Details

analyze2.8s (7.1%)

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)

sample76.0ms (0.2%)

Algorithm

1×

intervals

Results

57.0ms

256×

body

128

valid

Compiler

Compiled 84 to 62 computations (26.2% saved)

simplify73.0ms (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

prune8.0ms (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

28.2b

Counts

3 → 1

Alt Table

Status	Error	Program
▶	28.2b	(/.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

▶

28.2b

(/.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)

localize47.0ms (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)
✓	0.3b	(fma.f64 x 104109730557/25000000000 393497462077/5000000000)
✓	27.4b	(/.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))

series877.0ms (2.2%)

Counts

4 → 84

Calls

4 calls:

845.0ms	(/.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))
22.0ms	(fma.f64 x (fma.f64 x (fma.f64 x 104109730557/25000000000 393497462077/5000000000) 4297481763/31250000) y)
6.0ms	(fma.f64 x (fma.f64 x 104109730557/25000000000 393497462077/5000000000) 4297481763/31250000)
3.0ms	(fma.f64 x 104109730557/25000000000 393497462077/5000000000)

rewrite18.0ms (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:

10.0ms	(/.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))
1.0ms	(fma.f64 x (fma.f64 x 104109730557/25000000000 393497462077/5000000000) 4297481763/31250000)
1.0ms	(fma.f64 x 104109730557/25000000000 393497462077/5000000000)
1.0ms	(fma.f64 x (fma.f64 x (fma.f64 x 104109730557/25000000000 393497462077/5000000000) 4297481763/31250000) y)

simplify374.0ms (1%)

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

prune427.0ms (1.1%)

Pruning

6 alts after pruning (6 fresh and 0 done)

	Pruned	Kept	Total
New	119	6	125
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	120	6	126

Error

0.3b

Counts

126 → 6

Alt Table

Status	Error	Program
	32.9b	(-.f64 (+.f64 (fma.f64 x 104109730557/25000000000 (/.f64 2284450290879775841688574159837293/625000000000000000000000000000 x)) (/.f64 y (.f64 x x))) (+.f64 13764240537310136880149/125000000000000000000 (/.f64 409304707811198655637810418659684985388407301/3125000000000000000000000000000000000000 (.f64 x x))))
	28.3b	(.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)))
	28.2b	(/.f64 (.f64 (-.f64 x 2) (fma.f64 x (fma.f64 x (+.f64 (fma.f64 104109730557/25000000000 (.f64 x x) (*.f64 x 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))
	27.7b	(.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))))
▶	27.2b	(/.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)))
	28.2b	(-.f64 (fma.f64 1759267849271/25000000000 (/.f64 (pow.f64 x 4) (+.f64 (pow.f64 x 4) (+.f64 23533438303/500000000 (fma.f64 x 156699607947/500000000 (.f64 (.f64 x x) (+.f64 263505074721/1000000000 (.f64 216700011257/5000000000 x))))))) (fma.f64 104109730557/25000000000 (/.f64 (pow.f64 x 5) (+.f64 (pow.f64 x 4) (+.f64 23533438303/500000000 (fma.f64 x 156699607947/500000000 (.f64 (.f64 x x) (+.f64 263505074721/1000000000 (.f64 216700011257/5000000000 x))))))) (fma.f64 (/.f64 z (+.f64 (pow.f64 x 4) (+.f64 23533438303/500000000 (fma.f64 x 156699607947/500000000 (.f64 (.f64 x x) (+.f64 263505074721/1000000000 (.f64 216700011257/5000000000 x))))))) x (/.f64 (.f64 x (.f64 x y)) (+.f64 (pow.f64 x 4) (+.f64 23533438303/500000000 (fma.f64 x 156699607947/500000000 (.f64 (.f64 x x) (+.f64 263505074721/1000000000 (.f64 216700011257/5000000000 x)))))))))) (fma.f64 2 (fma.f64 (/.f64 y (+.f64 (pow.f64 x 4) (+.f64 23533438303/500000000 (fma.f64 x 156699607947/500000000 (.f64 (.f64 x x) (+.f64 263505074721/1000000000 (.f64 216700011257/5000000000 x))))))) x (/.f64 z (+.f64 (pow.f64 x 4) (+.f64 23533438303/500000000 (fma.f64 x 156699607947/500000000 (.f64 (.f64 x x) (+.f64 263505074721/1000000000 (.f64 216700011257/5000000000 x)))))))) (fma.f64 4297481763/15625000 (/.f64 (.f64 x x) (+.f64 (pow.f64 x 4) (+.f64 23533438303/500000000 (fma.f64 x 156699607947/500000000 (.f64 (.f64 x x) (+.f64 263505074721/1000000000 (.f64 216700011257/5000000000 x))))))) (.f64 49698921037/2500000000 (/.f64 (pow.f64 x 3) (+.f64 (pow.f64 x 4) (+.f64 23533438303/500000000 (fma.f64 x 156699607947/500000000 (.f64 (.f64 x x) (+.f64 263505074721/1000000000 (.f64 216700011257/5000000000 x)))))))))))

