Details

analyze509.0ms (11%)

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
18.7%	81.1%	0.1%	6
25%	74.9%	0.1%	7
31.2%	68.6%	0.1%	8
45.2%	53.8%	0.9%	9
50.3%	47.8%	1.9%	10
54%	43.6%	2.4%	11
61.7%	32.9%	5.4%	12
64.1%	28.3%	7.6%	13
66.2%	24.7%	9.2%	14

Compiler

Compiled 16 to 11 computations (31.3% saved)

sample1.1s (24%)

Results

947.0ms	8256×	body	128	valid
143.0ms	1241×	body	128	invalid

Compiler

Compiled 32 to 22 computations (31.3% saved)

preprocess36.0ms (0.8%)

Algorithm

2×	egg-herbie

Rules

802×	`times-frac_binary64`
679×	`fma-neg_binary64`
418×	`fma-def_binary64`
329×	`cancel-sign-sub-inv_binary64`
220×	`distribute-rgt-in_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	28	72
1	71	72
2	154	72
3	269	72
4	474	64
5	890	64
6	1410	64
7	2303	64
0	3	3

Stop Event

1×	saturated
1×	node limit

Compiler

Compiled 15 to 10 computations (33.3% saved)

simplify43.0ms (0.9%)

Algorithm

1×	egg-herbie

Rules

1128×	`fma-def_binary64`
1073×	`fma-neg_binary64`
226×	`cancel-sign-sub-inv_binary64`
222×	`distribute-rgt-in_binary64`
162×	`distribute-lft-in_binary64`

Iterations

Useful iterations: 8 (0.0ms)

Iter	Nodes	Cost
0	11	18
1	22	18
2	46	18
3	78	18
4	141	16
5	274	16
6	443	16
7	744	16
8	1785	13
9	3544	13
10	4642	13
11	4838	13
12	4935	13
13	4935	13

Stop Event

1×

saturated

Counts

1 → 2

prune3.0ms (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

0.0b

Counts

3 → 2

Alt Table

Status	Error	Program
▶	2.5b	(fabs.f64 (-.f64 (/.f64 (+.f64 x 4) y) (*.f64 (/.f64 x y) z)))
	3.6b	(fabs.f64 (/.f64 (-.f64 (fma.f64 x z -4) x) y))

Compiler

Compiled 78 to 51 computations (34.6% saved)

localize7.0ms (0.2%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.0b	(/.f64 (+.f64 x 4) y)
✓	0.0b	(-.f64 (/.f64 (+.f64 x 4) y) (*.f64 (/.f64 x y) z))
✓	3.5b	(*.f64 (/.f64 x y) z)

series38.0ms (0.8%)

Counts

3 → 96

Calls

24 calls:

4.0ms	(-.f64 (/.f64 (+.f64 x 4) y) (*.f64 (/.f64 x y) z))	z	0
2.0ms	(-.f64 (/.f64 (+.f64 x 4) y) (*.f64 (/.f64 x y) z))	x	-inf
2.0ms	(-.f64 (/.f64 (+.f64 x 4) y) (*.f64 (/.f64 x y) z))	x	inf
2.0ms	(-.f64 (/.f64 (+.f64 x 4) y) (*.f64 (/.f64 x y) z))	z	inf
2.0ms	(-.f64 (/.f64 (+.f64 x 4) y) (*.f64 (/.f64 x y) z))	z	-inf

rewrite71.0ms (1.5%)

Algorithm

1×	batch-egg-rewrite

Rules

334×	`fma-def_binary64`
220×	`expm1-udef_binary64`
220×	`log1p-udef_binary64`
202×	`fma-neg_binary64`
184×	`log-pow_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	10	30
1	236	27
2	3526	27

Stop Event

1×	node limit

Counts

3 → 176

simplify79.0ms (1.7%)

Algorithm

1×	egg-herbie

Rules

739×	`fma-neg_binary64`
323×	`fma-def_binary64`
185×	`distribute-rgt-in_binary64`
176×	`cancel-sign-sub-inv_binary64`
160×	`unsub-neg_binary64`

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	31	1102
1	78	1102
2	186	952
3	442	860
4	951	790
5	2039	790
6	3042	790
7	3589	790
8	3601	790
9	3601	790

Stop Event

1×

saturated

Counts

272 → 194

prune131.0ms (2.8%)

