Details

analyze754.0ms (9.1%)

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
12.5%	87.4%	0.1%	5
18.7%	81.2%	0.1%	6
28.1%	71.8%	0.1%	7
32.8%	67.1%	0.1%	8
38.2%	61.7%	0.1%	9
41%	58.9%	0.1%	10
43.9%	56%	0.1%	11
45.4%	54.5%	0.1%	12
46.9%	53%	0.1%	13
47.7%	52.2%	0.1%	14

Compiler

Compiled 19 to 9 computations (52.6% saved)

sample3.8s (45.5%)

Results

2.1s	3934×	body	8192	exit
806.0ms	6769×	body	128	valid
447.0ms	4079×	body	128	invalid
192.0ms	692×	body	512	valid
143.0ms	774×	body	256	valid
8.0ms	21×	body	1024	valid

Compiler

Compiled 38 to 18 computations (52.6% saved)

preprocess37.0ms (0.4%)

Algorithm

2×	egg-herbie

Rules

385×	`div-sub_binary64`
340×	`times-frac_binary64`
270×	`distribute-rgt-in_binary64`
248×	`distribute-rgt-neg-in_binary64`
229×	`associate-/l*_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	15	46
1	40	46
2	109	46
3	303	42
4	831	36
5	3257	36
0	2	2

Stop Event

1×	saturated
1×	node limit

Compiler

Compiled 18 to 8 computations (55.6% saved)

simplify30.0ms (0.4%)

Algorithm

1×	egg-herbie

Rules

503×	`fma-def_binary64`
481×	`div-sub_binary64`
467×	`fma-neg_binary64`
288×	`associate-/r*_binary64`
282×	`associate-/l/_binary64`

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	9	23
1	22	23
2	58	23
3	155	21
4	432	18
5	1495	18
6	4690	18

Stop Event

1×	node limit

Counts

1 → 2

prune3.0ms (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

13.3b

Counts

3 → 2

Alt Table

Status	Error	Program
▶	13.3b	(+.f64 wj (/.f64 (-.f64 (/.f64 x (exp.f64 wj)) wj) (+.f64 wj 1)))
	14.8b	(-.f64 wj (/.f64 (-.f64 (.f64 wj (exp.f64 wj)) x) (+.f64 (exp.f64 wj) (.f64 wj (exp.f64 wj)))))

Compiler

Compiled 94 to 48 computations (48.9% saved)

localize7.0ms (0.1%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.0b	(/.f64 (-.f64 (/.f64 x (exp.f64 wj)) wj) (+.f64 wj 1))
✓	0.2b	(/.f64 x (exp.f64 wj))
✓	3.9b	(+.f64 wj (/.f64 (-.f64 (/.f64 x (exp.f64 wj)) wj) (+.f64 wj 1)))

series45.0ms (0.5%)

Counts

3 → 52

Calls

18 calls:

6.0ms	(+.f64 wj (/.f64 (-.f64 (/.f64 x (exp.f64 wj)) wj) (+.f64 wj 1)))	x	0
4.0ms	(+.f64 wj (/.f64 (-.f64 (/.f64 x (exp.f64 wj)) wj) (+.f64 wj 1)))	x	-inf
4.0ms	(+.f64 wj (/.f64 (-.f64 (/.f64 x (exp.f64 wj)) wj) (+.f64 wj 1)))	x	inf
3.0ms	(/.f64 (-.f64 (/.f64 x (exp.f64 wj)) wj) (+.f64 wj 1))	x	-inf
3.0ms	(/.f64 (-.f64 (/.f64 x (exp.f64 wj)) wj) (+.f64 wj 1))	x	inf

rewrite74.0ms (0.9%)

Algorithm

1×	batch-egg-rewrite

Rules

528×	`fma-def_binary64`
354×	`fma-neg_binary64`
218×	`log1p-udef_binary64`
217×	`expm1-udef_binary64`
125×	`add-sqr-sqrt_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	10	39
1	232	39
2	3723	39

