Details

analyze795.0ms (12.8%)

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
12.5%	87.4%	0.1%	7
18.7%	81.1%	0.1%	8
18.7%	81.1%	0.1%	9
42.1%	57.7%	0.1%	10
49.1%	50.7%	0.1%	11
49.1%	50.7%	0.1%	12
66.9%	33%	0.1%	13
71.7%	28.2%	0.1%	14

Compiler

Compiled 25 to 19 computations (24% saved)

sample1.2s (19.2%)

Results

1.2s

8256×

body

128

valid

Compiler

Compiled 50 to 38 computations (24% saved)

preprocess62.0ms (1%)

Algorithm

2×	egg-herbie

Rules

2164×	`fma-def_binary64`
374×	`distribute-rgt-out_binary64`
341×	`associate-/l*_binary64`
257×	`associate-l_binary64`
220×	`*-commutative_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	42	100
1	109	100
2	233	92
3	599	92
4	1224	92
5	2221	92
6	2611	92
7	3018	92
8	3530	92
9	4245	92
10	4268	92
0	3	3

Stop Event

1×	saturated
1×	node limit

Compiler

Compiled 24 to 18 computations (25% saved)

simplify24.0ms (0.4%)

Algorithm

1×	egg-herbie

Rules

722×	`fma-def_binary64`
94×	`distribute-rgt-out_binary64`
88×	`associate-/l*_binary64`
68×	`associate-l_binary64`
64×	`*-commutative_binary64`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	19	25
1	39	25
2	74	23
3	175	23
4	349	23
5	607	23
6	878	23
7	1010	23
8	1256	23
9	1671	23
10	1735	23
11	1736	23

Stop Event

1×

saturated

Counts

1 → 2

prune5.0ms (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

15.1b

Counts

3 → 2

Alt Table

Status	Error	Program
	19.6b	(+.f64 x (/.f64 (.f64 y (+.f64 (.f64 (+.f64 (.f64 z 692910599291889/10000000000000000) 307332350656623/625000000000000) z) 11167812716741/40000000000000)) (+.f64 (.f64 (+.f64 z 6012459259764103/1000000000000000) z) 104698244219447/31250000000000)))
▶	15.1b	(fma.f64 y (/.f64 (fma.f64 z (fma.f64 z 692910599291889/10000000000000000 307332350656623/625000000000000) 11167812716741/40000000000000) (fma.f64 z (+.f64 z 6012459259764103/1000000000000000) 104698244219447/31250000000000)) x)

Status

Error

Program

19.6b

(+.f64 x (/.f64 (*.f64 y (+.f64 (*.f64 (+.f64 (*.f64 z 692910599291889/10000000000000000) 307332350656623/625000000000000) z) 11167812716741/40000000000000)) (+.f64 (*.f64 (+.f64 z 6012459259764103/1000000000000000) z) 104698244219447/31250000000000)))

▶

15.1b

(fma.f64 y (/.f64 (fma.f64 z (fma.f64 z 692910599291889/10000000000000000 307332350656623/625000000000000) 11167812716741/40000000000000) (fma.f64 z (+.f64 z 6012459259764103/1000000000000000) 104698244219447/31250000000000)) x)

Compiler

Compiled 129 to 93 computations (27.9% saved)

localize11.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.1b	(fma.f64 z (fma.f64 z 692910599291889/10000000000000000 307332350656623/625000000000000) 11167812716741/40000000000000)
✓	0.2b	(fma.f64 y (/.f64 (fma.f64 z (fma.f64 z 692910599291889/10000000000000000 307332350656623/625000000000000) 11167812716741/40000000000000) (fma.f64 z (+.f64 z 6012459259764103/1000000000000000) 104698244219447/31250000000000)) x)
✓	0.3b	(fma.f64 z 692910599291889/10000000000000000 307332350656623/625000000000000)
✓	14.6b	(/.f64 (fma.f64 z (fma.f64 z 692910599291889/10000000000000000 307332350656623/625000000000000) 11167812716741/40000000000000) (fma.f64 z (+.f64 z 6012459259764103/1000000000000000) 104698244219447/31250000000000))

series86.0ms (1.4%)

