Details

analyze1.4s (8.7%)

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)

sample1.6s (10.1%)

Results

1.6s	8256×	body	128	valid
2.0ms	10×	body	128	invalid

Compiler

Compiled 122 to 89 computations (27% saved)

simplify51.0ms (0.3%)

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

2 alts after pruning (2 fresh and 0 done)

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

Error

27.7b

Counts

3 → 1

Alt Table

Status	Error	Program
▶	27.7b	(/.f64 (.f64 (-.f64 x 2) (+.f64 (.f64 (+.f64 (.f64 (+.f64 (.f64 (+.f64 (.f64 x 104109730557/25000000000) 393497462077/5000000000) x) 4297481763/31250000) x) y) x) z)) (+.f64 (.f64 (+.f64 (.f64 (+.f64 (.f64 (+.f64 x 216700011257/5000000000) x) 263505074721/1000000000) x) 156699607947/500000000) x) 23533438303/500000000))

Status

Error

Program

▶

27.7b

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

Compiler

Compiled 150 to 106 computations (29.3% saved)

localize25.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.3b	(.f64 (+.f64 (.f64 (+.f64 (*.f64 x 104109730557/25000000000) 393497462077/5000000000) x) 4297481763/31250000) x)
✓	0.4b	(.f64 (+.f64 (.f64 (+.f64 x 216700011257/5000000000) x) 263505074721/1000000000) x)
✓	0.6b	(*.f64 x 104109730557/25000000000)
✓	26.8b	(/.f64 (.f64 (-.f64 x 2) (+.f64 (.f64 (+.f64 (.f64 (+.f64 (.f64 (+.f64 (.f64 x 104109730557/25000000000) 393497462077/5000000000) x) 4297481763/31250000) x) y) x) z)) (+.f64 (.f64 (+.f64 (.f64 (+.f64 (.f64 (+.f64 x 216700011257/5000000000) x) 263505074721/1000000000) x) 156699607947/500000000) x) 23533438303/500000000))

series343.0ms (2.1%)

Counts

4 → 72

Calls

4 calls:

336.0ms	(/.f64 (.f64 (-.f64 x 2) (+.f64 (.f64 (+.f64 (.f64 (+.f64 (.f64 (+.f64 (.f64 x 104109730557/25000000000) 393497462077/5000000000) x) 4297481763/31250000) x) y) x) z)) (+.f64 (.f64 (+.f64 (.f64 (+.f64 (.f64 (+.f64 x 216700011257/5000000000) x) 263505074721/1000000000) x) 156699607947/500000000) x) 23533438303/500000000))
3.0ms	(.f64 (+.f64 (.f64 (+.f64 (*.f64 x 104109730557/25000000000) 393497462077/5000000000) x) 4297481763/31250000) x)
3.0ms	(.f64 (+.f64 (.f64 (+.f64 x 216700011257/5000000000) x) 263505074721/1000000000) x)
2.0ms	(*.f64 x 104109730557/25000000000)

rewrite54.0ms (0.3%)

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 → 97

Calls

4 calls:

27.0ms	(/.f64 (.f64 (-.f64 x 2) (+.f64 (.f64 (+.f64 (.f64 (+.f64 (.f64 (+.f64 (.f64 x 104109730557/25000000000) 393497462077/5000000000) x) 4297481763/31250000) x) y) x) z)) (+.f64 (.f64 (+.f64 (.f64 (+.f64 (.f64 (+.f64 x 216700011257/5000000000) x) 263505074721/1000000000) x) 156699607947/500000000) x) 23533438303/500000000))
9.0ms	(.f64 (+.f64 (.f64 (+.f64 x 216700011257/5000000000) x) 263505074721/1000000000) x)
7.0ms	(.f64 (+.f64 (.f64 (+.f64 (*.f64 x 104109730557/25000000000) 393497462077/5000000000) x) 4297481763/31250000) x)
3.0ms	(*.f64 x 104109730557/25000000000)

simplify229.0ms (1.4%)

Algorithm

1×	egg-herbie

Rules

307×	`associate-r_binary64`
307×	`times-frac_binary64`
305×	`associate-l_binary64`
240×	`distribute-rgt-in_binary64`
239×	`fma-def_binary64`

