Details

analyze1.7s (10.1%)

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
0%	99.9%	0.1%	5
0%	99.9%	0.1%	6
6.2%	93.6%	0.1%	7
9.4%	90.5%	0.1%	8
14%	85.8%	0.1%	9
21.1%	78.8%	0.1%	10
24.6%	75.3%	0.1%	11
28.7%	71.2%	0.1%	12
33.4%	66.4%	0.1%	13
47.8%	52.1%	0.1%	14

Compiler

Compiled 41 to 30 computations (26.8% saved)

sample1.5s (8.5%)

Results

1.4s	8256×	body	128	valid
1.0ms	6×	body	128	invalid

Compiler

Compiled 82 to 60 computations (26.8% saved)

preprocess31.0ms (0.2%)

Algorithm

2×	egg-herbie

Rules

803×	`fma-def_binary64`
686×	`distribute-rgt-in_binary64`
682×	`distribute-lft-in_binary64`
346×	`associate-+r+_binary64`
346×	`associate-+l+_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	71	164
1	183	164
2	492	164
3	1779	164
0	3	3

Stop Event

1×	saturated
1×	node limit

Compiler

Compiled 40 to 29 computations (27.5% saved)

simplify541.0ms (3.2%)

Algorithm

1×	egg-herbie

Rules

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

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	30	41
1	64	41
2	157	41
3	531	41
4	1733	41

Stop Event

1×	node limit

Counts

1 → 2

prune12.0ms (0.1%)

Pruning

3 alts after pruning (3 fresh and 0 done)

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

Error

24.6b

Counts

3 → 2

Alt Table

Status	Error	Program
	26.2b	(/.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))
▶	24.7b	(*.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)))

Status

Error

Program

26.2b

(/.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))

▶

24.7b

(*.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)))

Compiler

Compiled 216 to 150 computations (30.6% saved)

localize21.0ms (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)
✓	23.8b	(/.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))

series572.0ms (3.3%)

Counts

4 → 108

Calls

27 calls:

60.0ms	(*.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)))	z	inf
58.0ms	(*.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)))	z	-inf
57.0ms	(*.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)))	y	-inf
56.0ms	(*.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)))	y	inf
45.0ms	(/.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))	z	inf

rewrite56.0ms (0.3%)

Algorithm

1×	batch-egg-rewrite

Rules

247×	`add-sqr-sqrt_binary64`
234×	`log1p-expm1-u_binary64`
234×	`expm1-log1p-u_binary64`
233×	`add-cbrt-cube_binary64`
233×	`add-log-exp_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	23	94
1	500	94

Stop Event

1×	node limit

Counts

4 → 89

simplify180.0ms (1%)

Algorithm

1×	egg-herbie

Rules

445×	`associate--l+_binary64`
303×	`cancel-sign-sub-inv_binary64`
277×	`associate-r_binary64`
253×	`associate-l_binary64`
245×	`fma-def_binary64`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	195	9748
1	596	9708
2	2023	9622

Stop Event

1×	node limit

Counts

197 → 157

prune234.0ms (1.4%)

Pruning

10 alts after pruning (10 fresh and 0 done)

	Pruned	Kept	Total
New	147	10	157
Fresh	1	0	1
Picked	1	0	1
Done	0	0	0
Total	149	10	159