Counts

4 → 72

Calls

18 calls:

13.0ms	(fma.f64 y (/.f64 (fma.f64 z (fma.f64 z 692910599291889/10000000000000000 307332350656623/625000000000000) 11167812716741/40000000000000) (fma.f64 z (+.f64 z 6012459259764103/1000000000000000) 104698244219447/31250000000000)) x)	x	-inf
13.0ms	(fma.f64 y (/.f64 (fma.f64 z (fma.f64 z 692910599291889/10000000000000000 307332350656623/625000000000000) 11167812716741/40000000000000) (fma.f64 z (+.f64 z 6012459259764103/1000000000000000) 104698244219447/31250000000000)) x)	y	inf
13.0ms	(fma.f64 y (/.f64 (fma.f64 z (fma.f64 z 692910599291889/10000000000000000 307332350656623/625000000000000) 11167812716741/40000000000000) (fma.f64 z (+.f64 z 6012459259764103/1000000000000000) 104698244219447/31250000000000)) x)	x	0
12.0ms	(fma.f64 y (/.f64 (fma.f64 z (fma.f64 z 692910599291889/10000000000000000 307332350656623/625000000000000) 11167812716741/40000000000000) (fma.f64 z (+.f64 z 6012459259764103/1000000000000000) 104698244219447/31250000000000)) x)	y	-inf
11.0ms	(fma.f64 y (/.f64 (fma.f64 z (fma.f64 z 692910599291889/10000000000000000 307332350656623/625000000000000) 11167812716741/40000000000000) (fma.f64 z (+.f64 z 6012459259764103/1000000000000000) 104698244219447/31250000000000)) x)	y	0

rewrite80.0ms (1.3%)

Algorithm

1×	batch-egg-rewrite

Rules

285×	`expm1-udef_binary64`
285×	`log1p-udef_binary64`
160×	`add-sqr-sqrt_binary64`
159×	`prod-diff_binary64`
152×	`log1p-expm1-u_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	15	56
1	323	56
2	3886	56

Stop Event

1×	node limit

Counts

4 → 102

simplify71.0ms (1.1%)

Algorithm

1×	egg-herbie

Rules

611×	`cancel-sign-sub-inv_binary64`
508×	`associate-l_binary64`
322×	`fma-neg_binary64`
300×	`fma-def_binary64`
183×	`associate-/r*_binary64`

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	96	1961
1	280	1748
2	767	1567
3	2287	1270

Stop Event

1×	node limit

Counts

174 → 151

prune234.0ms (3.8%)

Pruning

8 alts after pruning (8 fresh and 0 done)

	Pruned	Kept	Total
New	143	8	151
Fresh	1	0	1
Picked	1	0	1
Done	0	0	0
Total	145	8	153

