Details

analyze7.0ms (0.2%)

Algorithm

1×

Search

True	Other	False	Iter
0%	100%	0%	0
0%	100%	0%	1
0%	100%	0%	2
0%	100%	0%	3
50%	50%	0%	4
75%	25%	0%	5
87.5%	12.5%	0%	6
93.7%	6.2%	0%	7
96.8%	3.1%	0%	8
98.4%	1.6%	0%	9
99.2%	0.8%	0%	10
99.6%	0.4%	0%	11
99.8%	0.2%	0%	12
99.9%	0.1%	0%	13
99.9%	0%	0%	14

Compiler

Compiled 15 to 11 computations (26.7% saved)

sample1.5s (42.8%)

Results

615.0ms	2055×	body	1024	valid
439.0ms	4454×	body	128	valid
247.0ms	1046×	body	512	valid
79.0ms	486×	body	256	valid
77.0ms	215×	body	2048	valid

Compiler

Compiled 30 to 22 computations (26.7% saved)

preprocess98.0ms (2.9%)

Algorithm

2×	egg-herbie

Rules

859×	`fma-neg_binary64`
764×	`fma-def_binary64`
321×	`div-sub_binary64`
169×	`associate-/l*_binary64`
149×	`sub-neg_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	8	19
1	16	19
2	22	19
3	34	19
4	60	19
5	100	19
6	205	19
7	377	19
8	951	19
9	2127	19
10	2751	19
11	3062	19
12	3879	19
13	4173	19
14	4215	19
15	4217	19
16	4219	19
17	4229	19
18	4229	19
0	1	1

Stop Event

1×	saturated
1×	saturated

Compiler

Compiled 14 to 10 computations (28.6% saved)

simplify61.0ms (1.8%)

Algorithm

1×	egg-herbie

Rules

859×	`fma-neg_binary64`
764×	`fma-def_binary64`
321×	`div-sub_binary64`
169×	`associate-/l*_binary64`
149×	`sub-neg_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	8	19
1	16	19
2	22	19
3	34	19
4	60	19
5	100	19
6	205	19
7	377	19
8	951	19
9	2127	19
10	2751	19
11	3062	19
12	3879	19
13	4173	19
14	4215	19
15	4217	19
16	4219	19
17	4229	19
18	4229	19

Stop Event

1×

saturated

Counts

1 → 2

prune2.0ms (0.1%)

Pruning

2 alts after pruning (2 fresh and 0 done)

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

Error

30.5b

Counts

3 → 1

Alt Table

Status	Error	Program
▶	30.5b	(-.f64 (/.f64 x (+.f64 x 1)) (/.f64 (+.f64 x 1) (-.f64 x 1)))

Compiler

Compiled 55 to 39 computations (29.1% saved)

localize6.0ms (0.2%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.0b	(/.f64 x (+.f64 x 1))
✓	0.0b	(/.f64 (+.f64 x 1) (-.f64 x 1))
✓	3.2b	(-.f64 (/.f64 x (+.f64 x 1)) (/.f64 (+.f64 x 1) (-.f64 x 1)))

series7.0ms (0.2%)

Counts

3 → 36

Calls

9 calls:

1.0ms	(-.f64 (/.f64 x (+.f64 x 1)) (/.f64 (+.f64 x 1) (-.f64 x 1)))	x	-inf
1.0ms	(-.f64 (/.f64 x (+.f64 x 1)) (/.f64 (+.f64 x 1) (-.f64 x 1)))	x	inf
1.0ms	(-.f64 (/.f64 x (+.f64 x 1)) (/.f64 (+.f64 x 1) (-.f64 x 1)))	x	0
1.0ms	(/.f64 (+.f64 x 1) (-.f64 x 1))	x	-inf
1.0ms	(/.f64 x (+.f64 x 1))	x	0

rewrite76.0ms (2.2%)

Algorithm

1×	batch-egg-rewrite

Rules

470×	`fma-def_binary64`
286×	`fma-neg_binary64`
267×	`log-div_binary64`
210×	`egg-rr`
174×	`expm1-udef_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	8	36
1	195	36
2	3184	36

Stop Event

1×	node limit

Counts

3 → 210

simplify31.0ms (0.9%)