Pruning

6 alts after pruning (5 fresh and 1 done)

	Pruned	Kept	Total
New	190	4	194
Fresh	0	1	1
Picked	0	1	1
Done	0	0	0
Total	190	6	196

Error

Counts

196 → 6

Alt Table

Status	Error	Program
	33.2b	(fabs.f64 (/.f64 (-.f64 (.f64 (+.f64 x 4) y) (.f64 y (.f64 x z))) (.f64 y y)))
✓	2.5b	(fabs.f64 (-.f64 (/.f64 (+.f64 x 4) y) (*.f64 (/.f64 x y) z)))
	2.8b	(fabs.f64 (-.f64 (/.f64 (+.f64 x 4) y) (pow.f64 (cbrt.f64 (*.f64 (/.f64 x y) z)) 3)))
▶	2.6b	(fabs.f64 (-.f64 (/.f64 (+.f64 x 4) y) (/.f64 x (/.f64 y z))))
	31.4b	(fabs.f64 (*.f64 (-.f64 (/.f64 1 y) (/.f64 z y)) x))
	3.6b	(fabs.f64 (/.f64 (-.f64 (fma.f64 x z -4) x) y))

Compiler

Compiled 4145 to 2020 computations (51.3% saved)

localize9.0ms (0.2%)

Local error

Found 3 expressions with local error:

New	Error	Program
	0.0b	(/.f64 (+.f64 x 4) y)
✓	0.0b	(-.f64 (/.f64 (+.f64 x 4) y) (/.f64 x (/.f64 y z)))
✓	3.8b	(/.f64 x (/.f64 y z))

series32.0ms (0.7%)

Counts

2 → 72

Calls

18 calls:

4.0ms	(-.f64 (/.f64 (+.f64 x 4) y) (/.f64 x (/.f64 y z)))	x	-inf
3.0ms	(-.f64 (/.f64 (+.f64 x 4) y) (/.f64 x (/.f64 y z)))	z	-inf
2.0ms	(-.f64 (/.f64 (+.f64 x 4) y) (/.f64 x (/.f64 y z)))	x	inf
2.0ms	(-.f64 (/.f64 (+.f64 x 4) y) (/.f64 x (/.f64 y z)))	z	0
2.0ms	(-.f64 (/.f64 (+.f64 x 4) y) (/.f64 x (/.f64 y z)))	z	inf

rewrite66.0ms (1.4%)

Algorithm

1×	batch-egg-rewrite

Rules

256×	`fma-neg_binary64`
234×	`expm1-udef_binary64`
234×	`log1p-udef_binary64`
127×	`add-sqr-sqrt_binary64`
124×	`log1p-expm1-u_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	10	23
1	245	23
2	4001	23

Stop Event

1×	node limit

Counts

2 → 108

simplify63.0ms (1.4%)

Algorithm

1×	egg-herbie

Rules

739×	`fma-neg_binary64`
323×	`fma-def_binary64`
185×	`distribute-rgt-in_binary64`
178×	`cancel-sign-sub-inv_binary64`
160×	`unsub-neg_binary64`

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	30	880
1	78	880
2	186	730
3	442	638
4	952	631
5	2050	631
6	3051	631
7	3597	631
8	3609	631
9	3609	631

Stop Event

1×

saturated

Counts

180 → 122

prune109.0ms (2.4%)

Pruning

6 alts after pruning (4 fresh and 2 done)

	Pruned	Kept	Total
New	157	0	157
Fresh	0	4	4
Picked	0	1	1
Done	0	1	1
Total	157	6	163

Error

Counts

163 → 6

Alt Table

Status	Error	Program
	33.2b	(fabs.f64 (/.f64 (-.f64 (.f64 (+.f64 x 4) y) (.f64 y (.f64 x z))) (.f64 y y)))
✓	2.5b	(fabs.f64 (-.f64 (/.f64 (+.f64 x 4) y) (*.f64 (/.f64 x y) z)))
▶	2.8b	(fabs.f64 (-.f64 (/.f64 (+.f64 x 4) y) (pow.f64 (cbrt.f64 (*.f64 (/.f64 x y) z)) 3)))
✓	2.6b	(fabs.f64 (-.f64 (/.f64 (+.f64 x 4) y) (/.f64 x (/.f64 y z))))
	31.4b	(fabs.f64 (*.f64 (-.f64 (/.f64 1 y) (/.f64 z y)) x))
	3.6b	(fabs.f64 (/.f64 (-.f64 (fma.f64 x z -4) x) y))

