Details

analyze2.7s (21.5%)

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
0%	99.9%	0.1%	7
0%	99.9%	0.1%	8
0%	99.9%	0.1%	9
0%	99.9%	0.1%	10
0%	99.9%	0.1%	11
0%	99.9%	0.1%	12
0%	99.9%	0.1%	13
0%	99.9%	0.1%	14

Compiler

Compiled 41 to 30 computations (26.8% saved)

sample1.6s (12.6%)

Results

1.5s	8256×	body	128	valid
5.0ms	5×	body	8192	exit
1.0ms	4×	body	128	invalid

Compiler

Compiled 81 to 59 computations (27.2% saved)

simplify51.0ms (0.4%)

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

prune5.0ms (0%)

Pruning

3 alts after pruning (3 fresh and 0 done)

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

Error

26.9b

Counts

3 → 2

Alt Table

Status	Error	Program
	26.9b	(/.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))
▶	26.9b	(/.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

26.9b

(/.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))

▶

26.9b

(/.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 216 to 150 computations (30.6% saved)

localize26.0ms (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)
✓	26.0b	(/.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))

series423.0ms (3.4%)

Counts

4 → 72

Calls

4 calls:

414.0ms	(/.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))
4.0ms	(.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)

rewrite51.0ms (0.4%)

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))
7.0ms	(.f64 (+.f64 (.f64 (+.f64 (*.f64 x 104109730557/25000000000) 393497462077/5000000000) x) 4297481763/31250000) x)
7.0ms	(.f64 (+.f64 (.f64 (+.f64 x 216700011257/5000000000) x) 263505074721/1000000000) x)
3.0ms	(*.f64 x 104109730557/25000000000)

simplify227.0ms (1.8%)

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

prune477.0ms (3.8%)

Pruning

11 alts after pruning (11 fresh and 0 done)

	Pruned	Kept	Total
New	190	11	201
Fresh	1	0	1
Picked	1	0	1
Done	0	0	0
Total	192	11	203

Error

0.2b

Counts

203 → 11

Alt Table

Status	Error	Program
	47.6b	(cbrt.f64 (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)) 3))
	45.3b	(/.f64 (.f64 (-.f64 x 2) (+.f64 (.f64 (+.f64 (.f64 (.f64 (fma.f64 x (fma.f64 x 104109730557/25000000000 393497462077/5000000000) 4297481763/31250000) (sqrt.f64 x)) (sqrt.f64 x)) y) x) z)) (+.f64 (.f64 (+.f64 (.f64 (+.f64 (*.f64 (+.f64 x 216700011257/5000000000) x) 263505074721/1000000000) x) 156699607947/500000000) x) 23533438303/500000000))
	25.3b	(/.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)))
▶	24.9b	(.f64 (/.f64 (-.f64 x 2) 1) (/.f64 (+.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)))
	26.9b	(/.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 216700011257/5000000000 (pow.f64 x 2)) (+.f64 (pow.f64 x 3) (.f64 263505074721/1000000000 x))) 156699607947/500000000) x) 23533438303/500000000))
	32.6b	(-.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)))))
	35.8b	(/.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))))))
	34.0b	(-.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))))
	27.6b	(/.f64 (/.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 (cbrt.f64 (+.f64 (.f64 (+.f64 (.f64 (+.f64 (.f64 (+.f64 x 216700011257/5000000000) x) 263505074721/1000000000) x) 156699607947/500000000) x) 23533438303/500000000)) (cbrt.f64 (+.f64 (.f64 (+.f64 (.f64 (+.f64 (.f64 (+.f64 x 216700011257/5000000000) x) 263505074721/1000000000) x) 156699607947/500000000) x) 23533438303/500000000)))) (cbrt.f64 (+.f64 (.f64 (+.f64 (.f64 (+.f64 (*.f64 (+.f64 x 216700011257/5000000000) x) 263505074721/1000000000) x) 156699607947/500000000) x) 23533438303/500000000)))
	30.0b	(/.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 (expm1.f64 (log1p.f64 (*.f64 x (fma.f64 x (+.f64 x 216700011257/5000000000) 263505074721/1000000000)))) 156699607947/500000000) x) 23533438303/500000000))
	26.9b	(/.f64 (.f64 (-.f64 x 2) (+.f64 (.f64 (+.f64 (.f64 (+.f64 (.f64 (+.f64 (.f64 (.f64 x (sqrt.f64 104109730557/25000000000)) (sqrt.f64 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 10762 to 7583 computations (29.5% 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)
✓	24.1b	(/.f64 (+.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))

series337.0ms (2.7%)