Compiler

Compiled 5697 to 3844 computations (32.5% saved)

localize47.0ms (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))
✓	8.4b	(sqrt.f64 (fma.f64 x (fma.f64 x (fma.f64 x (+.f64 x 216700011257/5000000000) 263505074721/1000000000) 156699607947/500000000) 23533438303/500000000))
✓	16.4b	(/.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)))
✓	23.7b	(/.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)))

series1.5s (3.7%)

Counts

4 → 96

Calls

4 calls:

760.0ms	(/.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)))
685.0ms	(*.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))
12.0ms	(/.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)))
10.0ms	(sqrt.f64 (fma.f64 x (fma.f64 x (fma.f64 x (+.f64 x 216700011257/5000000000) 263505074721/1000000000) 156699607947/500000000) 23533438303/500000000))

rewrite103.0ms (0.3%)

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:

17.0ms	(/.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)))
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))) (fma.f64 x (fma.f64 x (fma.f64 x (fma.f64 x 104109730557/25000000000 393497462077/5000000000) 4297481763/31250000) y) z))
17.0ms	(/.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)))
2.0ms	(sqrt.f64 (fma.f64 x (fma.f64 x (fma.f64 x (+.f64 x 216700011257/5000000000) 263505074721/1000000000) 156699607947/500000000) 23533438303/500000000))

simplify690.0ms (1.8%)

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

prune995.0ms (2.5%)

Pruning

5 alts after pruning (5 fresh and 0 done)

	Pruned	Kept	Total
New	297	2	299
Fresh	2	3	5
Picked	1	0	1
Done	0	0	0
Total	300	5	305