Error

0.1b

Counts

153 → 8

Alt Table

Status	Error	Program
	19.6b	(+.f64 (.f64 307332350656623/625000000000000 (/.f64 (.f64 y z) (+.f64 104698244219447/31250000000000 (+.f64 (pow.f64 z 2) (.f64 6012459259764103/1000000000000000 z))))) (+.f64 (.f64 11167812716741/40000000000000 (/.f64 y (+.f64 104698244219447/31250000000000 (+.f64 (pow.f64 z 2) (.f64 6012459259764103/1000000000000000 z))))) (+.f64 (.f64 692910599291889/10000000000000000 (/.f64 (.f64 y (pow.f64 z 2)) (+.f64 104698244219447/31250000000000 (+.f64 (pow.f64 z 2) (.f64 6012459259764103/1000000000000000 z))))) x)))
	15.3b	(fma.f64 y (pow.f64 (pow.f64 (/.f64 (fma.f64 z (fma.f64 z 692910599291889/10000000000000000 307332350656623/625000000000000) 11167812716741/40000000000000) (fma.f64 z (+.f64 z 6012459259764103/1000000000000000) 104698244219447/31250000000000)) 3) 1/3) x)
	39.2b	(pow.f64 (sqrt.f64 (fma.f64 y (/.f64 (fma.f64 z (fma.f64 z 692910599291889/10000000000000000 307332350656623/625000000000000) 11167812716741/40000000000000) (fma.f64 z (+.f64 z 6012459259764103/1000000000000000) 104698244219447/31250000000000)) x)) 2)
	16.1b	(pow.f64 (cbrt.f64 (fma.f64 y (/.f64 (fma.f64 z (fma.f64 z 692910599291889/10000000000000000 307332350656623/625000000000000) 11167812716741/40000000000000) (fma.f64 z (+.f64 z 6012459259764103/1000000000000000) 104698244219447/31250000000000)) x)) 3)
	24.8b	(fma.f64 y (+.f64 692910599291889/10000000000000000 (-.f64 (/.f64 751220861604756070699018739433/10000000000000000000000000000000 z) (/.f64 (/.f64 4046220386999211718548694042263781576003973599/10000000000000000000000000000000000000000000000 z) z))) x)
	19.6b	(+.f64 x (/.f64 (*.f64 y (fma.f64 z (fma.f64 z 692910599291889/10000000000000000 307332350656623/625000000000000) 11167812716741/40000000000000)) (fma.f64 z (+.f64 z 6012459259764103/1000000000000000) 104698244219447/31250000000000)))
▶	15.2b	(fma.f64 y (/.f64 (pow.f64 (cbrt.f64 (fma.f64 z (fma.f64 z 692910599291889/10000000000000000 307332350656623/625000000000000) 11167812716741/40000000000000)) 3) (fma.f64 z (+.f64 z 6012459259764103/1000000000000000) 104698244219447/31250000000000)) x)
	15.9b	(+.f64 x (fma.f64 11167812716741/40000000000000 (/.f64 y (fma.f64 z (+.f64 z 6012459259764103/1000000000000000) 104698244219447/31250000000000)) (.f64 (/.f64 y (fma.f64 z (+.f64 z 6012459259764103/1000000000000000) 104698244219447/31250000000000)) (.f64 z (fma.f64 z 692910599291889/10000000000000000 307332350656623/625000000000000)))))

Compiler

Compiled 3650 to 2560 computations (29.9% saved)

localize13.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.2b	(pow.f64 (cbrt.f64 (fma.f64 z (fma.f64 z 692910599291889/10000000000000000 307332350656623/625000000000000) 11167812716741/40000000000000)) 3)
	0.3b	(fma.f64 z 692910599291889/10000000000000000 307332350656623/625000000000000)
✓	14.5b	(cbrt.f64 (fma.f64 z (fma.f64 z 692910599291889/10000000000000000 307332350656623/625000000000000) 11167812716741/40000000000000))
✓	14.6b	(/.f64 (pow.f64 (cbrt.f64 (fma.f64 z (fma.f64 z 692910599291889/10000000000000000 307332350656623/625000000000000) 11167812716741/40000000000000)) 3) (fma.f64 z (+.f64 z 6012459259764103/1000000000000000) 104698244219447/31250000000000))

series33.0ms (0.5%)

Counts

3 → 20

Calls

9 calls:

10.0ms	(pow.f64 (cbrt.f64 (fma.f64 z (fma.f64 z 692910599291889/10000000000000000 307332350656623/625000000000000) 11167812716741/40000000000000)) 3)	z	0
7.0ms	(cbrt.f64 (fma.f64 z (fma.f64 z 692910599291889/10000000000000000 307332350656623/625000000000000) 11167812716741/40000000000000))	z	0
4.0ms	(pow.f64 (cbrt.f64 (fma.f64 z (fma.f64 z 692910599291889/10000000000000000 307332350656623/625000000000000) 11167812716741/40000000000000)) 3)	z	inf
3.0ms	(pow.f64 (cbrt.f64 (fma.f64 z (fma.f64 z 692910599291889/10000000000000000 307332350656623/625000000000000) 11167812716741/40000000000000)) 3)	z	-inf
3.0ms	(/.f64 (pow.f64 (cbrt.f64 (fma.f64 z (fma.f64 z 692910599291889/10000000000000000 307332350656623/625000000000000) 11167812716741/40000000000000)) 3) (fma.f64 z (+.f64 z 6012459259764103/1000000000000000) 104698244219447/31250000000000))	z	-inf

rewrite70.0ms (1.1%)