Counts

169 → 201

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	332	8736
1	950	8327
2	3621	8327
3	4913	8327
4	4949	8327

prune355.0ms (2.2%)

Pruning

8 alts after pruning (8 fresh and 0 done)

	Pruned	Kept	Total
New	193	8	201
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	194	8	202

Error

0.2b

Counts

202 → 8

Alt Table

Status	Error	Program
▶	25.9b	(*.f64 (-.f64 x 2) (/.f64 (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)))
	27.7b	(-.f64 (fma.f64 1759267849271/25000000000 (/.f64 (pow.f64 x 4) (+.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)))))) (+.f64 (/.f64 (.f64 x (.f64 x y)) (+.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)))))) (fma.f64 104109730557/25000000000 (/.f64 (pow.f64 x 5) (+.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)))))) (/.f64 (.f64 z x) (+.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))))))))) (fma.f64 2 (/.f64 (.f64 x y) (+.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)))))) (fma.f64 2 (/.f64 z (+.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)))))) (fma.f64 4297481763/15625000 (/.f64 (.f64 x x) (+.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)))))) (.f64 49698921037/2500000000 (/.f64 (pow.f64 x 3) (+.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)))))))))))
	26.6b	(/.f64 (.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)))) (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 (.f64 (+.f64 (*.f64 (+.f64 x 216700011257/5000000000) x) 263505074721/1000000000) x) 156699607947/500000000) x) 23533438303/500000000)))
	31.8b	(-.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))))
	49.8b	(/.f64 (.f64 (-.f64 x 2) (+.f64 (pow.f64 (.f64 (+.f64 (.f64 (+.f64 (.f64 (+.f64 (.f64 x 104109730557/25000000000) 393497462077/5000000000) x) 4297481763/31250000) x) y) x) 3) (pow.f64 z 3))) (.f64 (fma.f64 x (fma.f64 x (fma.f64 x (+.f64 x 216700011257/5000000000) 263505074721/1000000000) 156699607947/500000000) 23533438303/500000000) (fma.f64 z (-.f64 z (.f64 x (fma.f64 x (fma.f64 x (fma.f64 x 104109730557/25000000000 393497462077/5000000000) 4297481763/31250000) y))) (.f64 (.f64 x (fma.f64 x (fma.f64 x (fma.f64 x 104109730557/25000000000 393497462077/5000000000) 4297481763/31250000) y)) (.f64 x (fma.f64 x (fma.f64 x (fma.f64 x 104109730557/25000000000 393497462077/5000000000) 4297481763/31250000) y))))))
	34.7b	(-.f64 (fma.f64 3140446455626174059100348970313144550000000/306719603372886620352117082586607327396481 (.f64 z (pow.f64 x 3)) (+.f64 (.f64 168466327098500000000/553822718361107519809 (fma.f64 z x (.f64 x (.f64 x y)))) (.f64 (pow.f64 x 3) 106576606695487271009549/2769113591805537599045))) (fma.f64 23298017199368982832548000000000/13033352773350869092174451844127 (.f64 z (.f64 x x)) (+.f64 (fma.f64 (.f64 x x) 137519416416/23533438303 (.f64 23298017199368982832548000000000/13033352773350869092174451844127 (.f64 y (pow.f64 x 3)))) (*.f64 1000000000/23533438303 (fma.f64 x y z)))))
	27.7b	(/.f64 (.f64 (-.f64 x 2) (+.f64 (.f64 (+.f64 (+.f64 (.f64 393497462077/5000000000 (pow.f64 x 2)) (+.f64 (.f64 104109730557/25000000000 (pow.f64 x 3)) (.f64 4297481763/31250000 x))) y) x) z)) (+.f64 (.f64 (+.f64 (.f64 (+.f64 (.f64 (+.f64 x 216700011257/5000000000) x) 263505074721/1000000000) x) 156699607947/500000000) x) 23533438303/500000000))
	26.3b	(/.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)) (sqrt.f64 (+.f64 (.f64 (+.f64 (.f64 (+.f64 (.f64 (+.f64 x 216700011257/5000000000) x) 263505074721/1000000000) x) 156699607947/500000000) x) 23533438303/500000000)))