Error

0.3b

Counts

305 → 5

Alt Table

Status	Error	Program
	32.9b	(-.f64 (+.f64 (fma.f64 x 104109730557/25000000000 (/.f64 2284450290879775841688574159837293/625000000000000000000000000000 x)) (/.f64 y (.f64 x x))) (+.f64 13764240537310136880149/125000000000000000000 (/.f64 409304707811198655637810418659684985388407301/3125000000000000000000000000000000000000 (.f64 x x))))
	28.3b	(.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)))
▶	27.5b	(/.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)) (.f64 (fabs.f64 (cbrt.f64 (fma.f64 x (fma.f64 x (fma.f64 x (+.f64 x 216700011257/5000000000) 263505074721/1000000000) 156699607947/500000000) 23533438303/500000000))) (sqrt.f64 (cbrt.f64 (fma.f64 x (fma.f64 x (fma.f64 x (+.f64 x 216700011257/5000000000) 263505074721/1000000000) 156699607947/500000000) 23533438303/500000000)))))
	27.6b	(/.f64 (.f64 (.f64 (cbrt.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))) (cbrt.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)))) (cbrt.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)))
	28.2b	(-.f64 (fma.f64 1759267849271/25000000000 (/.f64 (pow.f64 x 4) (+.f64 (pow.f64 x 4) (+.f64 23533438303/500000000 (fma.f64 x 156699607947/500000000 (.f64 (.f64 x x) (+.f64 263505074721/1000000000 (.f64 216700011257/5000000000 x))))))) (fma.f64 104109730557/25000000000 (/.f64 (pow.f64 x 5) (+.f64 (pow.f64 x 4) (+.f64 23533438303/500000000 (fma.f64 x 156699607947/500000000 (.f64 (.f64 x x) (+.f64 263505074721/1000000000 (.f64 216700011257/5000000000 x))))))) (fma.f64 (/.f64 z (+.f64 (pow.f64 x 4) (+.f64 23533438303/500000000 (fma.f64 x 156699607947/500000000 (.f64 (.f64 x x) (+.f64 263505074721/1000000000 (.f64 216700011257/5000000000 x))))))) x (/.f64 (.f64 x (.f64 x y)) (+.f64 (pow.f64 x 4) (+.f64 23533438303/500000000 (fma.f64 x 156699607947/500000000 (.f64 (.f64 x x) (+.f64 263505074721/1000000000 (.f64 216700011257/5000000000 x)))))))))) (fma.f64 2 (fma.f64 (/.f64 y (+.f64 (pow.f64 x 4) (+.f64 23533438303/500000000 (fma.f64 x 156699607947/500000000 (.f64 (.f64 x x) (+.f64 263505074721/1000000000 (.f64 216700011257/5000000000 x))))))) x (/.f64 z (+.f64 (pow.f64 x 4) (+.f64 23533438303/500000000 (fma.f64 x 156699607947/500000000 (.f64 (.f64 x x) (+.f64 263505074721/1000000000 (.f64 216700011257/5000000000 x)))))))) (fma.f64 4297481763/15625000 (/.f64 (.f64 x x) (+.f64 (pow.f64 x 4) (+.f64 23533438303/500000000 (fma.f64 x 156699607947/500000000 (.f64 (.f64 x x) (+.f64 263505074721/1000000000 (.f64 216700011257/5000000000 x))))))) (.f64 49698921037/2500000000 (/.f64 (pow.f64 x 3) (+.f64 (pow.f64 x 4) (+.f64 23533438303/500000000 (fma.f64 x 156699607947/500000000 (.f64 (.f64 x x) (+.f64 263505074721/1000000000 (.f64 216700011257/5000000000 x)))))))))))

Compiler

Compiled 18811 to 13150 computations (30.1% saved)

localize53.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	8.9b	(sqrt.f64 (cbrt.f64 (fma.f64 x (fma.f64 x (fma.f64 x (+.f64 x 216700011257/5000000000) 263505074721/1000000000) 156699607947/500000000) 23533438303/500000000)))
	16.4b	(/.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)))
✓	16.7b	(cbrt.f64 (fma.f64 x (fma.f64 x (fma.f64 x (+.f64 x 216700011257/5000000000) 263505074721/1000000000) 156699607947/500000000) 23533438303/500000000))
✓	23.7b	(/.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)) (.f64 (fabs.f64 (cbrt.f64 (fma.f64 x (fma.f64 x (fma.f64 x (+.f64 x 216700011257/5000000000) 263505074721/1000000000) 156699607947/500000000) 23533438303/500000000))) (sqrt.f64 (cbrt.f64 (fma.f64 x (fma.f64 x (fma.f64 x (+.f64 x 216700011257/5000000000) 263505074721/1000000000) 156699607947/500000000) 23533438303/500000000)))))

series2.8s (7.2%)

Counts

3 → 60

Calls

3 calls:

2.8s

(/.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)) (*.f64 (fabs.f64 (cbrt.f64 (fma.f64 x (fma.f64 x (fma.f64 x (+.f64 x 216700011257/5000000000) 263505074721/1000000000) 156699607947/500000000) 23533438303/500000000))) (sqrt.f64 (cbrt.f64 (fma.f64 x (fma.f64 x (fma.f64 x (+.f64 x 216700011257/5000000000) 263505074721/1000000000) 156699607947/500000000) 23533438303/500000000)))))