Algorithm

1×	egg-herbie

Rules

405×	`fma-neg_binary64`
344×	`cancel-sign-sub-inv_binary64`
288×	`fma-def_binary64`
287×	`associate-l_binary64`
233×	`associate-r_binary64`

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	64	475
1	204	443
2	627	430
3	1940	428

Stop Event

1×	node limit

Counts

246 → 250

prune224.0ms (6.5%)

Pruning

4 alts after pruning (4 fresh and 0 done)

	Pruned	Kept	Total
New	246	4	250
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	247	4	251

Error

0.0b

Counts

251 → 4

Alt Table

Status	Error	Program
	30.5b	(-.f64 (log.f64 (+.f64 1 (expm1.f64 (/.f64 x (+.f64 x 1))))) (/.f64 (+.f64 x 1) (-.f64 x 1)))
	30.5b	(fma.f64 (cbrt.f64 (-.f64 (/.f64 x (+.f64 x 1)) (/.f64 (+.f64 x 1) (+.f64 x -1)))) (pow.f64 (cbrt.f64 (-.f64 (/.f64 x (+.f64 x 1)) (/.f64 (+.f64 x 1) (+.f64 x -1)))) 2) (fma.f64 (neg.f64 (cbrt.f64 (/.f64 (+.f64 x 1) (+.f64 x -1)))) (pow.f64 (cbrt.f64 (/.f64 (+.f64 x 1) (+.f64 x -1))) 2) (/.f64 (+.f64 x 1) (+.f64 x -1))))
	31.0b	(+.f64 (/.f64 -3 x) (+.f64 (/.f64 -1 (*.f64 x x)) (/.f64 -3 (pow.f64 x 3))))
▶	30.5b	(/.f64 1 (/.f64 (+.f64 (/.f64 x (+.f64 x 1)) (/.f64 (+.f64 x 1) (+.f64 x -1))) (-.f64 (pow.f64 (/.f64 x (+.f64 x 1)) 2) (pow.f64 (/.f64 (+.f64 x 1) (+.f64 x -1)) 2))))

Compiler

Compiled 6244 to 4601 computations (26.3% saved)

localize11.0ms (0.3%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(+.f64 (/.f64 x (+.f64 x 1)) (/.f64 (+.f64 x 1) (+.f64 x -1)))
✓	0.0b	(/.f64 (+.f64 (/.f64 x (+.f64 x 1)) (/.f64 (+.f64 x 1) (+.f64 x -1))) (-.f64 (pow.f64 (/.f64 x (+.f64 x 1)) 2) (pow.f64 (/.f64 (+.f64 x 1) (+.f64 x -1)) 2)))
✓	0.0b	(pow.f64 (/.f64 x (+.f64 x 1)) 2)
✓	3.2b	(-.f64 (pow.f64 (/.f64 x (+.f64 x 1)) 2) (pow.f64 (/.f64 (+.f64 x 1) (+.f64 x -1)) 2))

series39.0ms (1.1%)

Counts

4 → 48

Calls

12 calls:

28.0ms	(-.f64 (pow.f64 (/.f64 x (+.f64 x 1)) 2) (pow.f64 (/.f64 (+.f64 x 1) (+.f64 x -1)) 2))	x	0
1.0ms	(-.f64 (pow.f64 (/.f64 x (+.f64 x 1)) 2) (pow.f64 (/.f64 (+.f64 x 1) (+.f64 x -1)) 2))	x	inf
1.0ms	(-.f64 (pow.f64 (/.f64 x (+.f64 x 1)) 2) (pow.f64 (/.f64 (+.f64 x 1) (+.f64 x -1)) 2))	x	-inf
1.0ms	(/.f64 (+.f64 (/.f64 x (+.f64 x 1)) (/.f64 (+.f64 x 1) (+.f64 x -1))) (-.f64 (pow.f64 (/.f64 x (+.f64 x 1)) 2) (pow.f64 (/.f64 (+.f64 x 1) (+.f64 x -1)) 2)))	x	-inf
1.0ms	(/.f64 (+.f64 (/.f64 x (+.f64 x 1)) (/.f64 (+.f64 x 1) (+.f64 x -1))) (-.f64 (pow.f64 (/.f64 x (+.f64 x 1)) 2) (pow.f64 (/.f64 (+.f64 x 1) (+.f64 x -1)) 2)))	x	inf

rewrite55.0ms (1.6%)