Stop Event

1×	node limit

Counts

3 → 159

simplify44.0ms (0.5%)

Algorithm

1×	egg-herbie

Rules

685×	`fma-neg_binary64`
565×	`sub-neg_binary64`
284×	`associate--l+_binary64`
259×	`fma-def_binary64`
242×	`associate--r+_binary64`

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	79	1071
1	245	1062
2	806	1046
3	3297	1040

Stop Event

1×	node limit

Counts

211 → 204

prune170.0ms (2.1%)

Pruning

3 alts after pruning (3 fresh and 0 done)

	Pruned	Kept	Total
New	201	3	204
Fresh	1	0	1
Picked	1	0	1
Done	0	0	0
Total	203	3	206

Error

0.0b

Counts

206 → 3

Alt Table

Status	Error	Program
▶	1.9b	(-.f64 (+.f64 (.f64 5/2 (.f64 (pow.f64 wj 2) x)) (+.f64 (pow.f64 wj 2) x)) (+.f64 (.f64 2 (.f64 wj x)) (+.f64 (.f64 8/3 (.f64 (pow.f64 wj 3) x)) (pow.f64 wj 3))))
	6.7b	(fma.f64 (/.f64 x (exp.f64 wj)) (/.f64 1 (+.f64 wj 1)) (neg.f64 (-.f64 (/.f64 wj (+.f64 wj 1)) wj)))
	31.8b	(/.f64 (-.f64 (*.f64 wj wj) (pow.f64 (/.f64 (-.f64 (/.f64 x (exp.f64 wj)) wj) (+.f64 wj 1)) 2)) (-.f64 wj (/.f64 (-.f64 (/.f64 x (exp.f64 wj)) wj) (+.f64 wj 1))))

Compiler

Compiled 4268 to 2053 computations (51.9% saved)

localize18.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.2b	(.f64 5/2 (.f64 (pow.f64 wj 2) x))
✓	0.2b	(-.f64 (+.f64 (.f64 5/2 (.f64 (pow.f64 wj 2) x)) (+.f64 (pow.f64 wj 2) x)) (+.f64 (.f64 2 (.f64 wj x)) (+.f64 (.f64 8/3 (.f64 (pow.f64 wj 3) x)) (pow.f64 wj 3))))
✓	3.5b	(*.f64 (pow.f64 wj 3) x)
✓	7.3b	(*.f64 (pow.f64 wj 2) x)

series57.0ms (0.7%)

Counts

4 → 12

Calls

24 calls:

11.0ms	(-.f64 (+.f64 (.f64 5/2 (.f64 (pow.f64 wj 2) x)) (+.f64 (pow.f64 wj 2) x)) (+.f64 (.f64 2 (.f64 wj x)) (+.f64 (.f64 8/3 (.f64 (pow.f64 wj 3) x)) (pow.f64 wj 3))))	x	-inf
6.0ms	(-.f64 (+.f64 (.f64 5/2 (.f64 (pow.f64 wj 2) x)) (+.f64 (pow.f64 wj 2) x)) (+.f64 (.f64 2 (.f64 wj x)) (+.f64 (.f64 8/3 (.f64 (pow.f64 wj 3) x)) (pow.f64 wj 3))))	x	inf
5.0ms	(-.f64 (+.f64 (.f64 5/2 (.f64 (pow.f64 wj 2) x)) (+.f64 (pow.f64 wj 2) x)) (+.f64 (.f64 2 (.f64 wj x)) (+.f64 (.f64 8/3 (.f64 (pow.f64 wj 3) x)) (pow.f64 wj 3))))	x	0
5.0ms	(-.f64 (+.f64 (.f64 5/2 (.f64 (pow.f64 wj 2) x)) (+.f64 (pow.f64 wj 2) x)) (+.f64 (.f64 2 (.f64 wj x)) (+.f64 (.f64 8/3 (.f64 (pow.f64 wj 3) x)) (pow.f64 wj 3))))	wj	inf
3.0ms	(*.f64 (pow.f64 wj 3) x)	x	-inf

rewrite48.0ms (0.6%)