14.0ms

(sqrt.f64 (cbrt.f64 (fma.f64 x (fma.f64 x (fma.f64 x (+.f64 x 216700011257/5000000000) 263505074721/1000000000) 156699607947/500000000) 23533438303/500000000)))

11.0ms

(cbrt.f64 (fma.f64 x (fma.f64 x (fma.f64 x (+.f64 x 216700011257/5000000000) 263505074721/1000000000) 156699607947/500000000) 23533438303/500000000))

rewrite45.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

24×	`add-cbrt-cube_binary64`
24×	`add-exp-log_binary64`
8×	`add-sqr-sqrt_binary64`
8×	`cbrt-undiv_binary64`
8×	`div-exp_binary64`

Counts

3 → 61

Calls

3 calls:

22.0ms

(/.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)) (*.f64 (fabs.f64 (cbrt.f64 (fma.f64 x (fma.f64 x (fma.f64 x (+.f64 x 216700011257/5000000000) 263505074721/1000000000) 156699607947/500000000) 23533438303/500000000))) (sqrt.f64 (cbrt.f64 (fma.f64 x (fma.f64 x (fma.f64 x (+.f64 x 216700011257/5000000000) 263505074721/1000000000) 156699607947/500000000) 23533438303/500000000)))))

3.0ms

(sqrt.f64 (cbrt.f64 (fma.f64 x (fma.f64 x (fma.f64 x (+.f64 x 216700011257/5000000000) 263505074721/1000000000) 156699607947/500000000) 23533438303/500000000)))

1.0ms

(cbrt.f64 (fma.f64 x (fma.f64 x (fma.f64 x (+.f64 x 216700011257/5000000000) 263505074721/1000000000) 156699607947/500000000) 23533438303/500000000))

simplify673.0ms (1.7%)

Algorithm

1×	egg-herbie

Rules

395×	`cancel-sign-sub-inv_binary64`
252×	`fma-neg_binary64`
249×	`associate-r_binary64`
247×	`times-frac_binary64`
233×	`associate-l_binary64`

Counts

121 → 146

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	331	15710
1	950	11592
2	3480	10903
3	4810	10871
4	4984	10871
5	4939	10871

prune1.1s (2.7%)

Pruning

5 alts after pruning (4 fresh and 1 done)

	Pruned	Kept	Total
New	247	1	248
Fresh	1	3	4
Picked	0	1	1
Done	0	0	0
Total	248	5	253