Algorithm

1×	batch-egg-rewrite

Rules

170×	`egg-rr`
160×	`log1p-expm1-u_binary64`
160×	`expm1-log1p-u_binary64`
159×	`add-sqr-sqrt_binary64`
155×	`add-cbrt-cube_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	14	100
1	331	76

Stop Event

1×	node limit

Counts

4 → 170

simplify41.0ms (1.2%)

Algorithm

1×	egg-herbie

Rules

739×	`fma-neg_binary64`
358×	`fma-def_binary64`
273×	`sub-neg_binary64`
161×	`distribute-rgt-neg-in_binary64`
159×	`distribute-rgt-in_binary64`

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	102	639
1	315	603
2	948	584
3	3052	577

Stop Event

1×	node limit

Counts

218 → 225

prune249.0ms (7.3%)

Pruning

5 alts after pruning (4 fresh and 1 done)

	Pruned	Kept	Total
New	224	1	225
Fresh	0	3	3
Picked	0	1	1
Done	0	0	0
Total	224	5	229

Error

Counts

229 → 5

Alt Table

Status	Error	Program
	30.5b	(-.f64 (log.f64 (+.f64 1 (expm1.f64 (/.f64 x (+.f64 x 1))))) (/.f64 (+.f64 x 1) (-.f64 x 1)))
	30.5b	(fma.f64 (cbrt.f64 (-.f64 (/.f64 x (+.f64 x 1)) (/.f64 (+.f64 x 1) (+.f64 x -1)))) (pow.f64 (cbrt.f64 (-.f64 (/.f64 x (+.f64 x 1)) (/.f64 (+.f64 x 1) (+.f64 x -1)))) 2) (fma.f64 (neg.f64 (cbrt.f64 (/.f64 (+.f64 x 1) (+.f64 x -1)))) (pow.f64 (cbrt.f64 (/.f64 (+.f64 x 1) (+.f64 x -1))) 2) (/.f64 (+.f64 x 1) (+.f64 x -1))))
	31.0b	(+.f64 (/.f64 -3 x) (+.f64 (/.f64 -1 (*.f64 x x)) (/.f64 -3 (pow.f64 x 3))))
✓	30.5b	(/.f64 1 (/.f64 (+.f64 (/.f64 x (+.f64 x 1)) (/.f64 (+.f64 x 1) (+.f64 x -1))) (-.f64 (pow.f64 (/.f64 x (+.f64 x 1)) 2) (pow.f64 (/.f64 (+.f64 x 1) (+.f64 x -1)) 2))))
▶	26.4b	(/.f64 1 (fma.f64 x -1/3 1/9))

Compiler

Compiled 8905 to 6800 computations (23.6% saved)

localize4.0ms (0.1%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.1b	(/.f64 1 (fma.f64 x -1/3 1/9))
✓	0.2b	(fma.f64 x -1/3 1/9)

series6.0ms (0.2%)

Counts

2 → 24

Calls

6 calls:

3.0ms	(/.f64 1 (fma.f64 x -1/3 1/9))	x	-inf
1.0ms	(/.f64 1 (fma.f64 x -1/3 1/9))	x	inf
1.0ms	(/.f64 1 (fma.f64 x -1/3 1/9))	x	0
1.0ms	(fma.f64 x -1/3 1/9)	x	-inf
1.0ms	(fma.f64 x -1/3 1/9)	x	inf

rewrite36.0ms (1%)

Algorithm

1×	batch-egg-rewrite

Rules

530×	`log1p-expm1-u_binary64`
530×	`expm1-log1p-u_binary64`
278×	`unpow-prod-down_binary64`
233×	`log-prod_binary64`
155×	`pow2_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	7	13
1	141	13
2	1480	13

Stop Event

1×	node limit

Counts

2 → 72

simplify26.0ms (0.8%)

Algorithm

1×	egg-herbie

Rules

630×	`fma-neg_binary64`
581×	`times-frac_binary64`
359×	`fma-def_binary64`
355×	`cancel-sign-sub-inv_binary64`
226×	`distribute-neg-frac_binary64`