Counts

1 → 36

Calls

1 calls:

337.0ms

(/.f64 (+.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))

rewrite27.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

9×	`*-un-lft-identity_binary64`
9×	`times-frac_binary64`
9×	`add-sqr-sqrt_binary64`
9×	`add-cube-cbrt_binary64`
3×	`associate-/r*_binary64`

Counts

1 → 33

Calls

1 calls:

24.0ms

(/.f64 (+.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))

simplify156.0ms (1.2%)

Algorithm

1×	egg-herbie

Rules

857×	`fma-def_binary64`
453×	`distribute-rgt-in_binary64`
435×	`distribute-lft-in_binary64`
410×	`associate-l_binary64`
189×	`cancel-sign-sub-inv_binary64`

Counts

69 → 84

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	181	5445
1	503	5295
2	1587	5093
3	4559	5093
4	4965	5093

prune335.0ms (2.7%)

Pruning

9 alts after pruning (9 fresh and 0 done)

	Pruned	Kept	Total
New	194	5	199
Fresh	6	4	10
Picked	1	0	1
Done	0	0	0
Total	201	9	210

Error

0.2b

Counts

210 → 9

Alt Table

Status	Error	Program
	27.6b	(/.f64 (/.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 (cbrt.f64 (+.f64 (.f64 (+.f64 (.f64 (+.f64 (.f64 (+.f64 x 216700011257/5000000000) x) 263505074721/1000000000) x) 156699607947/500000000) x) 23533438303/500000000)) (cbrt.f64 (+.f64 (.f64 (+.f64 (.f64 (+.f64 (.f64 (+.f64 x 216700011257/5000000000) x) 263505074721/1000000000) x) 156699607947/500000000) x) 23533438303/500000000)))) (cbrt.f64 (+.f64 (.f64 (+.f64 (.f64 (+.f64 (*.f64 (+.f64 x 216700011257/5000000000) x) 263505074721/1000000000) x) 156699607947/500000000) x) 23533438303/500000000)))
	45.6b	(*.f64 (/.f64 (-.f64 x 2) 1) (cbrt.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)))
	30.0b	(/.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 (expm1.f64 (log1p.f64 (*.f64 x (fma.f64 x (+.f64 x 216700011257/5000000000) 263505074721/1000000000)))) 156699607947/500000000) x) 23533438303/500000000))
▶	24.9b	(.f64 (/.f64 (-.f64 x 2) 1) (/.f64 (+.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 216700011257/5000000000 (pow.f64 x 2)) (+.f64 (.f64 263505074721/1000000000 x) (pow.f64 x 3))) 156699607947/500000000) x) 23533438303/500000000)))
	25.0b	(.f64 (/.f64 (-.f64 x 2) 1) (/.f64 (+.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 (cbrt.f64 (+.f64 (.f64 (+.f64 x 216700011257/5000000000) x) 263505074721/1000000000)) (cbrt.f64 (+.f64 (.f64 (+.f64 x 216700011257/5000000000) x) 263505074721/1000000000))) (*.f64 x (cbrt.f64 (fma.f64 x (+.f64 x 216700011257/5000000000) 263505074721/1000000000)))) 156699607947/500000000) x) 23533438303/500000000)))
	34.0b	(-.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))))
	25.7b	(.f64 (/.f64 (-.f64 x 2) 1) (.f64 (/.f64 (.f64 (cbrt.f64 (fma.f64 x (fma.f64 x (fma.f64 x (fma.f64 x 104109730557/25000000000 393497462077/5000000000) 4297481763/31250000) y) z)) (cbrt.f64 (fma.f64 x (fma.f64 x (fma.f64 x (fma.f64 x 104109730557/25000000000 393497462077/5000000000) 4297481763/31250000) y) z))) (.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 (cbrt.f64 (fma.f64 x (fma.f64 x (fma.f64 x (fma.f64 x 104109730557/25000000000 393497462077/5000000000) 4297481763/31250000) y) z)) (cbrt.f64 (fma.f64 x (fma.f64 x (fma.f64 x (+.f64 x 216700011257/5000000000) 263505074721/1000000000) 156699607947/500000000) 23533438303/500000000)))))
	32.6b	(-.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)))))
	44.6b	(.f64 (/.f64 (-.f64 x 2) 1) (/.f64 (+.f64 (.f64 (+.f64 (.f64 (.f64 (fma.f64 x (fma.f64 x 104109730557/25000000000 393497462077/5000000000) 4297481763/31250000) (sqrt.f64 x)) (sqrt.f64 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 10787 to 7701 computations (28.6% saved)

localize28.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.6b	(*.f64 x 104109730557/25000000000)
✓	0.7b	(*.f64 263505074721/1000000000 x)
✓	7.3b	(+.f64 (.f64 216700011257/5000000000 (pow.f64 x 2)) (+.f64 (.f64 263505074721/1000000000 x) (pow.f64 x 3)))
✓	24.1b	(/.f64 (+.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 216700011257/5000000000 (pow.f64 x 2)) (+.f64 (*.f64 263505074721/1000000000 x) (pow.f64 x 3))) 156699607947/500000000) x) 23533438303/500000000))

series343.0ms (2.7%)