Error

0.3b

Counts

253 → 5

Alt Table

Status	Error	Program
	32.9b	(-.f64 (+.f64 (fma.f64 x 104109730557/25000000000 (/.f64 2284450290879775841688574159837293/625000000000000000000000000000 x)) (/.f64 y (.f64 x x))) (+.f64 13764240537310136880149/125000000000000000000 (/.f64 409304707811198655637810418659684985388407301/3125000000000000000000000000000000000000 (.f64 x x))))
	28.3b	(.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)))
✓	27.5b	(/.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)) (.f64 (fabs.f64 (cbrt.f64 (fma.f64 x (fma.f64 x (fma.f64 x (+.f64 x 216700011257/5000000000) 263505074721/1000000000) 156699607947/500000000) 23533438303/500000000))) (sqrt.f64 (cbrt.f64 (fma.f64 x (fma.f64 x (fma.f64 x (+.f64 x 216700011257/5000000000) 263505074721/1000000000) 156699607947/500000000) 23533438303/500000000)))))
▶	27.3b	(/.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)) (.f64 (fabs.f64 (cbrt.f64 (fma.f64 x (fma.f64 x (fma.f64 x (+.f64 x 216700011257/5000000000) 263505074721/1000000000) 156699607947/500000000) 23533438303/500000000))) (expm1.f64 (log1p.f64 (sqrt.f64 (cbrt.f64 (fma.f64 x (fma.f64 x (fma.f64 x (+.f64 x 216700011257/5000000000) 263505074721/1000000000) 156699607947/500000000) 23533438303/500000000)))))))
	28.2b	(-.f64 (fma.f64 1759267849271/25000000000 (/.f64 (pow.f64 x 4) (+.f64 (pow.f64 x 4) (+.f64 23533438303/500000000 (fma.f64 x 156699607947/500000000 (.f64 (.f64 x x) (+.f64 263505074721/1000000000 (.f64 216700011257/5000000000 x))))))) (fma.f64 104109730557/25000000000 (/.f64 (pow.f64 x 5) (+.f64 (pow.f64 x 4) (+.f64 23533438303/500000000 (fma.f64 x 156699607947/500000000 (.f64 (.f64 x x) (+.f64 263505074721/1000000000 (.f64 216700011257/5000000000 x))))))) (fma.f64 (/.f64 z (+.f64 (pow.f64 x 4) (+.f64 23533438303/500000000 (fma.f64 x 156699607947/500000000 (.f64 (.f64 x x) (+.f64 263505074721/1000000000 (.f64 216700011257/5000000000 x))))))) x (/.f64 (.f64 x (.f64 x y)) (+.f64 (pow.f64 x 4) (+.f64 23533438303/500000000 (fma.f64 x 156699607947/500000000 (.f64 (.f64 x x) (+.f64 263505074721/1000000000 (.f64 216700011257/5000000000 x)))))))))) (fma.f64 2 (fma.f64 (/.f64 y (+.f64 (pow.f64 x 4) (+.f64 23533438303/500000000 (fma.f64 x 156699607947/500000000 (.f64 (.f64 x x) (+.f64 263505074721/1000000000 (.f64 216700011257/5000000000 x))))))) x (/.f64 z (+.f64 (pow.f64 x 4) (+.f64 23533438303/500000000 (fma.f64 x 156699607947/500000000 (.f64 (.f64 x x) (+.f64 263505074721/1000000000 (.f64 216700011257/5000000000 x)))))))) (fma.f64 4297481763/15625000 (/.f64 (.f64 x x) (+.f64 (pow.f64 x 4) (+.f64 23533438303/500000000 (fma.f64 x 156699607947/500000000 (.f64 (.f64 x x) (+.f64 263505074721/1000000000 (.f64 216700011257/5000000000 x))))))) (.f64 49698921037/2500000000 (/.f64 (pow.f64 x 3) (+.f64 (pow.f64 x 4) (+.f64 23533438303/500000000 (fma.f64 x 156699607947/500000000 (.f64 (.f64 x x) (+.f64 263505074721/1000000000 (.f64 216700011257/5000000000 x)))))))))))

Compiler

Compiled 19696 to 14043 computations (28.7% saved)

localize61.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
	8.9b	(sqrt.f64 (cbrt.f64 (fma.f64 x (fma.f64 x (fma.f64 x (+.f64 x 216700011257/5000000000) 263505074721/1000000000) 156699607947/500000000) 23533438303/500000000)))
	16.4b	(/.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)))
	16.7b	(cbrt.f64 (fma.f64 x (fma.f64 x (fma.f64 x (+.f64 x 216700011257/5000000000) 263505074721/1000000000) 156699607947/500000000) 23533438303/500000000))
✓	23.7b	(/.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)) (.f64 (fabs.f64 (cbrt.f64 (fma.f64 x (fma.f64 x (fma.f64 x (+.f64 x 216700011257/5000000000) 263505074721/1000000000) 156699607947/500000000) 23533438303/500000000))) (expm1.f64 (log1p.f64 (sqrt.f64 (cbrt.f64 (fma.f64 x (fma.f64 x (fma.f64 x (+.f64 x 216700011257/5000000000) 263505074721/1000000000) 156699607947/500000000) 23533438303/500000000)))))))

series2.9s (7.5%)

Counts

1 → 36

Calls

1 calls:

2.9s

(/.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)) (*.f64 (fabs.f64 (cbrt.f64 (fma.f64 x (fma.f64 x (fma.f64 x (+.f64 x 216700011257/5000000000) 263505074721/1000000000) 156699607947/500000000) 23533438303/500000000))) (expm1.f64 (log1p.f64 (sqrt.f64 (cbrt.f64 (fma.f64 x (fma.f64 x (fma.f64 x (+.f64 x 216700011257/5000000000) 263505074721/1000000000) 156699607947/500000000) 23533438303/500000000)))))))

rewrite39.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

22×	`add-cbrt-cube_binary64`
22×	`add-exp-log_binary64`
8×	`cbrt-undiv_binary64`
8×	`div-exp_binary64`
7×	`cbrt-unprod_binary64`

Counts

1 → 28

Calls

1 calls:

22.0ms

(/.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)) (*.f64 (fabs.f64 (cbrt.f64 (fma.f64 x (fma.f64 x (fma.f64 x (+.f64 x 216700011257/5000000000) 263505074721/1000000000) 156699607947/500000000) 23533438303/500000000))) (expm1.f64 (log1p.f64 (sqrt.f64 (cbrt.f64 (fma.f64 x (fma.f64 x (fma.f64 x (+.f64 x 216700011257/5000000000) 263505074721/1000000000) 156699607947/500000000) 23533438303/500000000)))))))

simplify431.0ms (1.1%)

Algorithm

1×	egg-herbie

Rules

524×	`distribute-rgt-in_binary64`
286×	`cancel-sign-sub-inv_binary64`
216×	`times-frac_binary64`
188×	`associate-r_binary64`
188×	`associate-l_binary64`

Counts

64 → 69

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	250	14347
1	754	10309
2	2865	8822
3	5367	8822

prune1.1s (2.7%)

Pruning

5 alts after pruning (3 fresh and 2 done)

	Pruned	Kept	Total
New	248	0	248
Fresh	0	3	3
Picked	0	1	1
Done	0	1	1
Total	248	5	253

Error

0.3b

Counts

253 → 5

Alt Table

Status	Error	Program
	32.9b	(-.f64 (+.f64 (fma.f64 x 104109730557/25000000000 (/.f64 2284450290879775841688574159837293/625000000000000000000000000000 x)) (/.f64 y (.f64 x x))) (+.f64 13764240537310136880149/125000000000000000000 (/.f64 409304707811198655637810418659684985388407301/3125000000000000000000000000000000000000 (.f64 x x))))
	28.3b	(.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)))
✓	27.5b	(/.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)) (.f64 (fabs.f64 (cbrt.f64 (fma.f64 x (fma.f64 x (fma.f64 x (+.f64 x 216700011257/5000000000) 263505074721/1000000000) 156699607947/500000000) 23533438303/500000000))) (sqrt.f64 (cbrt.f64 (fma.f64 x (fma.f64 x (fma.f64 x (+.f64 x 216700011257/5000000000) 263505074721/1000000000) 156699607947/500000000) 23533438303/500000000)))))
✓	27.3b	(/.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)) (.f64 (fabs.f64 (cbrt.f64 (fma.f64 x (fma.f64 x (fma.f64 x (+.f64 x 216700011257/5000000000) 263505074721/1000000000) 156699607947/500000000) 23533438303/500000000))) (expm1.f64 (log1p.f64 (sqrt.f64 (cbrt.f64 (fma.f64 x (fma.f64 x (fma.f64 x (+.f64 x 216700011257/5000000000) 263505074721/1000000000) 156699607947/500000000) 23533438303/500000000)))))))
	28.2b	(-.f64 (fma.f64 1759267849271/25000000000 (/.f64 (pow.f64 x 4) (+.f64 (pow.f64 x 4) (+.f64 23533438303/500000000 (fma.f64 x 156699607947/500000000 (.f64 (.f64 x x) (+.f64 263505074721/1000000000 (.f64 216700011257/5000000000 x))))))) (fma.f64 104109730557/25000000000 (/.f64 (pow.f64 x 5) (+.f64 (pow.f64 x 4) (+.f64 23533438303/500000000 (fma.f64 x 156699607947/500000000 (.f64 (.f64 x x) (+.f64 263505074721/1000000000 (.f64 216700011257/5000000000 x))))))) (fma.f64 (/.f64 z (+.f64 (pow.f64 x 4) (+.f64 23533438303/500000000 (fma.f64 x 156699607947/500000000 (.f64 (.f64 x x) (+.f64 263505074721/1000000000 (.f64 216700011257/5000000000 x))))))) x (/.f64 (.f64 x (.f64 x y)) (+.f64 (pow.f64 x 4) (+.f64 23533438303/500000000 (fma.f64 x 156699607947/500000000 (.f64 (.f64 x x) (+.f64 263505074721/1000000000 (.f64 216700011257/5000000000 x)))))))))) (fma.f64 2 (fma.f64 (/.f64 y (+.f64 (pow.f64 x 4) (+.f64 23533438303/500000000 (fma.f64 x 156699607947/500000000 (.f64 (.f64 x x) (+.f64 263505074721/1000000000 (.f64 216700011257/5000000000 x))))))) x (/.f64 z (+.f64 (pow.f64 x 4) (+.f64 23533438303/500000000 (fma.f64 x 156699607947/500000000 (.f64 (.f64 x x) (+.f64 263505074721/1000000000 (.f64 216700011257/5000000000 x)))))))) (fma.f64 4297481763/15625000 (/.f64 (.f64 x x) (+.f64 (pow.f64 x 4) (+.f64 23533438303/500000000 (fma.f64 x 156699607947/500000000 (.f64 (.f64 x x) (+.f64 263505074721/1000000000 (.f64 216700011257/5000000000 x))))))) (.f64 49698921037/2500000000 (/.f64 (pow.f64 x 3) (+.f64 (pow.f64 x 4) (+.f64 23533438303/500000000 (fma.f64 x 156699607947/500000000 (.f64 (.f64 x x) (+.f64 263505074721/1000000000 (.f64 216700011257/5000000000 x)))))))))))