Algorithm

1×	batch-egg-rewrite

Rules

241×	`add-sqr-sqrt_binary64`
234×	`pow1_binary64`
232×	`*-un-lft-identity_binary64`
228×	`add-log-exp_binary64`
228×	`log1p-expm1-u_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	20	64
1	479	62

Stop Event

1×	node limit

Counts

4 → 67

simplify28.0ms (0.3%)

Algorithm

1×	egg-herbie

Rules

866×	`fma-neg_binary64`
350×	`fma-def_binary64`
242×	`cancel-sign-sub-inv_binary64`
192×	`distribute-rgt-in_binary64`
176×	`sub-neg_binary64`

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	41	263
1	136	241
2	554	219
3	2406	207

Stop Event

1×	node limit

Counts

79 → 83

prune104.0ms (1.3%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	82	1	83
Fresh	0	2	2
Picked	0	1	1
Done	0	0	0
Total	82	4	86

Error

0.0b

Counts

86 → 4

Alt Table

Status	Error	Program
✓	1.9b	(-.f64 (+.f64 (.f64 5/2 (.f64 (pow.f64 wj 2) x)) (+.f64 (pow.f64 wj 2) x)) (+.f64 (.f64 2 (.f64 wj x)) (+.f64 (.f64 8/3 (.f64 (pow.f64 wj 3) x)) (pow.f64 wj 3))))
▶	6.7b	(fma.f64 (/.f64 x (exp.f64 wj)) (/.f64 1 (+.f64 wj 1)) (neg.f64 (-.f64 (/.f64 wj (+.f64 wj 1)) wj)))
	31.8b	(/.f64 (-.f64 (*.f64 wj wj) (pow.f64 (/.f64 (-.f64 (/.f64 x (exp.f64 wj)) wj) (+.f64 wj 1)) 2)) (-.f64 wj (/.f64 (-.f64 (/.f64 x (exp.f64 wj)) wj) (+.f64 wj 1))))
	39.2b	(/.f64 (-.f64 (pow.f64 (fma.f64 (.f64 (.f64 wj wj) x) 5/2 (fma.f64 wj wj x)) 3) (pow.f64 (fma.f64 2 (.f64 wj x) (fma.f64 (.f64 x (pow.f64 wj 3)) 8/3 (pow.f64 wj 3))) 3)) (+.f64 (pow.f64 (fma.f64 (.f64 (.f64 wj wj) x) 5/2 (fma.f64 wj wj x)) 2) (+.f64 (pow.f64 (fma.f64 2 (.f64 wj x) (fma.f64 (.f64 x (pow.f64 wj 3)) 8/3 (pow.f64 wj 3))) 2) (.f64 (fma.f64 (.f64 (.f64 wj wj) x) 5/2 (fma.f64 wj wj x)) (fma.f64 2 (.f64 wj x) (fma.f64 (*.f64 x (pow.f64 wj 3)) 8/3 (pow.f64 wj 3)))))))

Compiler

Compiled 3332 to 1941 computations (41.7% saved)

localize11.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(/.f64 wj (+.f64 wj 1))
✓	0.0b	(fma.f64 (/.f64 x (exp.f64 wj)) (/.f64 1 (+.f64 wj 1)) (neg.f64 (-.f64 (/.f64 wj (+.f64 wj 1)) wj)))
	0.2b	(/.f64 x (exp.f64 wj))
✓	3.5b	(-.f64 (/.f64 wj (+.f64 wj 1)) wj)

series19.0ms (0.2%)

Counts

3 → 48

Calls

12 calls:

3.0ms	(fma.f64 (/.f64 x (exp.f64 wj)) (/.f64 1 (+.f64 wj 1)) (neg.f64 (-.f64 (/.f64 wj (+.f64 wj 1)) wj)))	x	inf
3.0ms	(fma.f64 (/.f64 x (exp.f64 wj)) (/.f64 1 (+.f64 wj 1)) (neg.f64 (-.f64 (/.f64 wj (+.f64 wj 1)) wj)))	x	-inf
3.0ms	(fma.f64 (/.f64 x (exp.f64 wj)) (/.f64 1 (+.f64 wj 1)) (neg.f64 (-.f64 (/.f64 wj (+.f64 wj 1)) wj)))	x	0
2.0ms	(fma.f64 (/.f64 x (exp.f64 wj)) (/.f64 1 (+.f64 wj 1)) (neg.f64 (-.f64 (/.f64 wj (+.f64 wj 1)) wj)))	wj	-inf
1.0ms	(fma.f64 (/.f64 x (exp.f64 wj)) (/.f64 1 (+.f64 wj 1)) (neg.f64 (-.f64 (/.f64 wj (+.f64 wj 1)) wj)))	wj	0

rewrite154.0ms (1.9%)

Algorithm

1×	batch-egg-rewrite

Rules

993×	`prod-diff_binary64`
201×	`egg-rr`
187×	`egg-rr`
137×	`add-sqr-sqrt_binary64`
134×	`*-un-lft-identity_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	12	44
1	265	41
2	3829	41

Stop Event

1×	node limit

Counts

3 → 424

simplify52.0ms (0.6%)

Algorithm

1×	egg-herbie

Rules

465×	`fma-neg_binary64`
413×	`associate-l_binary64`
377×	`sub-neg_binary64`
352×	`associate-r_binary64`
194×	`fma-def_binary64`

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	70	731
1	208	721
2	613	709
3	2141	707

Stop Event

1×	node limit

Counts

472 → 472

prune582.0ms (7%)

Pruning

4 alts after pruning (2 fresh and 2 done)

	Pruned	Kept	Total
New	510	0	510
Fresh	0	2	2
Picked	0	1	1
Done	0	1	1
Total	510	4	514

Error

0.0b

Counts

514 → 4

Alt Table

Status	Error	Program
✓	1.9b	(-.f64 (+.f64 (.f64 5/2 (.f64 (pow.f64 wj 2) x)) (+.f64 (pow.f64 wj 2) x)) (+.f64 (.f64 2 (.f64 wj x)) (+.f64 (.f64 8/3 (.f64 (pow.f64 wj 3) x)) (pow.f64 wj 3))))
✓	6.7b	(fma.f64 (/.f64 x (exp.f64 wj)) (/.f64 1 (+.f64 wj 1)) (neg.f64 (-.f64 (/.f64 wj (+.f64 wj 1)) wj)))
▶	31.8b	(/.f64 (-.f64 (*.f64 wj wj) (pow.f64 (/.f64 (-.f64 (/.f64 x (exp.f64 wj)) wj) (+.f64 wj 1)) 2)) (-.f64 wj (/.f64 (-.f64 (/.f64 x (exp.f64 wj)) wj) (+.f64 wj 1))))
	39.2b	(/.f64 (-.f64 (pow.f64 (fma.f64 (.f64 (.f64 wj wj) x) 5/2 (fma.f64 wj wj x)) 3) (pow.f64 (fma.f64 2 (.f64 wj x) (fma.f64 (.f64 x (pow.f64 wj 3)) 8/3 (pow.f64 wj 3))) 3)) (+.f64 (pow.f64 (fma.f64 (.f64 (.f64 wj wj) x) 5/2 (fma.f64 wj wj x)) 2) (+.f64 (pow.f64 (fma.f64 2 (.f64 wj x) (fma.f64 (.f64 x (pow.f64 wj 3)) 8/3 (pow.f64 wj 3))) 2) (.f64 (fma.f64 (.f64 (.f64 wj wj) x) 5/2 (fma.f64 wj wj x)) (fma.f64 2 (.f64 wj x) (fma.f64 (*.f64 x (pow.f64 wj 3)) 8/3 (pow.f64 wj 3)))))))