Counts

3 → 44

Calls

3 calls:

337.0ms

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

4.0ms

(+.f64 (*.f64 216700011257/5000000000 (pow.f64 x 2)) (+.f64 (*.f64 263505074721/1000000000 x) (pow.f64 x 3)))

1.0ms

(*.f64 263505074721/1000000000 x)

rewrite41.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

15×	`add-sqr-sqrt_binary64`
13×	`*-un-lft-identity_binary64`
13×	`add-cube-cbrt_binary64`
9×	`times-frac_binary64`
8×	`add-log-exp_binary64`

Counts

3 → 69

Calls

3 calls:

24.0ms

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

7.0ms

(+.f64 (*.f64 216700011257/5000000000 (pow.f64 x 2)) (+.f64 (*.f64 263505074721/1000000000 x) (pow.f64 x 3)))

3.0ms

(*.f64 263505074721/1000000000 x)

simplify231.0ms (1.8%)

Algorithm

1×	egg-herbie

Rules

949×	`distribute-rgt-in_binary64`
329×	`fma-neg_binary64`
295×	`cancel-sign-sub-inv_binary64`
197×	`fma-def_binary64`
128×	`associate-l_binary64`

Counts

113 → 147

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	240	6302
1	663	6079
2	2176	6048
3	4835	6046
4	4972	6046

prune350.0ms (2.8%)

Pruning

9 alts after pruning (8 fresh and 1 done)

	Pruned	Kept	Total
New	166	1	167
Fresh	1	7	8
Picked	0	1	1
Done	0	0	0
Total	167	9	176

Error

0.2b

Counts

176 → 9

Alt Table

Status	Error	Program
	27.6b	(/.f64 (/.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 (cbrt.f64 (+.f64 (.f64 (+.f64 (.f64 (+.f64 (.f64 (+.f64 x 216700011257/5000000000) x) 263505074721/1000000000) x) 156699607947/500000000) x) 23533438303/500000000)) (cbrt.f64 (+.f64 (.f64 (+.f64 (.f64 (+.f64 (.f64 (+.f64 x 216700011257/5000000000) x) 263505074721/1000000000) x) 156699607947/500000000) x) 23533438303/500000000)))) (cbrt.f64 (+.f64 (.f64 (+.f64 (.f64 (+.f64 (*.f64 (+.f64 x 216700011257/5000000000) x) 263505074721/1000000000) x) 156699607947/500000000) x) 23533438303/500000000)))
	45.6b	(.f64 (/.f64 (-.f64 x 2) 1) (cbrt.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 (+.f64 156699607947/500000000 (fma.f64 (.f64 x x) 216700011257/5000000000 (fma.f64 x 263505074721/1000000000 (pow.f64 x 3)))) 23533438303/500000000)) 3)))
	30.0b	(/.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 (expm1.f64 (log1p.f64 (*.f64 x (fma.f64 x (+.f64 x 216700011257/5000000000) 263505074721/1000000000)))) 156699607947/500000000) x) 23533438303/500000000))
✓	24.9b	(.f64 (/.f64 (-.f64 x 2) 1) (/.f64 (+.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 216700011257/5000000000 (pow.f64 x 2)) (+.f64 (.f64 263505074721/1000000000 x) (pow.f64 x 3))) 156699607947/500000000) x) 23533438303/500000000)))
▶	25.0b	(.f64 (/.f64 (-.f64 x 2) 1) (/.f64 (+.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 (cbrt.f64 (+.f64 (.f64 (+.f64 x 216700011257/5000000000) x) 263505074721/1000000000)) (cbrt.f64 (+.f64 (.f64 (+.f64 x 216700011257/5000000000) x) 263505074721/1000000000))) (*.f64 x (cbrt.f64 (fma.f64 x (+.f64 x 216700011257/5000000000) 263505074721/1000000000)))) 156699607947/500000000) x) 23533438303/500000000)))
	34.0b	(-.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))))
	25.7b	(.f64 (/.f64 (-.f64 x 2) 1) (.f64 (/.f64 (.f64 (cbrt.f64 (fma.f64 x (fma.f64 x (fma.f64 x (fma.f64 x 104109730557/25000000000 393497462077/5000000000) 4297481763/31250000) y) z)) (cbrt.f64 (fma.f64 x (fma.f64 x (fma.f64 x (fma.f64 x 104109730557/25000000000 393497462077/5000000000) 4297481763/31250000) y) z))) (.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 (cbrt.f64 (fma.f64 x (fma.f64 x (fma.f64 x (fma.f64 x 104109730557/25000000000 393497462077/5000000000) 4297481763/31250000) y) z)) (cbrt.f64 (fma.f64 x (fma.f64 x (fma.f64 x (+.f64 x 216700011257/5000000000) 263505074721/1000000000) 156699607947/500000000) 23533438303/500000000)))))
	32.6b	(-.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)))))
	44.6b	(.f64 (/.f64 (-.f64 x 2) 1) (/.f64 (+.f64 (.f64 (+.f64 (.f64 (.f64 (fma.f64 x (fma.f64 x 104109730557/25000000000 393497462077/5000000000) 4297481763/31250000) (sqrt.f64 x)) (sqrt.f64 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 9955 to 7223 computations (27.4% saved)