Algorithm

1×	batch-egg-rewrite

Rules

258×	`expm1-udef_binary64`
258×	`log1p-udef_binary64`
170×	`fma-def_binary64`
147×	`add-sqr-sqrt_binary64`
144×	`log1p-expm1-u_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	15	39
1	325	39
2	3671	39

Stop Event

1×	node limit

Counts

3 → 96

simplify45.0ms (0.7%)

Algorithm

1×	egg-herbie

Rules

822×	`times-frac_binary64`
529×	`fma-neg_binary64`
285×	`fma-def_binary64`
241×	`associate-r_binary64`
201×	`associate-l_binary64`

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	89	412
1	257	406
2	803	393
3	3308	387

Stop Event

1×	node limit

Counts

116 → 124

prune212.0ms (3.4%)

Pruning

8 alts after pruning (7 fresh and 1 done)

	Pruned	Kept	Total
New	152	0	152
Fresh	0	7	7
Picked	0	1	1
Done	0	0	0
Total	152	8	160

Error

0.1b

Counts

160 → 8

Alt Table

Status	Error	Program
	19.6b	(+.f64 (.f64 307332350656623/625000000000000 (/.f64 (.f64 y z) (+.f64 104698244219447/31250000000000 (+.f64 (pow.f64 z 2) (.f64 6012459259764103/1000000000000000 z))))) (+.f64 (.f64 11167812716741/40000000000000 (/.f64 y (+.f64 104698244219447/31250000000000 (+.f64 (pow.f64 z 2) (.f64 6012459259764103/1000000000000000 z))))) (+.f64 (.f64 692910599291889/10000000000000000 (/.f64 (.f64 y (pow.f64 z 2)) (+.f64 104698244219447/31250000000000 (+.f64 (pow.f64 z 2) (.f64 6012459259764103/1000000000000000 z))))) x)))
▶	15.3b	(fma.f64 y (pow.f64 (pow.f64 (/.f64 (fma.f64 z (fma.f64 z 692910599291889/10000000000000000 307332350656623/625000000000000) 11167812716741/40000000000000) (fma.f64 z (+.f64 z 6012459259764103/1000000000000000) 104698244219447/31250000000000)) 3) 1/3) x)
	39.2b	(pow.f64 (sqrt.f64 (fma.f64 y (/.f64 (fma.f64 z (fma.f64 z 692910599291889/10000000000000000 307332350656623/625000000000000) 11167812716741/40000000000000) (fma.f64 z (+.f64 z 6012459259764103/1000000000000000) 104698244219447/31250000000000)) x)) 2)
	16.1b	(pow.f64 (cbrt.f64 (fma.f64 y (/.f64 (fma.f64 z (fma.f64 z 692910599291889/10000000000000000 307332350656623/625000000000000) 11167812716741/40000000000000) (fma.f64 z (+.f64 z 6012459259764103/1000000000000000) 104698244219447/31250000000000)) x)) 3)
	24.8b	(fma.f64 y (+.f64 692910599291889/10000000000000000 (-.f64 (/.f64 751220861604756070699018739433/10000000000000000000000000000000 z) (/.f64 (/.f64 4046220386999211718548694042263781576003973599/10000000000000000000000000000000000000000000000 z) z))) x)
	19.6b	(+.f64 x (/.f64 (*.f64 y (fma.f64 z (fma.f64 z 692910599291889/10000000000000000 307332350656623/625000000000000) 11167812716741/40000000000000)) (fma.f64 z (+.f64 z 6012459259764103/1000000000000000) 104698244219447/31250000000000)))
✓	15.2b	(fma.f64 y (/.f64 (pow.f64 (cbrt.f64 (fma.f64 z (fma.f64 z 692910599291889/10000000000000000 307332350656623/625000000000000) 11167812716741/40000000000000)) 3) (fma.f64 z (+.f64 z 6012459259764103/1000000000000000) 104698244219447/31250000000000)) x)
	15.9b	(+.f64 x (fma.f64 11167812716741/40000000000000 (/.f64 y (fma.f64 z (+.f64 z 6012459259764103/1000000000000000) 104698244219447/31250000000000)) (.f64 (/.f64 y (fma.f64 z (+.f64 z 6012459259764103/1000000000000000) 104698244219447/31250000000000)) (.f64 z (fma.f64 z 692910599291889/10000000000000000 307332350656623/625000000000000)))))