Error

0.2b

Counts

159 → 10

Alt Table

Status	Error	Program
	35.7b	(/.f64 (.f64 (+.f64 (.f64 104109730557/25000000000 (pow.f64 x 4)) (+.f64 z (+.f64 (.f64 4297481763/31250000 (pow.f64 x 2)) (.f64 393497462077/5000000000 (pow.f64 x 3))))) (-.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))))))
	43.2b	(cbrt.f64 (*.f64 (pow.f64 (/.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)) 3) (pow.f64 (+.f64 x -2) 3)))
	32.8b	(-.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)))))
	45.2b	(pow.f64 (sqrt.f64 (/.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))) 2)
	26.8b	(pow.f64 (cbrt.f64 (/.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))) 3)
	26.2b	(pow.f64 (/.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)
	24.8b	(.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) (/.f64 1 (fma.f64 x (fma.f64 x (fma.f64 x (+.f64 x 216700011257/5000000000) 263505074721/1000000000) 156699607947/500000000) 23533438303/500000000))))
▶	23.7b	(.f64 (+.f64 x -2) (+.f64 (+.f64 (/.f64 z (+.f64 (pow.f64 x 4) (+.f64 23533438303/500000000 (fma.f64 (.f64 x x) 263505074721/1000000000 (fma.f64 (pow.f64 x 3) 216700011257/5000000000 (.f64 x 156699607947/500000000)))))) (fma.f64 4297481763/31250000 (/.f64 x (/.f64 (+.f64 (pow.f64 x 4) (+.f64 23533438303/500000000 (fma.f64 (.f64 x x) 263505074721/1000000000 (fma.f64 (pow.f64 x 3) 216700011257/5000000000 (.f64 x 156699607947/500000000))))) x)) (.f64 393497462077/5000000000 (/.f64 (pow.f64 x 3) (+.f64 (pow.f64 x 4) (+.f64 23533438303/500000000 (fma.f64 (.f64 x x) 263505074721/1000000000 (fma.f64 (pow.f64 x 3) 216700011257/5000000000 (.f64 x 156699607947/500000000))))))))) (fma.f64 104109730557/25000000000 (/.f64 (pow.f64 x 4) (+.f64 (pow.f64 x 4) (+.f64 23533438303/500000000 (fma.f64 (.f64 x x) 263505074721/1000000000 (fma.f64 (pow.f64 x 3) 216700011257/5000000000 (.f64 x 156699607947/500000000)))))) (/.f64 y (/.f64 (+.f64 (pow.f64 x 4) (+.f64 23533438303/500000000 (fma.f64 (.f64 x x) 263505074721/1000000000 (fma.f64 (pow.f64 x 3) 216700011257/5000000000 (.f64 x 156699607947/500000000))))) x)))))
	24.8b	(/.f64 (.f64 1 (fma.f64 x x -4)) (.f64 (/.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 x -2)))
	32.8b	(*.f64 (+.f64 x -2) (+.f64 (+.f64 (/.f64 (/.f64 2157218858562374472887084159837293/625000000000000000000000000000 x) x) (/.f64 y (pow.f64 x 3))) (-.f64 104109730557/25000000000 (+.f64 (/.f64 12723143231740136880149/125000000000000000000 x) (/.f64 387732519225574910908939577061312055388407301/3125000000000000000000000000000000000000 (pow.f64 x 3))))))

Compiler

Compiled 6789 to 4683 computations (31% saved)

localize29.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	6.3b	(fma.f64 (.f64 x x) 263505074721/1000000000 (fma.f64 (pow.f64 x 3) 216700011257/5000000000 (.f64 x 156699607947/500000000)))
✓	8.0b	(+.f64 (pow.f64 x 4) (+.f64 23533438303/500000000 (fma.f64 (.f64 x x) 263505074721/1000000000 (fma.f64 (pow.f64 x 3) 216700011257/5000000000 (.f64 x 156699607947/500000000)))))
✓	22.8b	(/.f64 (pow.f64 x 4) (+.f64 (pow.f64 x 4) (+.f64 23533438303/500000000 (fma.f64 (.f64 x x) 263505074721/1000000000 (fma.f64 (pow.f64 x 3) 216700011257/5000000000 (.f64 x 156699607947/500000000))))))
✓	23.1b	(/.f64 (pow.f64 x 3) (+.f64 (pow.f64 x 4) (+.f64 23533438303/500000000 (fma.f64 (.f64 x x) 263505074721/1000000000 (fma.f64 (pow.f64 x 3) 216700011257/5000000000 (.f64 x 156699607947/500000000))))))

series16.0ms (0.1%)

Counts

4 → 48

Calls

12 calls:

5.0ms	(/.f64 (pow.f64 x 3) (+.f64 (pow.f64 x 4) (+.f64 23533438303/500000000 (fma.f64 (.f64 x x) 263505074721/1000000000 (fma.f64 (pow.f64 x 3) 216700011257/5000000000 (.f64 x 156699607947/500000000))))))	x	inf
1.0ms	(/.f64 (pow.f64 x 3) (+.f64 (pow.f64 x 4) (+.f64 23533438303/500000000 (fma.f64 (.f64 x x) 263505074721/1000000000 (fma.f64 (pow.f64 x 3) 216700011257/5000000000 (.f64 x 156699607947/500000000))))))	x	0
1.0ms	(/.f64 (pow.f64 x 3) (+.f64 (pow.f64 x 4) (+.f64 23533438303/500000000 (fma.f64 (.f64 x x) 263505074721/1000000000 (fma.f64 (pow.f64 x 3) 216700011257/5000000000 (.f64 x 156699607947/500000000))))))	x	-inf
1.0ms	(/.f64 (pow.f64 x 4) (+.f64 (pow.f64 x 4) (+.f64 23533438303/500000000 (fma.f64 (.f64 x x) 263505074721/1000000000 (fma.f64 (pow.f64 x 3) 216700011257/5000000000 (.f64 x 156699607947/500000000))))))	x	0
1.0ms	(fma.f64 (.f64 x x) 263505074721/1000000000 (fma.f64 (pow.f64 x 3) 216700011257/5000000000 (.f64 x 156699607947/500000000)))	x	-inf

rewrite64.0ms (0.4%)

Algorithm

1×	batch-egg-rewrite

Rules

186×	`add-sqr-sqrt_binary64`
186×	`log1p-expm1-u_binary64`
186×	`expm1-log1p-u_binary64`
183×	`add-cbrt-cube_binary64`
179×	`add-cube-cbrt_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	18	111
1	405	111

Stop Event

1×	node limit

Counts

4 → 135

simplify42.0ms (0.2%)

Algorithm

1×	egg-herbie

Rules

474×	`cancel-sign-sub-inv_binary64`
441×	`fma-neg_binary64`
288×	`fma-def_binary64`
259×	`*-commutative_binary64`
177×	`associate-/r*_binary64`

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	78	720
1	227	706
2	626	678
3	2020	667

Stop Event

1×	node limit

Counts

183 → 188

prune1.9s (10.8%)

Pruning

10 alts after pruning (9 fresh and 1 done)

	Pruned	Kept	Total
New	532	0	532
Fresh	0	9	9
Picked	0	1	1
Done	0	0	0
Total	532	10	542