localize90.0ms (0.7%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.6b	(*.f64 x 104109730557/25000000000)
✓	15.2b	(cbrt.f64 (+.f64 (*.f64 (+.f64 x 216700011257/5000000000) x) 263505074721/1000000000))
✓	15.2b	(cbrt.f64 (fma.f64 x (+.f64 x 216700011257/5000000000) 263505074721/1000000000))
✓	24.1b	(/.f64 (+.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 (cbrt.f64 (+.f64 (.f64 (+.f64 x 216700011257/5000000000) x) 263505074721/1000000000)) (cbrt.f64 (+.f64 (.f64 (+.f64 x 216700011257/5000000000) x) 263505074721/1000000000))) (.f64 x (cbrt.f64 (fma.f64 x (+.f64 x 216700011257/5000000000) 263505074721/1000000000)))) 156699607947/500000000) x) 23533438303/500000000))

series787.0ms (6.3%)

Counts

3 → 60

Calls

3 calls:

769.0ms

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

11.0ms

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

6.0ms

(cbrt.f64 (+.f64 (*.f64 (+.f64 x 216700011257/5000000000) x) 263505074721/1000000000))

rewrite49.0ms (0.4%)

Algorithm

1×	rewrite-expression-head

Rules

13×	`*-un-lft-identity_binary64`
13×	`add-sqr-sqrt_binary64`
13×	`add-cube-cbrt_binary64`
9×	`times-frac_binary64`
6×	`cbrt-prod_binary64`

Counts

3 → 61

Calls

3 calls:

38.0ms

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

4.0ms

(cbrt.f64 (+.f64 (*.f64 (+.f64 x 216700011257/5000000000) x) 263505074721/1000000000))

1.0ms

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

simplify172.0ms (1.4%)

Algorithm

1×	egg-herbie

Rules

539×	`distribute-rgt-in_binary64`
509×	`distribute-lft-in_binary64`
309×	`cancel-sign-sub-inv_binary64`
262×	`fma-def_binary64`
157×	`associate-r_binary64`

Counts

121 → 132

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	305	7890
1	832	6543
2	2587	6496
3	5219	6496

prune345.0ms (2.7%)

Pruning

9 alts after pruning (7 fresh and 2 done)

	Pruned	Kept	Total
New	168	1	169
Fresh	1	6	7
Picked	0	1	1
Done	0	1	1
Total	169	9	178