Compiler

Compiled 10870 to 7621 computations (29.9% saved)

localize20.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.1b	(fma.f64 x (fma.f64 x (fma.f64 x 104109730557/25000000000 393497462077/5000000000) 4297481763/31250000) y)
✓	0.3b	(*.f64 (-.f64 x 2) (/.f64 (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)))
✓	0.3b	(fma.f64 x 104109730557/25000000000 393497462077/5000000000)
✓	25.1b	(/.f64 (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))

series621.0ms (3.8%)

Counts

4 → 108

Calls

4 calls:

340.0ms	(*.f64 (-.f64 x 2) (/.f64 (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)))
269.0ms	(/.f64 (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))
10.0ms	(fma.f64 x (fma.f64 x (fma.f64 x 104109730557/25000000000 393497462077/5000000000) 4297481763/31250000) y)
2.0ms	(fma.f64 x 104109730557/25000000000 393497462077/5000000000)

rewrite37.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

27×	`add-sqr-sqrt_binary64`
22×	`*-un-lft-identity_binary64`
20×	`add-cube-cbrt_binary64`
19×	`times-frac_binary64`
13×	`associate-r_binary64`

Counts

4 → 89

Calls

4 calls:

28.0ms	(*.f64 (-.f64 x 2) (/.f64 (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)))
2.0ms	(/.f64 (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 (fma.f64 x (fma.f64 x 104109730557/25000000000 393497462077/5000000000) 4297481763/31250000) y)
0.0ms	(fma.f64 x 104109730557/25000000000 393497462077/5000000000)

simplify521.0ms (3.2%)

Algorithm

1×	egg-herbie

Rules

631×	`distribute-rgt-in_binary64`
307×	`cancel-sign-sub-inv_binary64`
251×	`fma-def_binary64`
175×	`sub-neg_binary64`
169×	`+-commutative_binary64`

Counts

197 → 175

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	326	13671
1	856	13218
2	2919	13132
3	5211	13132

prune592.0ms (3.6%)

Pruning

9 alts after pruning (9 fresh and 0 done)

	Pruned	Kept	Total
New	169	6	175
Fresh	4	3	7
Picked	1	0	1
Done	0	0	0
Total	174	9	183