Compiler

Compiled 21088 to 12823 computations (39.2% saved)

localize13.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(pow.f64 (/.f64 (-.f64 (/.f64 x (exp.f64 wj)) wj) (+.f64 wj 1)) 2)
	0.2b	(/.f64 x (exp.f64 wj))
✓	2.6b	(-.f64 (*.f64 wj wj) (pow.f64 (/.f64 (-.f64 (/.f64 x (exp.f64 wj)) wj) (+.f64 wj 1)) 2))
✓	18.8b	(/.f64 (-.f64 (*.f64 wj wj) (pow.f64 (/.f64 (-.f64 (/.f64 x (exp.f64 wj)) wj) (+.f64 wj 1)) 2)) (-.f64 wj (/.f64 (-.f64 (/.f64 x (exp.f64 wj)) wj) (+.f64 wj 1))))

series283.0ms (3.4%)

Counts

3 → 72

Calls

18 calls:

97.0ms	(/.f64 (-.f64 (*.f64 wj wj) (pow.f64 (/.f64 (-.f64 (/.f64 x (exp.f64 wj)) wj) (+.f64 wj 1)) 2)) (-.f64 wj (/.f64 (-.f64 (/.f64 x (exp.f64 wj)) wj) (+.f64 wj 1))))	x	inf
96.0ms	(/.f64 (-.f64 (*.f64 wj wj) (pow.f64 (/.f64 (-.f64 (/.f64 x (exp.f64 wj)) wj) (+.f64 wj 1)) 2)) (-.f64 wj (/.f64 (-.f64 (/.f64 x (exp.f64 wj)) wj) (+.f64 wj 1))))	x	-inf
15.0ms	(-.f64 (*.f64 wj wj) (pow.f64 (/.f64 (-.f64 (/.f64 x (exp.f64 wj)) wj) (+.f64 wj 1)) 2))	x	-inf
14.0ms	(/.f64 (-.f64 (*.f64 wj wj) (pow.f64 (/.f64 (-.f64 (/.f64 x (exp.f64 wj)) wj) (+.f64 wj 1)) 2)) (-.f64 wj (/.f64 (-.f64 (/.f64 x (exp.f64 wj)) wj) (+.f64 wj 1))))	x	0
14.0ms	(-.f64 (*.f64 wj wj) (pow.f64 (/.f64 (-.f64 (/.f64 x (exp.f64 wj)) wj) (+.f64 wj 1)) 2))	x	inf

rewrite50.0ms (0.6%)

Algorithm

1×	batch-egg-rewrite

Rules

187×	`add-sqr-sqrt_binary64`
184×	`pow1_binary64`
183×	`*-un-lft-identity_binary64`
176×	`add-log-exp_binary64`
175×	`log1p-expm1-u_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	15	86
1	356	60

Stop Event

1×	node limit

Counts

3 → 100

simplify125.0ms (1.5%)

Algorithm

1×	egg-herbie

Rules

641×	`associate-/r*_binary64`
619×	`associate-/l*_binary64`
551×	`fma-def_binary64`
227×	`associate-*l/_binary64`
183×	`+-commutative_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	495	9555
1	2001	9306

Stop Event

1×	node limit

Counts

172 → 185

prune271.0ms (3.3%)

Pruning

3 alts after pruning (1 fresh and 2 done)

	Pruned	Kept	Total
New	260	1	261
Fresh	1	0	1
Picked	1	0	1
Done	0	2	2
Total	262	3	265