Error

0.2b

Counts

178 → 9

Alt Table

Status	Error	Program
	27.6b	(/.f64 (/.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 (cbrt.f64 (+.f64 (.f64 (+.f64 (.f64 (+.f64 (.f64 (+.f64 x 216700011257/5000000000) x) 263505074721/1000000000) x) 156699607947/500000000) x) 23533438303/500000000)) (cbrt.f64 (+.f64 (.f64 (+.f64 (.f64 (+.f64 (.f64 (+.f64 x 216700011257/5000000000) x) 263505074721/1000000000) x) 156699607947/500000000) x) 23533438303/500000000)))) (cbrt.f64 (+.f64 (.f64 (+.f64 (.f64 (+.f64 (*.f64 (+.f64 x 216700011257/5000000000) x) 263505074721/1000000000) x) 156699607947/500000000) x) 23533438303/500000000)))
	45.6b	(.f64 (/.f64 (-.f64 x 2) 1) (cbrt.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 (+.f64 156699607947/500000000 (fma.f64 (.f64 x x) 216700011257/5000000000 (fma.f64 x 263505074721/1000000000 (pow.f64 x 3)))) 23533438303/500000000)) 3)))
	30.0b	(/.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 (expm1.f64 (log1p.f64 (*.f64 x (fma.f64 x (+.f64 x 216700011257/5000000000) 263505074721/1000000000)))) 156699607947/500000000) x) 23533438303/500000000))
✓	24.9b	(.f64 (/.f64 (-.f64 x 2) 1) (/.f64 (+.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 216700011257/5000000000 (pow.f64 x 2)) (+.f64 (.f64 263505074721/1000000000 x) (pow.f64 x 3))) 156699607947/500000000) x) 23533438303/500000000)))
✓	25.0b	(.f64 (/.f64 (-.f64 x 2) 1) (/.f64 (+.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 (cbrt.f64 (+.f64 (.f64 (+.f64 x 216700011257/5000000000) x) 263505074721/1000000000)) (cbrt.f64 (+.f64 (.f64 (+.f64 x 216700011257/5000000000) x) 263505074721/1000000000))) (*.f64 x (cbrt.f64 (fma.f64 x (+.f64 x 216700011257/5000000000) 263505074721/1000000000)))) 156699607947/500000000) x) 23533438303/500000000)))
	25.2b	(.f64 (/.f64 (-.f64 x 2) 1) (/.f64 (+.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 (cbrt.f64 (+.f64 (.f64 (+.f64 x 216700011257/5000000000) x) 263505074721/1000000000)) (cbrt.f64 (+.f64 (.f64 (+.f64 x 216700011257/5000000000) x) 263505074721/1000000000))) (*.f64 x (expm1.f64 (log1p.f64 (cbrt.f64 (fma.f64 x (+.f64 x 216700011257/5000000000) 263505074721/1000000000)))))) 156699607947/500000000) x) 23533438303/500000000)))
	34.0b	(-.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))))
	32.6b	(-.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)))))
	44.6b	(.f64 (/.f64 (-.f64 x 2) 1) (/.f64 (+.f64 (.f64 (+.f64 (.f64 (.f64 (fma.f64 x (fma.f64 x 104109730557/25000000000 393497462077/5000000000) 4297481763/31250000) (sqrt.f64 x)) (sqrt.f64 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 12076 to 8894 computations (26.3% saved)

regimes3.3s (26.4%)

Accuracy

Total 0.6b remaining (68.5%)

Threshold costs 0.6b (68.5%)

Counts

227 → 3

Compiler

Compiled 41114 to 30032 computations (27% saved)

bsearch88.0ms (0.7%)

Steps

Iters	Range		Point
10	6.415444412924441e+61	1.841899419054641e+79	6.7265151660717154e+75
8	-5.974725362329573e+48	-1.7253104831864385e+44	-4.459699750903103e+47

Compiler

Compiled 4 to 3 computations (25% saved)

simplify8.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

19×	`+-commutative_binary64`
14×	`*-commutative_binary64`
8×	`sub-neg_binary64`
5×	`neg-sub0_binary64`
5×	`neg-mul-1_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	59	121
1	88	121
2	105	121
3	127	121
4	135	121
5	138	121
6	132	121

end292.0ms (2.3%)

Compiler: Compiled 616 to 445 computations (27.8% saved)

Details

analyze2.7s (21.5%)

sample1.6s (12.6%)

simplify51.0ms (0.4%)

prune5.0ms (0%)

localize26.0ms (0.2%)

series423.0ms (3.4%)

rewrite51.0ms (0.4%)

simplify227.0ms (1.8%)

prune477.0ms (3.8%)

localize25.0ms (0.2%)

series337.0ms (2.7%)

rewrite27.0ms (0.2%)

simplify156.0ms (1.2%)

prune335.0ms (2.7%)

localize28.0ms (0.2%)

series343.0ms (2.7%)

rewrite41.0ms (0.3%)

simplify231.0ms (1.8%)

prune350.0ms (2.8%)

localize90.0ms (0.7%)

series787.0ms (6.3%)

rewrite49.0ms (0.4%)

simplify172.0ms (1.4%)

prune345.0ms (2.7%)

regimes3.3s (26.4%)

bsearch88.0ms (0.7%)

simplify8.0ms (0.1%)

end292.0ms (2.3%)

Profiling