Compiler

Compiled 4221 to 3100 computations (26.6% saved)

localize16.0ms (0.3%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.3b	(fma.f64 z 692910599291889/10000000000000000 307332350656623/625000000000000)
✓	0.8b	(pow.f64 (/.f64 (fma.f64 z (fma.f64 z 692910599291889/10000000000000000 307332350656623/625000000000000) 11167812716741/40000000000000) (fma.f64 z (+.f64 z 6012459259764103/1000000000000000) 104698244219447/31250000000000)) 3)
✓	1.0b	(pow.f64 (pow.f64 (/.f64 (fma.f64 z (fma.f64 z 692910599291889/10000000000000000 307332350656623/625000000000000) 11167812716741/40000000000000) (fma.f64 z (+.f64 z 6012459259764103/1000000000000000) 104698244219447/31250000000000)) 3) 1/3)
	14.6b	(/.f64 (fma.f64 z (fma.f64 z 692910599291889/10000000000000000 307332350656623/625000000000000) 11167812716741/40000000000000) (fma.f64 z (+.f64 z 6012459259764103/1000000000000000) 104698244219447/31250000000000))

series31.0ms (0.5%)

Counts

2 → 24

Calls

6 calls:

10.0ms	(pow.f64 (pow.f64 (/.f64 (fma.f64 z (fma.f64 z 692910599291889/10000000000000000 307332350656623/625000000000000) 11167812716741/40000000000000) (fma.f64 z (+.f64 z 6012459259764103/1000000000000000) 104698244219447/31250000000000)) 3) 1/3)	z	-inf
9.0ms	(pow.f64 (pow.f64 (/.f64 (fma.f64 z (fma.f64 z 692910599291889/10000000000000000 307332350656623/625000000000000) 11167812716741/40000000000000) (fma.f64 z (+.f64 z 6012459259764103/1000000000000000) 104698244219447/31250000000000)) 3) 1/3)	z	inf
8.0ms	(pow.f64 (pow.f64 (/.f64 (fma.f64 z (fma.f64 z 692910599291889/10000000000000000 307332350656623/625000000000000) 11167812716741/40000000000000) (fma.f64 z (+.f64 z 6012459259764103/1000000000000000) 104698244219447/31250000000000)) 3) 1/3)	z	0
1.0ms	(pow.f64 (/.f64 (fma.f64 z (fma.f64 z 692910599291889/10000000000000000 307332350656623/625000000000000) 11167812716741/40000000000000) (fma.f64 z (+.f64 z 6012459259764103/1000000000000000) 104698244219447/31250000000000)) 3)	z	-inf
1.0ms	(pow.f64 (/.f64 (fma.f64 z (fma.f64 z 692910599291889/10000000000000000 307332350656623/625000000000000) 11167812716741/40000000000000) (fma.f64 z (+.f64 z 6012459259764103/1000000000000000) 104698244219447/31250000000000)) 3)	z	inf

rewrite75.0ms (1.2%)

Algorithm

1×	batch-egg-rewrite

Rules

273×	`expm1-udef_binary64`
273×	`log1p-udef_binary64`
157×	`log1p-expm1-u_binary64`
157×	`expm1-log1p-u_binary64`
156×	`add-sqr-sqrt_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	16	41
1	344	41
2	3922	41

Stop Event

1×	node limit

Counts

2 → 78

simplify65.0ms (1%)

Algorithm

1×	egg-herbie

Rules

385×	`fma-def_binary64`
297×	`associate-r_binary64`
276×	`associate-l_binary64`
224×	`cancel-sign-sub-inv_binary64`
223×	`associate-/r*_binary64`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	116	752
1	336	712
2	1124	696