Error

0.2b

Counts

542 → 10

Alt Table

Status	Error	Program
	35.7b	(/.f64 (.f64 (+.f64 (.f64 104109730557/25000000000 (pow.f64 x 4)) (+.f64 z (+.f64 (.f64 4297481763/31250000 (pow.f64 x 2)) (.f64 393497462077/5000000000 (pow.f64 x 3))))) (-.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))))))
	43.2b	(cbrt.f64 (*.f64 (pow.f64 (/.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)) 3) (pow.f64 (+.f64 x -2) 3)))
	32.8b	(-.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)))))
	45.2b	(pow.f64 (sqrt.f64 (/.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))) 2)
	26.8b	(pow.f64 (cbrt.f64 (/.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))) 3)
	26.2b	(pow.f64 (/.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)
	24.8b	(.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) (/.f64 1 (fma.f64 x (fma.f64 x (fma.f64 x (+.f64 x 216700011257/5000000000) 263505074721/1000000000) 156699607947/500000000) 23533438303/500000000))))
✓	23.7b	(.f64 (+.f64 x -2) (+.f64 (+.f64 (/.f64 z (+.f64 (pow.f64 x 4) (+.f64 23533438303/500000000 (fma.f64 (.f64 x x) 263505074721/1000000000 (fma.f64 (pow.f64 x 3) 216700011257/5000000000 (.f64 x 156699607947/500000000)))))) (fma.f64 4297481763/31250000 (/.f64 x (/.f64 (+.f64 (pow.f64 x 4) (+.f64 23533438303/500000000 (fma.f64 (.f64 x x) 263505074721/1000000000 (fma.f64 (pow.f64 x 3) 216700011257/5000000000 (.f64 x 156699607947/500000000))))) x)) (.f64 393497462077/5000000000 (/.f64 (pow.f64 x 3) (+.f64 (pow.f64 x 4) (+.f64 23533438303/500000000 (fma.f64 (.f64 x x) 263505074721/1000000000 (fma.f64 (pow.f64 x 3) 216700011257/5000000000 (.f64 x 156699607947/500000000))))))))) (fma.f64 104109730557/25000000000 (/.f64 (pow.f64 x 4) (+.f64 (pow.f64 x 4) (+.f64 23533438303/500000000 (fma.f64 (.f64 x x) 263505074721/1000000000 (fma.f64 (pow.f64 x 3) 216700011257/5000000000 (.f64 x 156699607947/500000000)))))) (/.f64 y (/.f64 (+.f64 (pow.f64 x 4) (+.f64 23533438303/500000000 (fma.f64 (.f64 x x) 263505074721/1000000000 (fma.f64 (pow.f64 x 3) 216700011257/5000000000 (.f64 x 156699607947/500000000))))) x)))))
▶	24.8b	(/.f64 (.f64 1 (fma.f64 x x -4)) (.f64 (/.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 x -2)))
	32.8b	(*.f64 (+.f64 x -2) (+.f64 (+.f64 (/.f64 (/.f64 2157218858562374472887084159837293/625000000000000000000000000000 x) x) (/.f64 y (pow.f64 x 3))) (-.f64 104109730557/25000000000 (+.f64 (/.f64 12723143231740136880149/125000000000000000000 x) (/.f64 387732519225574910908939577061312055388407301/3125000000000000000000000000000000000000 (pow.f64 x 3))))))

Compiler

Compiled 70815 to 49803 computations (29.7% saved)

localize25.0ms (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	(fma.f64 x 104109730557/25000000000 393497462077/5000000000)
✓	12.9b	(/.f64 (.f64 1 (fma.f64 x x -4)) (.f64 (/.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 x -2)))
✓	23.8b	(/.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))

series728.0ms (4.2%)

Counts

2 → 72

Calls

18 calls:

74.0ms	(/.f64 (.f64 1 (fma.f64 x x -4)) (.f64 (/.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 x -2)))	z	inf
70.0ms	(/.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))	z	-inf
69.0ms	(/.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))	z	inf
69.0ms	(/.f64 (.f64 1 (fma.f64 x x -4)) (.f64 (/.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 x -2)))	z	-inf
69.0ms	(/.f64 (.f64 1 (fma.f64 x x -4)) (.f64 (/.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 x -2)))	y	-inf

rewrite46.0ms (0.3%)

Algorithm

1×	batch-egg-rewrite

Rules

273×	`log1p-expm1-u_binary64`
273×	`expm1-log1p-u_binary64`
272×	`add-cbrt-cube_binary64`
271×	`add-log-exp_binary64`
270×	`add-cube-cbrt_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	28	83
1	609	83

Stop Event

1×	node limit

Counts

2 → 37

simplify262.0ms (1.5%)

Algorithm

1×	egg-herbie

Rules

742×	`associate-/l*_binary64`
362×	`+-commutative_binary64`
323×	`associate-+r+_binary64`
323×	`fma-def_binary64`
253×	`*-commutative_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	969	19077
1	3408	19063

Stop Event

1×	node limit

Counts

109 → 109

prune386.0ms (2.2%)

Pruning

8 alts after pruning (6 fresh and 2 done)

	Pruned	Kept	Total
New	159	3	162
Fresh	5	3	8
Picked	0	1	1
Done	0	1	1
Total	164	8	172