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	44	267
1	116	253
2	303	232
3	925	225
4	2727	225

Stop Event

1×	node limit

Counts

96 → 91

prune48.0ms (1.4%)

Pruning

5 alts after pruning (3 fresh and 2 done)

	Pruned	Kept	Total
New	91	0	91
Fresh	0	3	3
Picked	0	1	1
Done	0	1	1
Total	91	5	96

Error

Counts

96 → 5

Alt Table

Status	Error	Program
▶	30.5b	(-.f64 (log.f64 (+.f64 1 (expm1.f64 (/.f64 x (+.f64 x 1))))) (/.f64 (+.f64 x 1) (-.f64 x 1)))
	30.5b	(fma.f64 (cbrt.f64 (-.f64 (/.f64 x (+.f64 x 1)) (/.f64 (+.f64 x 1) (+.f64 x -1)))) (pow.f64 (cbrt.f64 (-.f64 (/.f64 x (+.f64 x 1)) (/.f64 (+.f64 x 1) (+.f64 x -1)))) 2) (fma.f64 (neg.f64 (cbrt.f64 (/.f64 (+.f64 x 1) (+.f64 x -1)))) (pow.f64 (cbrt.f64 (/.f64 (+.f64 x 1) (+.f64 x -1))) 2) (/.f64 (+.f64 x 1) (+.f64 x -1))))
	31.0b	(+.f64 (/.f64 -3 x) (+.f64 (/.f64 -1 (*.f64 x x)) (/.f64 -3 (pow.f64 x 3))))
✓	30.5b	(/.f64 1 (/.f64 (+.f64 (/.f64 x (+.f64 x 1)) (/.f64 (+.f64 x 1) (+.f64 x -1))) (-.f64 (pow.f64 (/.f64 x (+.f64 x 1)) 2) (pow.f64 (/.f64 (+.f64 x 1) (+.f64 x -1)) 2))))
✓	26.4b	(/.f64 1 (fma.f64 x -1/3 1/9))

Compiler

Compiled 1282 to 1087 computations (15.2% saved)

localize11.0ms (0.3%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.5b	(+.f64 1 (expm1.f64 (/.f64 x (+.f64 x 1))))
✓	0.5b	(expm1.f64 (/.f64 x (+.f64 x 1)))
✓	1.3b	(log.f64 (+.f64 1 (expm1.f64 (/.f64 x (+.f64 x 1)))))
✓	3.2b	(-.f64 (log.f64 (+.f64 1 (expm1.f64 (/.f64 x (+.f64 x 1))))) (/.f64 (+.f64 x 1) (-.f64 x 1)))

series15.0ms (0.4%)

Counts

4 → 48

Calls

12 calls:

2.0ms	(+.f64 1 (expm1.f64 (/.f64 x (+.f64 x 1))))	x	inf
2.0ms	(-.f64 (log.f64 (+.f64 1 (expm1.f64 (/.f64 x (+.f64 x 1))))) (/.f64 (+.f64 x 1) (-.f64 x 1)))	x	inf
2.0ms	(-.f64 (log.f64 (+.f64 1 (expm1.f64 (/.f64 x (+.f64 x 1))))) (/.f64 (+.f64 x 1) (-.f64 x 1)))	x	-inf
1.0ms	(log.f64 (+.f64 1 (expm1.f64 (/.f64 x (+.f64 x 1)))))	x	inf
1.0ms	(log.f64 (+.f64 1 (expm1.f64 (/.f64 x (+.f64 x 1)))))	x	-inf

rewrite84.0ms (2.5%)

Algorithm

1×	batch-egg-rewrite

Rules

567×	`fma-def_binary64`
350×	`fma-neg_binary64`
255×	`egg-rr`
209×	`expm1-udef_binary64`
208×	`log1p-udef_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	11	44
1	243	44
2	3663	44

Stop Event

1×	node limit

Counts

4 → 255

simplify38.0ms (1.1%)

Algorithm

1×	egg-herbie

Rules

431×	`cancel-sign-sub-inv_binary64`
425×	`fma-neg_binary64`
289×	`fma-def_binary64`
279×	`sub-neg_binary64`
214×	`associate-/r*_binary64`