Compiler

Compiled 3063 to 1536 computations (49.9% saved)

localize11.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(-.f64 (/.f64 (+.f64 x 4) y) (pow.f64 (cbrt.f64 (*.f64 (/.f64 x y) z)) 3))
✓	0.6b	(pow.f64 (cbrt.f64 (*.f64 (/.f64 x y) z)) 3)
	3.5b	(*.f64 (/.f64 x y) z)
✓	11.2b	(cbrt.f64 (*.f64 (/.f64 x y) z))

series1.3s (28.9%)

Counts

3 → 108

Calls

27 calls:

89.0ms	(pow.f64 (cbrt.f64 (*.f64 (/.f64 x y) z)) 3)	y	-inf
86.0ms	(pow.f64 (cbrt.f64 (*.f64 (/.f64 x y) z)) 3)	z	-inf
86.0ms	(pow.f64 (cbrt.f64 (*.f64 (/.f64 x y) z)) 3)	z	0
81.0ms	(pow.f64 (cbrt.f64 (*.f64 (/.f64 x y) z)) 3)	x	-inf
72.0ms	(pow.f64 (cbrt.f64 (*.f64 (/.f64 x y) z)) 3)	x	inf

rewrite71.0ms (1.5%)

Algorithm

1×	batch-egg-rewrite

Rules

344×	`fma-def_binary64`
244×	`expm1-udef_binary64`
244×	`log1p-udef_binary64`
211×	`fma-neg_binary64`
174×	`egg-rr`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	13	32
1	294	29
2	3929	29

Stop Event

1×	node limit

Counts

3 → 174

simplify57.0ms (1.2%)

Algorithm

1×	egg-herbie

Rules

581×	`associate-l_binary64`
507×	`fma-def_binary64`
203×	`distribute-rgt-in_binary64`
163×	`distribute-lft-in_binary64`
160×	`exp-sum_binary64`

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	97	2044
1	275	2044
2	680	1822
3	1942	1110

Stop Event

1×	node limit

Counts

282 → 213

prune172.0ms (3.7%)

Pruning

6 alts after pruning (3 fresh and 3 done)

	Pruned	Kept	Total
New	238	0	238
Fresh	0	3	3
Picked	0	1	1
Done	0	2	2
Total	238	6	244

Error

Counts

244 → 6

Alt Table

Status	Error	Program
	33.2b	(fabs.f64 (/.f64 (-.f64 (.f64 (+.f64 x 4) y) (.f64 y (.f64 x z))) (.f64 y y)))
✓	2.5b	(fabs.f64 (-.f64 (/.f64 (+.f64 x 4) y) (*.f64 (/.f64 x y) z)))
✓	2.8b	(fabs.f64 (-.f64 (/.f64 (+.f64 x 4) y) (pow.f64 (cbrt.f64 (*.f64 (/.f64 x y) z)) 3)))
✓	2.6b	(fabs.f64 (-.f64 (/.f64 (+.f64 x 4) y) (/.f64 x (/.f64 y z))))
	31.4b	(fabs.f64 (*.f64 (-.f64 (/.f64 1 y) (/.f64 z y)) x))
▶	3.6b	(fabs.f64 (/.f64 (-.f64 (fma.f64 x z -4) x) y))

Compiler

Compiled 4893 to 2474 computations (49.4% saved)

localize6.0ms (0.1%)

Local error

Found 1 expressions with local error:

New	Error	Program
✓	3.4b	(/.f64 (-.f64 (fma.f64 x z -4) x) y)

series14.0ms (0.3%)

Counts

1 → 36

Calls

9 calls:

2.0ms	(/.f64 (-.f64 (fma.f64 x z -4) x) y)	z	-inf
2.0ms	(/.f64 (-.f64 (fma.f64 x z -4) x) y)	z	inf
2.0ms	(/.f64 (-.f64 (fma.f64 x z -4) x) y)	y	-inf
2.0ms	(/.f64 (-.f64 (fma.f64 x z -4) x) y)	x	-inf
2.0ms	(/.f64 (-.f64 (fma.f64 x z -4) x) y)	x	inf

rewrite84.0ms (1.8%)