Error

0.2b

Counts

183 → 9

Alt Table

Status	Error	Program
	27.7b	(/.f64 (.f64 (-.f64 x 2) (+.f64 (.f64 (+.f64 (+.f64 (.f64 393497462077/5000000000 (pow.f64 x 2)) (+.f64 (.f64 104109730557/25000000000 (pow.f64 x 3)) (.f64 4297481763/31250000 x))) y) x) z)) (+.f64 (.f64 (+.f64 (.f64 (+.f64 (.f64 (+.f64 x 216700011257/5000000000) x) 263505074721/1000000000) x) 156699607947/500000000) x) 23533438303/500000000))
	26.9b	(.f64 (.f64 (cbrt.f64 (-.f64 x 2)) (cbrt.f64 (-.f64 x 2))) (*.f64 (cbrt.f64 (-.f64 x 2)) (/.f64 (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))))
	49.8b	(/.f64 (.f64 (-.f64 x 2) (+.f64 (pow.f64 (.f64 (+.f64 (.f64 (+.f64 (.f64 (+.f64 (.f64 x 104109730557/25000000000) 393497462077/5000000000) x) 4297481763/31250000) x) y) x) 3) (pow.f64 z 3))) (.f64 (fma.f64 x (fma.f64 x (fma.f64 x (+.f64 x 216700011257/5000000000) 263505074721/1000000000) 156699607947/500000000) 23533438303/500000000) (fma.f64 z (-.f64 z (.f64 x (fma.f64 x (fma.f64 x (fma.f64 x 104109730557/25000000000 393497462077/5000000000) 4297481763/31250000) y))) (.f64 (.f64 x (fma.f64 x (fma.f64 x (fma.f64 x 104109730557/25000000000 393497462077/5000000000) 4297481763/31250000) y)) (.f64 x (fma.f64 x (fma.f64 x (fma.f64 x 104109730557/25000000000 393497462077/5000000000) 4297481763/31250000) y))))))
	31.9b	(.f64 (-.f64 x 2) (-.f64 (+.f64 104109730557/25000000000 (+.f64 (/.f64 2157218858562374472887084159837293/625000000000000000000000000000 (.f64 x x)) (/.f64 y (pow.f64 x 3)))) (+.f64 (/.f64 12723143231740136880149/125000000000000000000 x) (/.f64 387732519225574910908939577061312055388407301/3125000000000000000000000000000000000000 (pow.f64 x 3)))))
	34.7b	(-.f64 (fma.f64 (.f64 z (pow.f64 x 3)) 3140446455626174059100348970313144550000000/306719603372886620352117082586607327396481 (+.f64 (.f64 168466327098500000000/553822718361107519809 (.f64 x (fma.f64 y x z))) (.f64 (pow.f64 x 3) 106576606695487271009549/2769113591805537599045))) (fma.f64 (.f64 z (.f64 x x)) 23298017199368982832548000000000/13033352773350869092174451844127 (+.f64 (.f64 (.f64 x x) (+.f64 137519416416/23533438303 (.f64 (.f64 y 23298017199368982832548000000000/13033352773350869092174451844127) x))) (*.f64 1000000000/23533438303 (fma.f64 y x z)))))
	45.4b	(.f64 (-.f64 x 2) (/.f64 (fma.f64 x (.f64 (sqrt.f64 (fma.f64 x (fma.f64 x (fma.f64 x 104109730557/25000000000 393497462077/5000000000) 4297481763/31250000) y)) (sqrt.f64 (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)))
▶	26.1b	(.f64 (-.f64 x 2) (/.f64 (fma.f64 x (.f64 (*.f64 (cbrt.f64 (fma.f64 x (fma.f64 x (fma.f64 x 104109730557/25000000000 393497462077/5000000000) 4297481763/31250000) y)) (cbrt.f64 (fma.f64 x (fma.f64 x (fma.f64 x 104109730557/25000000000 393497462077/5000000000) 4297481763/31250000) y))) (cbrt.f64 (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)))
	26.3b	(.f64 (.f64 (-.f64 x 2) (/.f64 1 (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))))
	31.8b	(-.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))))

Compiler

Compiled 8528 to 5746 computations (32.6% saved)

localize54.0ms (0.3%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.3b	(fma.f64 x 104109730557/25000000000 393497462077/5000000000)
✓	0.4b	(*.f64 (cbrt.f64 (fma.f64 x (fma.f64 x (fma.f64 x 104109730557/25000000000 393497462077/5000000000) 4297481763/31250000) y)) (cbrt.f64 (fma.f64 x (fma.f64 x (fma.f64 x 104109730557/25000000000 393497462077/5000000000) 4297481763/31250000) y)))
✓	22.4b	(cbrt.f64 (fma.f64 x (fma.f64 x (fma.f64 x 104109730557/25000000000 393497462077/5000000000) 4297481763/31250000) y))
✓	25.1b	(/.f64 (fma.f64 x (.f64 (.f64 (cbrt.f64 (fma.f64 x (fma.f64 x (fma.f64 x 104109730557/25000000000 393497462077/5000000000) 4297481763/31250000) y)) (cbrt.f64 (fma.f64 x (fma.f64 x (fma.f64 x 104109730557/25000000000 393497462077/5000000000) 4297481763/31250000) y))) (cbrt.f64 (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))

series817.0ms (5%)

Counts

3 → 84

Calls

3 calls:

559.0ms

(/.f64 (fma.f64 x (*.f64 (*.f64 (cbrt.f64 (fma.f64 x (fma.f64 x (fma.f64 x 104109730557/25000000000 393497462077/5000000000) 4297481763/31250000) y)) (cbrt.f64 (fma.f64 x (fma.f64 x (fma.f64 x 104109730557/25000000000 393497462077/5000000000) 4297481763/31250000) y))) (cbrt.f64 (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))

173.0ms

(*.f64 (cbrt.f64 (fma.f64 x (fma.f64 x (fma.f64 x 104109730557/25000000000 393497462077/5000000000) 4297481763/31250000) y)) (cbrt.f64 (fma.f64 x (fma.f64 x (fma.f64 x 104109730557/25000000000 393497462077/5000000000) 4297481763/31250000) y)))