Stop Event

1×	node limit

Counts

102 → 106

prune1.1s (18.2%)

Pruning

9 alts after pruning (7 fresh and 2 done)

	Pruned	Kept	Total
New	179	2	181
Fresh	1	5	6
Picked	0	1	1
Done	0	1	1
Total	180	9	189

Error

0.1b

Counts

189 → 9

Alt Table

Status	Error	Program
	19.6b	(+.f64 (.f64 307332350656623/625000000000000 (/.f64 (.f64 y z) (+.f64 104698244219447/31250000000000 (+.f64 (pow.f64 z 2) (.f64 6012459259764103/1000000000000000 z))))) (+.f64 (.f64 11167812716741/40000000000000 (/.f64 y (+.f64 104698244219447/31250000000000 (+.f64 (pow.f64 z 2) (.f64 6012459259764103/1000000000000000 z))))) (+.f64 (.f64 692910599291889/10000000000000000 (/.f64 (.f64 y (pow.f64 z 2)) (+.f64 104698244219447/31250000000000 (+.f64 (pow.f64 z 2) (.f64 6012459259764103/1000000000000000 z))))) x)))
✓	15.3b	(fma.f64 y (pow.f64 (pow.f64 (/.f64 (fma.f64 z (fma.f64 z 692910599291889/10000000000000000 307332350656623/625000000000000) 11167812716741/40000000000000) (fma.f64 z (+.f64 z 6012459259764103/1000000000000000) 104698244219447/31250000000000)) 3) 1/3) x)
	10.6b	(fma.f64 y (pow.f64 332683769813656330865983273121589448716828369/1000000000000000000000000000000000000000000000000 1/3) x)
▶	10.5b	(fma.f64 y (cbrt.f64 332683769813656330865983273121589448716828369/1000000000000000000000000000000000000000000000000) x)
	39.2b	(pow.f64 (sqrt.f64 (fma.f64 y (/.f64 (fma.f64 z (fma.f64 z 692910599291889/10000000000000000 307332350656623/625000000000000) 11167812716741/40000000000000) (fma.f64 z (+.f64 z 6012459259764103/1000000000000000) 104698244219447/31250000000000)) x)) 2)
	16.1b	(pow.f64 (cbrt.f64 (fma.f64 y (/.f64 (fma.f64 z (fma.f64 z 692910599291889/10000000000000000 307332350656623/625000000000000) 11167812716741/40000000000000) (fma.f64 z (+.f64 z 6012459259764103/1000000000000000) 104698244219447/31250000000000)) x)) 3)
	19.6b	(+.f64 x (/.f64 (*.f64 y (fma.f64 z (fma.f64 z 692910599291889/10000000000000000 307332350656623/625000000000000) 11167812716741/40000000000000)) (fma.f64 z (+.f64 z 6012459259764103/1000000000000000) 104698244219447/31250000000000)))
✓	15.2b	(fma.f64 y (/.f64 (pow.f64 (cbrt.f64 (fma.f64 z (fma.f64 z 692910599291889/10000000000000000 307332350656623/625000000000000) 11167812716741/40000000000000)) 3) (fma.f64 z (+.f64 z 6012459259764103/1000000000000000) 104698244219447/31250000000000)) x)
	15.9b	(+.f64 x (fma.f64 11167812716741/40000000000000 (/.f64 y (fma.f64 z (+.f64 z 6012459259764103/1000000000000000) 104698244219447/31250000000000)) (.f64 (/.f64 y (fma.f64 z (+.f64 z 6012459259764103/1000000000000000) 104698244219447/31250000000000)) (.f64 z (fma.f64 z 692910599291889/10000000000000000 307332350656623/625000000000000)))))

Compiler

Compiled 5279 to 3970 computations (24.8% saved)

localize4.0ms (0.1%)

Local error

Found 1 expressions with local error:

New	Error	Program
✓	0.3b	(fma.f64 y (cbrt.f64 332683769813656330865983273121589448716828369/1000000000000000000000000000000000000000000000000) x)

series34.0ms (0.5%)