Compiler

Compiled 19964 to 14386 computations (27.9% saved)

regimes19.2s (48.8%)

Accuracy

Total 0.8b remaining (73%)

Threshold costs 0.8b (73%)

Counts

390 → 3

Compiler

Compiled 93840 to 66928 computations (28.7% saved)

bsearch194.0ms (0.5%)

Steps

Iters	Range		Point
7	1.9269183885021452e+36	4.1006832354306375e+37	6.654331205362247e+36
11	-2.2180290161594404e+39	-16058839023971303000.0	-4.737801379487723e+38

Compiler

Compiled 4 to 3 computations (25% saved)

simplify21.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

10×	`+-commutative_binary64`
8×	`*-commutative_binary64`
5×	`sub-neg_binary64`
3×	`neg-sub0_binary64`
3×	`neg-mul-1_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	60	316
1	77	316
2	90	316
3	100	316
4	104	316
5	105	316
6	103	316

end6.0ms (0%)

Compiler: Compiled 219 to 147 computations (32.9% saved)

sample2.7s (6.8%)

Algorithm

1×

intervals

Results

1.5s	8000×	body	128	valid
1.0ms	7×	body	128	invalid

Compiler

Compiled 641 to 440 computations (31.4% saved)

Details

analyze2.8s (7.1%)

sample76.0ms (0.2%)

simplify73.0ms (0.2%)

prune8.0ms (0%)

localize47.0ms (0.1%)

series877.0ms (2.2%)

rewrite18.0ms (0%)

simplify374.0ms (1%)

prune427.0ms (1.1%)

localize47.0ms (0.1%)

series1.5s (3.7%)

rewrite103.0ms (0.3%)

simplify690.0ms (1.8%)

prune995.0ms (2.5%)

localize53.0ms (0.1%)

series2.8s (7.2%)

rewrite45.0ms (0.1%)

simplify673.0ms (1.7%)

prune1.1s (2.7%)

localize61.0ms (0.2%)

series2.9s (7.5%)

rewrite39.0ms (0.1%)

simplify431.0ms (1.1%)

prune1.1s (2.7%)

regimes19.2s (48.8%)

bsearch194.0ms (0.5%)

simplify21.0ms (0.1%)

end6.0ms (0%)

sample2.7s (6.8%)

Profiling