84.0ms

(cbrt.f64 (fma.f64 x (fma.f64 x (fma.f64 x 104109730557/25000000000 393497462077/5000000000) 4297481763/31250000) y))

rewrite32.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

28×	`add-sqr-sqrt_binary64`
20×	`*-un-lft-identity_binary64`
20×	`add-cube-cbrt_binary64`
19×	`cbrt-prod_binary64`
10×	`pow1_binary64`

Counts

3 → 84

Calls

3 calls:

9.0ms

(*.f64 (cbrt.f64 (fma.f64 x (fma.f64 x (fma.f64 x 104109730557/25000000000 393497462077/5000000000) 4297481763/31250000) y)) (cbrt.f64 (fma.f64 x (fma.f64 x (fma.f64 x 104109730557/25000000000 393497462077/5000000000) 4297481763/31250000) y)))

5.0ms

(/.f64 (fma.f64 x (*.f64 (*.f64 (cbrt.f64 (fma.f64 x (fma.f64 x (fma.f64 x 104109730557/25000000000 393497462077/5000000000) 4297481763/31250000) y)) (cbrt.f64 (fma.f64 x (fma.f64 x (fma.f64 x 104109730557/25000000000 393497462077/5000000000) 4297481763/31250000) y))) (cbrt.f64 (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

(cbrt.f64 (fma.f64 x (fma.f64 x (fma.f64 x 104109730557/25000000000 393497462077/5000000000) 4297481763/31250000) y))

simplify517.0ms (3.2%)

Algorithm

1×	egg-herbie

Rules

677×	`fma-def_binary64`
452×	`associate-l_binary64`
208×	`*-commutative_binary64`
172×	`times-frac_binary64`
155×	`associate-/r*_binary64`

Counts

168 → 220

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	669	12320
1	1960	11668
2	4956	11538
3	4947	11538

prune1.9s (11.8%)

Pruning

9 alts after pruning (8 fresh and 1 done)

	Pruned	Kept	Total
New	387	1	388
Fresh	1	7	8
Picked	0	1	1
Done	0	0	0
Total	388	9	397

Error

0.2b

Counts

397 → 9

Alt Table

Status	Error	Program
	27.7b	(/.f64 (.f64 (-.f64 x 2) (+.f64 (.f64 (+.f64 (+.f64 (.f64 393497462077/5000000000 (pow.f64 x 2)) (+.f64 (.f64 104109730557/25000000000 (pow.f64 x 3)) (.f64 4297481763/31250000 x))) y) x) z)) (+.f64 (.f64 (+.f64 (.f64 (+.f64 (.f64 (+.f64 x 216700011257/5000000000) x) 263505074721/1000000000) x) 156699607947/500000000) x) 23533438303/500000000))
	26.9b	(.f64 (.f64 (cbrt.f64 (-.f64 x 2)) (cbrt.f64 (-.f64 x 2))) (*.f64 (cbrt.f64 (-.f64 x 2)) (/.f64 (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))))
	40.5b	(.f64 (-.f64 x 2) (/.f64 (fma.f64 x (.f64 (cbrt.f64 (*.f64 y y)) (cbrt.f64 (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)))
	31.9b	(.f64 (-.f64 x 2) (-.f64 (+.f64 104109730557/25000000000 (+.f64 (/.f64 2157218858562374472887084159837293/625000000000000000000000000000 (.f64 x x)) (/.f64 y (pow.f64 x 3)))) (+.f64 (/.f64 12723143231740136880149/125000000000000000000 x) (/.f64 387732519225574910908939577061312055388407301/3125000000000000000000000000000000000000 (pow.f64 x 3)))))
	34.7b	(-.f64 (fma.f64 (.f64 z (pow.f64 x 3)) 3140446455626174059100348970313144550000000/306719603372886620352117082586607327396481 (+.f64 (.f64 168466327098500000000/553822718361107519809 (.f64 x (fma.f64 y x z))) (.f64 (pow.f64 x 3) 106576606695487271009549/2769113591805537599045))) (fma.f64 (.f64 z (.f64 x x)) 23298017199368982832548000000000/13033352773350869092174451844127 (+.f64 (.f64 (.f64 x x) (+.f64 137519416416/23533438303 (.f64 (.f64 y 23298017199368982832548000000000/13033352773350869092174451844127) x))) (*.f64 1000000000/23533438303 (fma.f64 y x z)))))
	45.4b	(.f64 (-.f64 x 2) (/.f64 (fma.f64 x (.f64 (sqrt.f64 (fma.f64 x (fma.f64 x (fma.f64 x 104109730557/25000000000 393497462077/5000000000) 4297481763/31250000) y)) (sqrt.f64 (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)))
✓	26.1b	(.f64 (-.f64 x 2) (/.f64 (fma.f64 x (.f64 (*.f64 (cbrt.f64 (fma.f64 x (fma.f64 x (fma.f64 x 104109730557/25000000000 393497462077/5000000000) 4297481763/31250000) y)) (cbrt.f64 (fma.f64 x (fma.f64 x (fma.f64 x 104109730557/25000000000 393497462077/5000000000) 4297481763/31250000) y))) (cbrt.f64 (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)))
▶	26.3b	(.f64 (.f64 (-.f64 x 2) (/.f64 1 (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))))
	31.8b	(-.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))))