Error

0.0b

Counts

265 → 3

Alt Table

Status	Error	Program
✓	1.9b	(-.f64 (+.f64 (.f64 5/2 (.f64 (pow.f64 wj 2) x)) (+.f64 (pow.f64 wj 2) x)) (+.f64 (.f64 2 (.f64 wj x)) (+.f64 (.f64 8/3 (.f64 (pow.f64 wj 3) x)) (pow.f64 wj 3))))
✓	6.7b	(fma.f64 (/.f64 x (exp.f64 wj)) (/.f64 1 (+.f64 wj 1)) (neg.f64 (-.f64 (/.f64 wj (+.f64 wj 1)) wj)))
	32.4b	(/.f64 (pow.f64 (cbrt.f64 (-.f64 (*.f64 wj wj) (pow.f64 (/.f64 (-.f64 (/.f64 x (exp.f64 wj)) wj) (+.f64 wj 1)) 2))) 3) (-.f64 wj (/.f64 (-.f64 (/.f64 x (exp.f64 wj)) wj) (+.f64 wj 1))))

Compiler

Compiled 15447 to 8199 computations (46.9% saved)

regimes1.4s (16.9%)

Accuracy

Total 0.5b remaining (80.6%)

Threshold costs 0.5b (80.6%)

Counts

221 → 2

Compiler

Compiled 14070 to 9285 computations (34% saved)

bsearch8.0ms (0.1%)

Algorithm

1×	left-value

Calls

1 calls:

0.0ms

(-.f64 wj (/.f64 (-.f64 (*.f64 wj (exp.f64 wj)) x) (+.f64 (exp.f64 wj) (*.f64 wj (exp.f64 wj)))))

Steps

Iters	Point		Range
1.9941353552350148e-22	∈ [	1.9941353552350148e-22	,	1.6666921475170346e-20	]

Compiler

Compiled 18 to 8 computations (55.6% saved)

simplify11.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

73×	`distribute-rgt-neg-in_binary64`
69×	`cancel-sign-sub-inv_binary64`
54×	`distribute-lft-neg-out_binary64`
51×	`neg-sub0_binary64`
51×	`neg-mul-1_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	36	92
1	56	92
2	77	92
3	103	92
4	162	92
5	243	92
6	331	92
7	429	92
8	509	92
9	566	92
10	598	92
11	615	92
12	619	92

Stop Event

1×

saturated

end109.0ms (1.3%)

Stop Event

1×

fuel

Compiler

Compiled 215 to 130 computations (39.5% saved)

Iter	Nodes	Cost
0	36	92
1	56	92
2	77	92
3	103	92
4	162	92
5	243	92
6	331	92
7	429	92
8	509	92
9	566	92
10	598	92
11	615	92
12	619	92

Iter	Nodes	Cost
0	36	92
1	56	92
2	77	92
3	103	92
4	162	92
5	243	92
6	331	92
7	429	92
8	509	92
9	566	92
10	598	92
11	615	92
12	619	92

Details

analyze754.0ms (9.1%)

sample3.8s (45.5%)

preprocess37.0ms (0.4%)

simplify30.0ms (0.4%)

prune3.0ms (0%)

localize7.0ms (0.1%)

series45.0ms (0.5%)

rewrite74.0ms (0.9%)

simplify44.0ms (0.5%)

prune170.0ms (2.1%)

localize18.0ms (0.2%)

series57.0ms (0.7%)

rewrite48.0ms (0.6%)

simplify28.0ms (0.3%)

prune104.0ms (1.3%)

localize11.0ms (0.1%)

series19.0ms (0.2%)

rewrite154.0ms (1.9%)

simplify52.0ms (0.6%)

prune582.0ms (7%)

localize13.0ms (0.2%)

series283.0ms (3.4%)

rewrite50.0ms (0.6%)

simplify125.0ms (1.5%)

prune271.0ms (3.3%)

regimes1.4s (16.9%)

bsearch8.0ms (0.1%)

simplify11.0ms (0.1%)

end109.0ms (1.3%)

Profiling

Iter	Nodes	Cost
0	36	92
1	56	92
2	77	92
3	103	92
4	162	92
5	243	92
6	331	92
7	429	92
8	509	92
9	566	92
10	598	92
11	615	92
12	619	92