000000000 (pow.f64 x 2)) (+.f64 (.f64 216700011257/5000000000 (pow.f64 x 3)) (.f64 156699607947/500000000 x))))))) (.f64 49698921037/2500000000 (/.f64 (pow.f64 x 3) (+.f64 (pow.f64 x 4) (+.f64 23533438303/500000000 (+.f64 (.f64 263505074721/1000000000 (pow.f64 x 2)) (+.f64 (.f64 216700011257/5000000000 (pow.f64 x 3)) (*.f64 156699607947/500000000 x)))))))))))
✓	22.8b	(*.f64 (/.f64 (-.f64 x 2) (sqrt.f64 (fma.f64 x (fma.f64 x (fma.f64 x (+.f64 x 216700011257/5000000000) 263505074721/1000000000) 156699607947/500000000) 23533438303/500000000))) (/.f64 (fma.f64 x (fma.f64 x (fma.f64 x (fma.f64 x 104109730557/25000000000 393497462077/5000000000) 4297481763/31250000) y) z) (sqrt.f64 (fma.f64 x (fma.f64 x (fma.f64 x (+.f64 x 216700011257/5000000000) 263505074721/1000000000) 156699607947/500000000) 23533438303/500000000))))
	23.3b	(/.f64 (.f64 (.f64 (/.f64 (-.f64 x 2) (sqrt.f64 (fma.f64 x (fma.f64 x (fma.f64 x (+.f64 x 216700011257/5000000000) 263505074721/1000000000) 156699607947/500000000) 23533438303/500000000))) (*.f64 (cbrt.f64 (fma.f64 x (fma.f64 x (fma.f64 x (fma.f64 x 104109730557/25000000000 393497462077/5000000000) 4297481763/31250000) y) z)) (cbrt.f64 (fma.f64 x (fma.f64 x (fma.f64 x (fma.f64 x 104109730557/25000000000 393497462077/5000000000) 4297481763/31250000) y) z)))) (cbrt.f64 (fma.f64 x (fma.f64 x (fma.f64 x (fma.f64 x 104109730557/25000000000 393497462077/5000000000) 4297481763/31250000) y) z))) (sqrt.f64 (fma.f64 x (fma.f64 x (fma.f64 x (+.f64 x 216700011257/5000000000) 263505074721/1000000000) 156699607947/500000000) 23533438303/500000000)))
✓	22.8b	(/.f64 (.f64 (/.f64 (-.f64 (pow.f64 x 3) (pow.f64 2 3)) (.f64 (sqrt.f64 (fma.f64 x (fma.f64 x (fma.f64 x (+.f64 x 216700011257/5000000000) 263505074721/1000000000) 156699607947/500000000) 23533438303/500000000)) (fma.f64 x x (fma.f64 x 2 4)))) (fma.f64 x (fma.f64 x (fma.f64 x (fma.f64 x 104109730557/25000000000 393497462077/5000000000) 4297481763/31250000) y) z)) (sqrt.f64 (fma.f64 x (fma.f64 x (fma.f64 x (+.f64 x 216700011257/5000000000) 263505074721/1000000000) 156699607947/500000000) 23533438303/500000000)))

Compiler

Compiled 25102 to 17795 computations (29.1% saved)

regimes14.8s (60.5%)

Accuracy

Total 0.7b remaining (74.1%)

Threshold costs 0.7b (74.1%)

Counts

583 → 3

Compiler

Compiled 139544 to 98700 computations (29.3% saved)

bsearch111.0ms (0.5%)

Steps

Iters	Range		Point
9	8.069121769658908e+39	1.2527038717267837e+49	7.137094911429642e+41
8	-4.181176544609709e+47	-2.7215681741393526e+43	-8.61896290076241e+46

Compiler

Compiled 4 to 3 computations (25% saved)

simplify8.0ms (0%)

Algorithm

1×	egg-herbie

Rules

7×	`+-commutative_binary64`
4×	`sub-neg_binary64`
3×	`*-commutative_binary64`
2×	`distribute-neg-in_binary64`
2×	`neg-sub0_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	41	111
1	50	111
2	61	111
3	69	111
4	72	111
5	73	111
6	70	111

end380.0ms (1.6%)

Compiler: Compiled 786 to 558 computations (29% saved)

Details

analyze1.3s (5.4%)

sample1.5s (6%)

simplify49.0ms (0.2%)

prune4.0ms (0%)

localize22.0ms (0.1%)

series329.0ms (1.3%)

rewrite10.0ms (0%)

simplify189.0ms (0.8%)

prune227.0ms (0.9%)

localize22.0ms (0.1%)

series576.0ms (2.4%)

rewrite44.0ms (0.2%)

simplify523.0ms (2.1%)

prune525.0ms (2.1%)

localize23.0ms (0.1%)

series564.0ms (2.3%)

rewrite45.0ms (0.2%)

simplify335.0ms (1.4%)

prune653.0ms (2.7%)

localize32.0ms (0.1%)

series951.0ms (3.9%)

rewrite75.0ms (0.3%)

simplify387.0ms (1.6%)

prune774.0ms (3.2%)

regimes14.8s (60.5%)

bsearch111.0ms (0.5%)

simplify8.0ms (0%)

end380.0ms (1.6%)

Profiling