Error

0.2b

Counts

172 → 8

Alt Table

Status	Error	Program
	32.8b	(*.f64 (+.f64 x -2) (+.f64 (+.f64 (/.f64 (/.f64 2157218858562374472887084159837293/625000000000000000000000000000 x) x) (/.f64 y (pow.f64 x 3))) (-.f64 104109730557/25000000000 (+.f64 (/.f64 12723143231740136880149/125000000000000000000 x) (/.f64 387732519225574910908939577061312055388407301/3125000000000000000000000000000000000000 (pow.f64 x 3))))))
	48.4b	(/.f64 (.f64 1 (fma.f64 x x -4)) (.f64 (+.f64 25000000000/104109730557 (/.f64 63615716158700684400745/10838835996651139530249 x)) (-.f64 x -2)))
	35.7b	(/.f64 (.f64 (+.f64 (.f64 104109730557/25000000000 (pow.f64 x 4)) (+.f64 z (+.f64 (.f64 4297481763/31250000 (pow.f64 x 2)) (.f64 393497462077/5000000000 (pow.f64 x 3))))) (-.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))))))
	32.8b	(-.f64 (+.f64 (+.f64 (.f64 x 104109730557/25000000000) (/.f64 2284450290879775841688574159837293/625000000000000000000000000000 x)) (/.f64 y (.f64 x x))) (+.f64 13764240537310136880149/125000000000000000000 (/.f64 409304707811198655637810418659684985388407301/3125000000000000000000000000000000000000 (*.f64 x x))))
	25.3b	(pow.f64 (cbrt.f64 (/.f64 (fma.f64 x x -4) (*.f64 (/.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 x 2)))) 3)
▶	24.8b	(.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) (/.f64 1 (fma.f64 x (fma.f64 x (fma.f64 x (+.f64 x 216700011257/5000000000) 263505074721/1000000000) 156699607947/500000000) 23533438303/500000000))))
✓	23.7b	(.f64 (+.f64 x -2) (+.f64 (+.f64 (/.f64 z (+.f64 (pow.f64 x 4) (+.f64 23533438303/500000000 (fma.f64 (.f64 x x) 263505074721/1000000000 (fma.f64 (pow.f64 x 3) 216700011257/5000000000 (.f64 x 156699607947/500000000)))))) (fma.f64 4297481763/31250000 (/.f64 x (/.f64 (+.f64 (pow.f64 x 4) (+.f64 23533438303/500000000 (fma.f64 (.f64 x x) 263505074721/1000000000 (fma.f64 (pow.f64 x 3) 216700011257/5000000000 (.f64 x 156699607947/500000000))))) x)) (.f64 393497462077/5000000000 (/.f64 (pow.f64 x 3) (+.f64 (pow.f64 x 4) (+.f64 23533438303/500000000 (fma.f64 (.f64 x x) 263505074721/1000000000 (fma.f64 (pow.f64 x 3) 216700011257/5000000000 (.f64 x 156699607947/500000000))))))))) (fma.f64 104109730557/25000000000 (/.f64 (pow.f64 x 4) (+.f64 (pow.f64 x 4) (+.f64 23533438303/500000000 (fma.f64 (.f64 x x) 263505074721/1000000000 (fma.f64 (pow.f64 x 3) 216700011257/5000000000 (.f64 x 156699607947/500000000)))))) (/.f64 y (/.f64 (+.f64 (pow.f64 x 4) (+.f64 23533438303/500000000 (fma.f64 (.f64 x x) 263505074721/1000000000 (fma.f64 (pow.f64 x 3) 216700011257/5000000000 (.f64 x 156699607947/500000000))))) x)))))
✓	24.8b	(/.f64 (.f64 1 (fma.f64 x x -4)) (.f64 (/.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 x -2)))

Compiler

Compiled 17750 to 12332 computations (30.5% saved)

localize20.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	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) (/.f64 1 (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)
✓	0.4b	(/.f64 1 (fma.f64 x (fma.f64 x (fma.f64 x (+.f64 x 216700011257/5000000000) 263505074721/1000000000) 156699607947/500000000) 23533438303/500000000))
✓	24.0b	(*.f64 (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)))

series534.0ms (3.1%)

Counts

3 → 84

Calls

21 calls:

57.0ms	(.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) (/.f64 1 (fma.f64 x (fma.f64 x (fma.f64 x (+.f64 x 216700011257/5000000000) 263505074721/1000000000) 156699607947/500000000) 23533438303/500000000))))	z	-inf
54.0ms	(.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) (/.f64 1 (fma.f64 x (fma.f64 x (fma.f64 x (+.f64 x 216700011257/5000000000) 263505074721/1000000000) 156699607947/500000000) 23533438303/500000000))))	y	-inf
53.0ms	(.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) (/.f64 1 (fma.f64 x (fma.f64 x (fma.f64 x (+.f64 x 216700011257/5000000000) 263505074721/1000000000) 156699607947/500000000) 23533438303/500000000))))	z	inf
52.0ms	(.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) (/.f64 1 (fma.f64 x (fma.f64 x (fma.f64 x (+.f64 x 216700011257/5000000000) 263505074721/1000000000) 156699607947/500000000) 23533438303/500000000))))	y	inf
43.0ms	(*.f64 (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)))	y	-inf

rewrite48.0ms (0.3%)

Algorithm

1×	batch-egg-rewrite

Rules

261×	`add-sqr-sqrt_binary64`
246×	`add-cbrt-cube_binary64`
246×	`log1p-expm1-u_binary64`
246×	`expm1-log1p-u_binary64`
245×	`add-log-exp_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	25	95
1	536	95

Stop Event

1×	node limit

Counts

3 → 51

simplify182.0ms (1.1%)

Algorithm

1×	egg-herbie

Rules

355×	`cancel-sign-sub-inv_binary64`
276×	`associate-r_binary64`
268×	`associate-l_binary64`
238×	`fma-def_binary64`
187×	`fma-neg_binary64`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	208	9515
1	640	9491
2	2171	9447

Stop Event

1×	node limit

Counts

135 → 116

prune153.0ms (0.9%)

Pruning

8 alts after pruning (5 fresh and 3 done)

	Pruned	Kept	Total
New	136	2	138
Fresh	2	3	5
Picked	0	1	1
Done	0	2	2
Total	138	8	146

Error

0.2b

Counts

146 → 8

Alt Table

Status	Error	Program
	32.8b	(*.f64 (+.f64 x -2) (+.f64 (+.f64 (/.f64 (/.f64 2157218858562374472887084159837293/625000000000000000000000000000 x) x) (/.f64 y (pow.f64 x 3))) (-.f64 104109730557/25000000000 (+.f64 (/.f64 12723143231740136880149/125000000000000000000 x) (/.f64 387732519225574910908939577061312055388407301/3125000000000000000000000000000000000000 (pow.f64 x 3))))))
	48.4b	(/.f64 (.f64 1 (fma.f64 x x -4)) (.f64 (+.f64 25000000000/104109730557 (/.f64 63615716158700684400745/10838835996651139530249 x)) (-.f64 x -2)))
	35.7b	(/.f64 (.f64 (+.f64 (.f64 104109730557/25000000000 (pow.f64 x 4)) (+.f64 z (+.f64 (.f64 4297481763/31250000 (pow.f64 x 2)) (.f64 393497462077/5000000000 (pow.f64 x 3))))) (-.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))))))
	34.2b	(/.f64 (+.f64 z (fma.f64 104109730557/25000000000 (pow.f64 x 4) (.f64 (.f64 x x) (+.f64 4297481763/31250000 (.f64 393497462077/5000000000 x))))) (/.f64 (+.f64 (pow.f64 x 4) (+.f64 23533438303/500000000 (fma.f64 (.f64 x x) 263505074721/1000000000 (fma.f64 (pow.f64 x 3) 216700011257/5000000000 (*.f64 x 156699607947/500000000))))) (-.f64 x 2)))
	32.8b	(+.f64 (fma.f64 x 104109730557/25000000000 (/.f64 2284450290879775841688574159837293/625000000000000000000000000000 x)) (-.f64 (/.f64 y (.f64 x x)) (+.f64 13764240537310136880149/125000000000000000000 (/.f64 409304707811198655637810418659684985388407301/3125000000000000000000000000000000000000 (.f64 x x)))))
✓	24.8b	(.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) (/.f64 1 (fma.f64 x (fma.f64 x (fma.f64 x (+.f64 x 216700011257/5000000000) 263505074721/1000000000) 156699607947/500000000) 23533438303/500000000))))
✓	23.7b	(.f64 (+.f64 x -2) (+.f64 (+.f64 (/.f64 z (+.f64 (pow.f64 x 4) (+.f64 23533438303/500000000 (fma.f64 (.f64 x x) 263505074721/1000000000 (fma.f64 (pow.f64 x 3) 216700011257/5000000000 (.f64 x 156699607947/500000000)))))) (fma.f64 4297481763/31250000 (/.f64 x (/.f64 (+.f64 (pow.f64 x 4) (+.f64 23533438303/500000000 (fma.f64 (.f64 x x) 263505074721/1000000000 (fma.f64 (pow.f64 x 3) 216700011257/5000000000 (.f64 x 156699607947/500000000))))) x)) (.f64 393497462077/5000000000 (/.f64 (pow.f64 x 3) (+.f64 (pow.f64 x 4) (+.f64 23533438303/500000000 (fma.f64 (.f64 x x) 263505074721/1000000000 (fma.f64 (pow.f64 x 3) 216700011257/5000000000 (.f64 x 156699607947/500000000))))))))) (fma.f64 104109730557/25000000000 (/.f64 (pow.f64 x 4) (+.f64 (pow.f64 x 4) (+.f64 23533438303/500000000 (fma.f64 (.f64 x x) 263505074721/1000000000 (fma.f64 (pow.f64 x 3) 216700011257/5000000000 (.f64 x 156699607947/500000000)))))) (/.f64 y (/.f64 (+.f64 (pow.f64 x 4) (+.f64 23533438303/500000000 (fma.f64 (.f64 x x) 263505074721/1000000000 (fma.f64 (pow.f64 x 3) 216700011257/5000000000 (.f64 x 156699607947/500000000))))) x)))))
✓	24.8b	(/.f64 (.f64 1 (fma.f64 x x -4)) (.f64 (/.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 x -2)))