Compiler

Compiled 33976 to 24389 computations (28.2% saved)

localize47.0ms (0.3%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	7.9b	(sqrt.f64 (fma.f64 x (fma.f64 x (fma.f64 x (+.f64 x 216700011257/5000000000) 263505074721/1000000000) 156699607947/500000000) 23533438303/500000000))
✓	15.9b	(*.f64 (-.f64 x 2) (/.f64 1 (sqrt.f64 (fma.f64 x (fma.f64 x (fma.f64 x (+.f64 x 216700011257/5000000000) 263505074721/1000000000) 156699607947/500000000) 23533438303/500000000))))
✓	16.6b	(.f64 (.f64 (-.f64 x 2) (/.f64 1 (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))))
✓	21.5b	(/.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)))

series952.0ms (5.9%)

Counts

4 → 96

Calls

4 calls:

473.0ms	(.f64 (.f64 (-.f64 x 2) (/.f64 1 (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))))
469.0ms	(/.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)))
6.0ms	(*.f64 (-.f64 x 2) (/.f64 1 (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))

rewrite54.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

62×	`add-sqr-sqrt_binary64`
58×	`times-frac_binary64`
51×	`*-un-lft-identity_binary64`
50×	`add-exp-log_binary64`
47×	`add-cube-cbrt_binary64`

Counts

4 → 175

Calls

4 calls:

14.0ms	(.f64 (.f64 (-.f64 x 2) (/.f64 1 (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))))
12.0ms	(*.f64 (-.f64 x 2) (/.f64 1 (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)))
1.0ms	(sqrt.f64 (fma.f64 x (fma.f64 x (fma.f64 x (+.f64 x 216700011257/5000000000) 263505074721/1000000000) 156699607947/500000000) 23533438303/500000000))

simplify367.0ms (2.3%)

Algorithm

1×	egg-herbie

Rules

340×	`fma-def_binary64`
308×	`associate-l_binary64`
305×	`associate-r_binary64`
203×	`fma-neg_binary64`
192×	`associate-+r+_binary64`

Counts

271 → 309

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	491	19697
1	1373	17799
2	4876	17795
3	4983	17795

prune577.0ms (3.5%)

Pruning

8 alts after pruning (6 fresh and 2 done)

	Pruned	Kept	Total
New	339	1	340
Fresh	2	5	7
Picked	0	1	1
Done	0	1	1
Total	341	8	349