Counts

1 → 24

Calls

6 calls:

8.0ms	(fma.f64 y (cbrt.f64 332683769813656330865983273121589448716828369/1000000000000000000000000000000000000000000000000) x)	y	inf
6.0ms	(fma.f64 y (cbrt.f64 332683769813656330865983273121589448716828369/1000000000000000000000000000000000000000000000000) x)	x	-inf
5.0ms	(fma.f64 y (cbrt.f64 332683769813656330865983273121589448716828369/1000000000000000000000000000000000000000000000000) x)	y	-inf
5.0ms	(fma.f64 y (cbrt.f64 332683769813656330865983273121589448716828369/1000000000000000000000000000000000000000000000000) x)	y	0
5.0ms	(fma.f64 y (cbrt.f64 332683769813656330865983273121589448716828369/1000000000000000000000000000000000000000000000000) x)	x	0

rewrite41.0ms (0.7%)

Algorithm

1×	batch-egg-rewrite

Rules

484×	`log1p-expm1-u_binary64`
484×	`expm1-log1p-u_binary64`
249×	`unpow-prod-down_binary64`
234×	`log-prod_binary64`
146×	`pow2_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	6	7
1	118	7
2	1310	7

Stop Event

1×	node limit

Counts

1 → 36

simplify13.0ms (0.2%)

Algorithm

1×	egg-herbie

Rules

2×	`fma-def_binary64`
1×	`+-commutative_binary64`
1×	`*-commutative_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	7	147
1	10	147
2	11	147

Stop Event

1×

saturated

Counts

60 → 39

prune38.0ms (0.6%)

Pruning

11 alts after pruning (8 fresh and 3 done)

	Pruned	Kept	Total
New	36	3	39
Fresh	1	5	6
Picked	0	1	1
Done	0	2	2
Total	37	11	48

Error

0.1b

Counts

48 → 11

Alt Table

Status	Error	Program
	37.1b	(pow.f64 (sqrt.f64 (fma.f64 y (cbrt.f64 332683769813656330865983273121589448716828369/1000000000000000000000000000000000000000000000000) x)) 2)
	39.2b	(pow.f64 (sqrt.f64 (fma.f64 y (/.f64 (fma.f64 z (fma.f64 z 692910599291889/10000000000000000 307332350656623/625000000000000) 11167812716741/40000000000000) (fma.f64 z (+.f64 z 6012459259764103/1000000000000000) 104698244219447/31250000000000)) x)) 2)
	11.6b	(*.f64 (cbrt.f64 (fma.f64 y (cbrt.f64 332683769813656330865983273121589448716828369/1000000000000000000000000000000000000000000000000) x)) (pow.f64 (cbrt.f64 (fma.f64 y (cbrt.f64 332683769813656330865983273121589448716828369/1000000000000000000000000000000000000000000000000) x)) 2))
	19.6b	(+.f64 x (/.f64 (*.f64 y (fma.f64 z (fma.f64 z 692910599291889/10000000000000000 307332350656623/625000000000000) 11167812716741/40000000000000)) (fma.f64 z (+.f64 z 6012459259764103/1000000000000000) 104698244219447/31250000000000)))
	19.6b	(+.f64 (.f64 307332350656623/625000000000000 (/.f64 (.f64 y z) (+.f64 104698244219447/31250000000000 (+.f64 (pow.f64 z 2) (.f64 6012459259764103/1000000000000000 z))))) (+.f64 (.f64 11167812716741/40000000000000 (/.f64 y (+.f64 104698244219447/31250000000000 (+.f64 (pow.f64 z 2) (.f64 6012459259764103/1000000000000000 z))))) (+.f64 (.f64 692910599291889/10000000000000000 (/.f64 (.f64 y (pow.f64 z 2)) (+.f64 104698244219447/31250000000000 (+.f64 (pow.f64 z 2) (.f64 6012459259764103/1000000000000000 z))))) x)))
✓	15.3b	(fma.f64 y (pow.f64 (pow.f64 (/.f64 (fma.f64 z (fma.f64 z 692910599291889/10000000000000000 307332350656623/625000000000000) 11167812716741/40000000000000) (fma.f64 z (+.f64 z 6012459259764103/1000000000000000) 104698244219447/31250000000000)) 3) 1/3) x)
	10.6b	(fma.f64 y (pow.f64 332683769813656330865983273121589448716828369/1000000000000000000000000000000000000000000000000 1/3) x)
✓	10.5b	(fma.f64 y (cbrt.f64 332683769813656330865983273121589448716828369/1000000000000000000000000000000000000000000000000) x)
	32.8b	(/.f64 (-.f64 (pow.f64 (.f64 y (cbrt.f64 332683769813656330865983273121589448716828369/1000000000000000000000000000000000000000000000000)) 2) (.f64 x x)) (fma.f64 y (cbrt.f64 332683769813656330865983273121589448716828369/1000000000000000000000000000000000000000000000000) (neg.f64 x)))
✓	15.2b	(fma.f64 y (/.f64 (pow.f64 (cbrt.f64 (fma.f64 z (fma.f64 z 692910599291889/10000000000000000 307332350656623/625000000000000) 11167812716741/40000000000000)) 3) (fma.f64 z (+.f64 z 6012459259764103/1000000000000000) 104698244219447/31250000000000)) x)
	15.9b	(+.f64 x (fma.f64 11167812716741/40000000000000 (/.f64 y (fma.f64 z (+.f64 z 6012459259764103/1000000000000000) 104698244219447/31250000000000)) (.f64 (/.f64 y (fma.f64 z (+.f64 z 6012459259764103/1000000000000000) 104698244219447/31250000000000)) (.f64 z (fma.f64 z 692910599291889/10000000000000000 307332350656623/625000000000000)))))