Compiler

Compiled 5424 to 3789 computations (30.1% saved)

regimes7.4s (43.3%)

Accuracy

Total 0.6b remaining (75.9%)

Threshold costs 0.6b (75.9%)

Counts

343 → 3

Compiler

Compiled 92016 to 65948 computations (28.3% saved)

bsearch83.0ms (0.5%)

Algorithm

2×	binary-search

Calls

2 calls:

35.0ms	x
15.0ms	x

Steps

Iters	Point		Range
1.0463787894136359e+46	∈ [	1.2810868028843165e+39	,	1.059186613521135e+46	]
-7.441593577102361e+43	∈ [	-7.56646453431466e+43	,	-4.0153714716135897e+43	]

Compiler

Compiled 4 to 3 computations (25% saved)

simplify16.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

19×	`+-commutative_binary64`
11×	`*-commutative_binary64`
9×	`sub-neg_binary64`
6×	`neg-sub0_binary64`
6×	`neg-mul-1_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	73	366
1	94	366
2	114	366
3	138	366
4	147	366
5	150	366

Stop Event

1×

saturated

end388.0ms (2.3%)

Stop Event

1×

fuel

Compiler

Compiled 876 to 619 computations (29.3% saved)

Details

analyze1.7s (10.1%)

sample1.5s (8.5%)

preprocess31.0ms (0.2%)

simplify541.0ms (3.2%)

prune12.0ms (0.1%)

localize21.0ms (0.1%)

series572.0ms (3.3%)

rewrite56.0ms (0.3%)

simplify180.0ms (1%)

prune234.0ms (1.4%)

localize29.0ms (0.2%)

series16.0ms (0.1%)

rewrite64.0ms (0.4%)

simplify42.0ms (0.2%)

prune1.9s (10.8%)

localize25.0ms (0.1%)

series728.0ms (4.2%)

rewrite46.0ms (0.3%)

simplify262.0ms (1.5%)

prune386.0ms (2.2%)

localize20.0ms (0.1%)

series534.0ms (3.1%)

rewrite48.0ms (0.3%)

simplify182.0ms (1.1%)

prune153.0ms (0.9%)

regimes7.4s (43.3%)

bsearch83.0ms (0.5%)

simplify16.0ms (0.1%)

end388.0ms (2.3%)

Profiling