Error

0.2b

Counts

349 → 8

Alt Table

Status	Error	Program
	27.7b	(/.f64 (.f64 (-.f64 x 2) (+.f64 (.f64 (+.f64 (+.f64 (.f64 393497462077/5000000000 (pow.f64 x 2)) (+.f64 (.f64 104109730557/25000000000 (pow.f64 x 3)) (.f64 4297481763/31250000 x))) y) x) z)) (+.f64 (.f64 (+.f64 (.f64 (+.f64 (.f64 (+.f64 x 216700011257/5000000000) x) 263505074721/1000000000) x) 156699607947/500000000) x) 23533438303/500000000))
	26.9b	(.f64 (.f64 (cbrt.f64 (-.f64 x 2)) (cbrt.f64 (-.f64 x 2))) (*.f64 (cbrt.f64 (-.f64 x 2)) (/.f64 (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))))
	26.5b	(.f64 (.f64 (-.f64 x 2) (/.f64 1 (sqrt.f64 (fma.f64 x (fma.f64 x (fma.f64 x (+.f64 x 216700011257/5000000000) 263505074721/1000000000) 156699607947/500000000) 23533438303/500000000)))) (*.f64 (/.f64 1 (fabs.f64 (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) (sqrt.f64 (cbrt.f64 (fma.f64 x (fma.f64 x (fma.f64 x (+.f64 x 216700011257/5000000000) 263505074721/1000000000) 156699607947/500000000) 23533438303/500000000))))))
	40.5b	(.f64 (-.f64 x 2) (/.f64 (fma.f64 x (.f64 (cbrt.f64 (*.f64 y y)) (cbrt.f64 (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)))
	34.7b	(-.f64 (fma.f64 (.f64 z (pow.f64 x 3)) 3140446455626174059100348970313144550000000/306719603372886620352117082586607327396481 (+.f64 (.f64 168466327098500000000/553822718361107519809 (.f64 x (fma.f64 y x z))) (.f64 (pow.f64 x 3) 106576606695487271009549/2769113591805537599045))) (fma.f64 (.f64 z (.f64 x x)) 23298017199368982832548000000000/13033352773350869092174451844127 (+.f64 (.f64 (.f64 x x) (+.f64 137519416416/23533438303 (.f64 (.f64 y 23298017199368982832548000000000/13033352773350869092174451844127) x))) (*.f64 1000000000/23533438303 (fma.f64 y x z)))))
✓	26.1b	(.f64 (-.f64 x 2) (/.f64 (fma.f64 x (.f64 (*.f64 (cbrt.f64 (fma.f64 x (fma.f64 x (fma.f64 x 104109730557/25000000000 393497462077/5000000000) 4297481763/31250000) y)) (cbrt.f64 (fma.f64 x (fma.f64 x (fma.f64 x 104109730557/25000000000 393497462077/5000000000) 4297481763/31250000) y))) (cbrt.f64 (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)))
✓	26.3b	(.f64 (.f64 (-.f64 x 2) (/.f64 1 (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))))
	31.8b	(-.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))))

Compiler

Compiled 21302 to 14899 computations (30.1% saved)

regimes4.7s (28.7%)

Accuracy

Total 0.8b remaining (75.6%)

Threshold costs 0.8b (75.6%)

Counts

304 → 3

Compiler

Compiled 53283 to 37961 computations (28.8% saved)

bsearch89.0ms (0.5%)

Steps

Iters	Range		Point
8	3.603622604703289e+68	9.714317157730933e+71	5.231744192883358e+71
10	-1.705184863683026e+77	-5.035087549088895e+60	-8.740636302896971e+72

Compiler

Compiled 4 to 3 computations (25% saved)

simplify3.0ms (0%)

Algorithm

1×	egg-herbie

Rules

3×	`+-commutative_binary64`
3×	`*-commutative_binary64`
1×	`sub-neg_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	33	66
1	41	66
2	42	66
3	41	66

end252.0ms (1.5%)

Compiler: Compiled 476 to 327 computations (31.3% saved)

Details

analyze1.4s (8.7%)

sample1.6s (10.1%)

simplify51.0ms (0.3%)

prune4.0ms (0%)

localize25.0ms (0.2%)

series343.0ms (2.1%)

rewrite54.0ms (0.3%)

simplify229.0ms (1.4%)

prune355.0ms (2.2%)

localize20.0ms (0.1%)

series621.0ms (3.8%)

rewrite37.0ms (0.2%)

simplify521.0ms (3.2%)

prune592.0ms (3.6%)

localize54.0ms (0.3%)

series817.0ms (5%)

rewrite32.0ms (0.2%)

simplify517.0ms (3.2%)

prune1.9s (11.8%)

localize47.0ms (0.3%)

series952.0ms (5.9%)

rewrite54.0ms (0.3%)

simplify367.0ms (2.3%)

prune577.0ms (3.5%)

regimes4.7s (28.7%)

bsearch89.0ms (0.5%)

simplify3.0ms (0%)

end252.0ms (1.5%)

Profiling