Algorithm

1×	batch-egg-rewrite

Rules

541×	`prod-diff_binary64`
232×	`fma-def_binary64`
171×	`expm1-udef_binary64`
171×	`log1p-udef_binary64`
169×	`egg-rr`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	8	11
1	180	11
2	2573	11

Stop Event

1×	node limit

Counts

1 → 169

simplify61.0ms (1.3%)

Algorithm

1×	egg-herbie

Rules

774×	`fma-neg_binary64`
321×	`fma-def_binary64`
203×	`cancel-sign-sub-inv_binary64`
178×	`unsub-neg_binary64`
166×	`distribute-rgt-in_binary64`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	33	617
1	85	617
2	203	375
3	451	375
4	1032	375
5	2193	375
6	3268	375
7	3474	375
8	3480	375
9	3480	375

Stop Event

1×

saturated

Counts

205 → 182

prune147.0ms (3.2%)

Pruning

6 alts after pruning (2 fresh and 4 done)

	Pruned	Kept	Total
New	182	0	182
Fresh	0	2	2
Picked	0	1	1
Done	0	3	3
Total	182	6	188

Error

Counts

188 → 6

Alt Table

Status	Error	Program
	33.2b	(fabs.f64 (/.f64 (-.f64 (.f64 (+.f64 x 4) y) (.f64 y (.f64 x z))) (.f64 y y)))
✓	2.5b	(fabs.f64 (-.f64 (/.f64 (+.f64 x 4) y) (*.f64 (/.f64 x y) z)))
✓	2.8b	(fabs.f64 (-.f64 (/.f64 (+.f64 x 4) y) (pow.f64 (cbrt.f64 (*.f64 (/.f64 x y) z)) 3)))
✓	2.6b	(fabs.f64 (-.f64 (/.f64 (+.f64 x 4) y) (/.f64 x (/.f64 y z))))
	31.4b	(fabs.f64 (*.f64 (-.f64 (/.f64 1 y) (/.f64 z y)) x))
✓	3.6b	(fabs.f64 (/.f64 (-.f64 (fma.f64 x z -4) x) y))

Compiler

Compiled 7174 to 3380 computations (52.9% saved)

regimes230.0ms (5%)

Accuracy

Total 0.1b remaining (87.5%)

Threshold costs 0.1b (87.5%)

Counts

31 → 3

Compiler

Compiled 2037 to 1426 computations (30% saved)

bsearch14.0ms (0.3%)

Algorithm

2×	binary-search

Calls

2 calls:

9.0ms	x
5.0ms	x

Steps

Iters	Point		Range
0.07597955292762652	∈ [	0.02661987467155214	,	0.08227955654372106	]
-0.013284199379893075	∈ [	-0.06419377276191666	,	-0.007518762654055452	]

Compiler

Compiled 4 to 3 computations (25% saved)

simplify6.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

12×	`+-commutative_binary64`
11×	`sub-neg_binary64`
8×	`*-commutative_binary64`
7×	`neg-sub0_binary64`
7×	`neg-mul-1_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	23	61
1	37	61
2	57	61
3	72	61
4	87	61
5	94	61
6	96	61

Stop Event

1×

saturated

end103.0ms (2.2%)

Stop Event

1×

fuel

Compiler

Compiled 180 to 114 computations (36.7% saved)

Details

analyze509.0ms (11%)

sample1.1s (24%)

preprocess36.0ms (0.8%)

simplify43.0ms (0.9%)

prune3.0ms (0.1%)

localize7.0ms (0.2%)

series38.0ms (0.8%)

rewrite71.0ms (1.5%)

simplify79.0ms (1.7%)

prune131.0ms (2.8%)

localize9.0ms (0.2%)

series32.0ms (0.7%)

rewrite66.0ms (1.4%)

simplify63.0ms (1.4%)

prune109.0ms (2.4%)

localize11.0ms (0.2%)

series1.3s (28.9%)

rewrite71.0ms (1.5%)

simplify57.0ms (1.2%)

prune172.0ms (3.7%)

localize6.0ms (0.1%)

series14.0ms (0.3%)

rewrite84.0ms (1.8%)

simplify61.0ms (1.3%)

prune147.0ms (3.2%)

regimes230.0ms (5%)

bsearch14.0ms (0.3%)

simplify6.0ms (0.1%)

end103.0ms (2.2%)

Profiling