Compiler

Compiled 677 to 507 computations (25.1% saved)

regimes1.6s (25.7%)

Accuracy

Total 0.1b remaining (69.8%)

Threshold costs 0.1b (69.8%)

Counts

159 → 3

Compiler

Compiled 18928 to 14128 computations (25.4% saved)

bsearch31.0ms (0.5%)

Algorithm

2×	binary-search

Calls

2 calls:

17.0ms	z
5.0ms	z

Steps

Iters	Point		Range
18895967.63042804	∈ [	1.332850349918073	,	57462521.04941301	]
-2.4499162731112108e+22	∈ [	-2.2330619283647796e+24	,	-5.258754857812395e+21	]

Compiler

Compiled 4 to 3 computations (25% saved)

simplify8.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

8×	`+-commutative_binary64`
7×	`*-commutative_binary64`
4×	`sub-neg_binary64`
3×	`neg-sub0_binary64`
3×	`neg-mul-1_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	45	82
1	62	82
2	71	82
3	77	82
4	82	82
5	85	82
6	86	82

Stop Event

1×

saturated

end187.0ms (3%)

Stop Event

1×

fuel

Compiler

Compiled 359 to 263 computations (26.7% saved)

Details

analyze795.0ms (12.8%)

sample1.2s (19.2%)

preprocess62.0ms (1%)

simplify24.0ms (0.4%)

prune5.0ms (0.1%)

localize11.0ms (0.2%)

series86.0ms (1.4%)

rewrite80.0ms (1.3%)

simplify71.0ms (1.1%)

prune234.0ms (3.8%)

localize13.0ms (0.2%)

series33.0ms (0.5%)

rewrite70.0ms (1.1%)

simplify45.0ms (0.7%)

prune212.0ms (3.4%)

localize16.0ms (0.3%)

series31.0ms (0.5%)

rewrite75.0ms (1.2%)

simplify65.0ms (1%)

prune1.1s (18.2%)

localize4.0ms (0.1%)

series34.0ms (0.5%)

rewrite41.0ms (0.7%)

simplify13.0ms (0.2%)

prune38.0ms (0.6%)

regimes1.6s (25.7%)

bsearch31.0ms (0.5%)

simplify8.0ms (0.1%)

end187.0ms (3%)

Profiling