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	85	696
1	255	659
2	713	616
3	2297	607

Stop Event

1×	node limit

Counts

303 → 309

prune280.0ms (8.2%)

Pruning

5 alts after pruning (2 fresh and 3 done)

	Pruned	Kept	Total
New	309	0	309
Fresh	0	2	2
Picked	0	1	1
Done	0	2	2
Total	309	5	314

Error

Counts

314 → 5

Alt Table

Status	Error	Program
✓	30.5b	(-.f64 (log.f64 (+.f64 1 (expm1.f64 (/.f64 x (+.f64 x 1))))) (/.f64 (+.f64 x 1) (-.f64 x 1)))
	30.5b	(fma.f64 (cbrt.f64 (-.f64 (/.f64 x (+.f64 x 1)) (/.f64 (+.f64 x 1) (+.f64 x -1)))) (pow.f64 (cbrt.f64 (-.f64 (/.f64 x (+.f64 x 1)) (/.f64 (+.f64 x 1) (+.f64 x -1)))) 2) (fma.f64 (neg.f64 (cbrt.f64 (/.f64 (+.f64 x 1) (+.f64 x -1)))) (pow.f64 (cbrt.f64 (/.f64 (+.f64 x 1) (+.f64 x -1))) 2) (/.f64 (+.f64 x 1) (+.f64 x -1))))
	31.0b	(+.f64 (/.f64 -3 x) (+.f64 (/.f64 -1 (*.f64 x x)) (/.f64 -3 (pow.f64 x 3))))
✓	30.5b	(/.f64 1 (/.f64 (+.f64 (/.f64 x (+.f64 x 1)) (/.f64 (+.f64 x 1) (+.f64 x -1))) (-.f64 (pow.f64 (/.f64 x (+.f64 x 1)) 2) (pow.f64 (/.f64 (+.f64 x 1) (+.f64 x -1)) 2))))
✓	26.4b	(/.f64 1 (fma.f64 x -1/3 1/9))

Compiler

Compiled 7709 to 5756 computations (25.3% saved)

regimes336.0ms (9.8%)

Accuracy

Total 0.0b remaining (45.7%)

Threshold costs 0.0b (45.7%)

Counts

131 → 3

Compiler

Compiled 4444 to 3374 computations (24.1% saved)

bsearch40.0ms (1.2%)

Algorithm

2×	binary-search

Calls

2 calls:

19.0ms	x
17.0ms	x

Steps

Iters	Point		Range
443381.0077497065	∈ [	114.16695661632089	,	8.702577025547048e+20	]
-10731.07214304758	∈ [	-129912705.965539	,	-48.08906437878235	]

Compiler

Compiled 2 to 1 computations (50% saved)

simplify4.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

10×	`+-commutative_binary64`
5×	`sub-neg_binary64`
3×	`*-commutative_binary64`
3×	`neg-sub0_binary64`
3×	`neg-mul-1_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	34	96
1	45	96
2	53	96
3	61	96
4	65	96
5	66	96

Stop Event

1×

saturated

end126.0ms (3.7%)

Stop Event

1×

fuel

Compiler

Compiled 266 to 201 computations (24.4% saved)

Details

analyze7.0ms (0.2%)

sample1.5s (42.8%)

preprocess98.0ms (2.9%)

simplify61.0ms (1.8%)

prune2.0ms (0.1%)

localize6.0ms (0.2%)

series7.0ms (0.2%)

rewrite76.0ms (2.2%)

simplify31.0ms (0.9%)

prune224.0ms (6.5%)

localize11.0ms (0.3%)

series39.0ms (1.1%)

rewrite55.0ms (1.6%)

simplify41.0ms (1.2%)

prune249.0ms (7.3%)

localize4.0ms (0.1%)

series6.0ms (0.2%)

rewrite36.0ms (1%)

simplify26.0ms (0.8%)

prune48.0ms (1.4%)

localize11.0ms (0.3%)

series15.0ms (0.4%)

rewrite84.0ms (2.5%)

simplify38.0ms (1.1%)

prune280.0ms (8.2%)

regimes336.0ms (9.8%)

bsearch40.0ms (1.2%)

simplify4.0ms (0.1%)

end126.0ms (3.7%)

Profiling