Details

analyze6.0ms (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
75%	25%	0%	4
87.5%	12.5%	0%	5
93.7%	6.2%	0%	6
96.8%	3.1%	0%	7
98.4%	1.6%	0%	8
99.2%	0.8%	0%	9
99.6%	0.4%	0%	10
99.8%	0.2%	0%	11
99.9%	0.1%	0%	12
99.9%	0%	0%	13
99.9%	0%	0%	14

Compiler

Compiled 15 to 11 computations (26.7% saved)

sample1.6s (49.4%)

Results

653.0ms	2073×	body	1024	valid
439.0ms	4439×	body	128	valid
231.0ms	995×	body	512	valid
90.0ms	218×	body	2048	valid
87.0ms	531×	body	256	valid

Compiler

Compiled 44 to 32 computations (27.3% saved)

simplify62.0ms (1.9%)

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

31.7b

Counts

3 → 1

Alt Table

Status	Error	Program
▶	31.7b	(-.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))
✓	2.7b	(-.f64 (/.f64 x (+.f64 x 1)) (/.f64 (+.f64 x 1) (-.f64 x 1)))

series7.0ms (0.2%)

Counts

3 → 36

Calls

3 calls:

3.0ms	(-.f64 (/.f64 x (+.f64 x 1)) (/.f64 (+.f64 x 1) (-.f64 x 1)))
2.0ms	(/.f64 (+.f64 x 1) (-.f64 x 1))
2.0ms	(/.f64 x (+.f64 x 1))

rewrite74.0ms (2.3%)

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

Calls

3 calls:

70.0ms	(/.f64 x (+.f64 x 1))
70.0ms	(/.f64 (+.f64 x 1) (-.f64 x 1))
70.0ms	(-.f64 (/.f64 x (+.f64 x 1)) (/.f64 (+.f64 x 1) (-.f64 x 1)))

simplify33.0ms (1%)

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

prune223.0ms (7%)

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
▶	29.5b	(+.f64 (/.f64 -1 (*.f64 x x)) (+.f64 (/.f64 -3 (pow.f64 x 3)) (+.f64 (/.f64 -3 x) (/.f64 -1 (pow.f64 x 4)))))
	31.3b	(/.f64 (-.f64 (.f64 (neg.f64 x) (/.f64 (+.f64 x -1) (+.f64 x 1))) (.f64 (fma.f64 -1 x -1) 1)) (*.f64 (fma.f64 -1 x -1) (/.f64 (+.f64 x -1) (+.f64 x 1))))
	31.7b	(-.f64 (log.f64 (exp.f64 (/.f64 x (+.f64 x 1)))) (/.f64 (+.f64 x 1) (-.f64 x 1)))
	34.7b	(+.f64 1 (+.f64 (pow.f64 x 2) (+.f64 (.f64 3 x) (.f64 3 (pow.f64 x 3)))))

Compiler

Compiled 6160 to 4539 computations (26.3% saved)

localize13.0ms (0.4%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.2b	(/.f64 -3 (pow.f64 x 3))
✓	0.3b	(/.f64 -1 (pow.f64 x 4))
✓	0.3b	(/.f64 -1 (*.f64 x x))
✓	10.5b	(+.f64 (/.f64 -3 (pow.f64 x 3)) (+.f64 (/.f64 -3 x) (/.f64 -1 (pow.f64 x 4))))

series11.0ms (0.3%)

Counts

4 → 24

Calls

4 calls:

3.0ms	(+.f64 (/.f64 -3 (pow.f64 x 3)) (+.f64 (/.f64 -3 x) (/.f64 -1 (pow.f64 x 4))))
3.0ms	(/.f64 -1 (pow.f64 x 4))
3.0ms	(/.f64 -3 (pow.f64 x 3))
2.0ms	(/.f64 -1 (*.f64 x x))

rewrite46.0ms (1.4%)

Algorithm

1×	batch-egg-rewrite

Rules

164×	`log1p-expm1-u_binary64`
164×	`expm1-log1p-u_binary64`
163×	`add-sqr-sqrt_binary64`
162×	`add-cbrt-cube_binary64`
156×	`add-cube-cbrt_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	15	43
1	353	37

Stop Event

1×	node limit

Counts

4 → 125

Calls

4 calls:

43.0ms	(/.f64 -3 (pow.f64 x 3))
43.0ms	(/.f64 -1 (pow.f64 x 4))
43.0ms	(/.f64 -1 (*.f64 x x))
43.0ms	(+.f64 (/.f64 -3 (pow.f64 x 3)) (+.f64 (/.f64 -3 x) (/.f64 -1 (pow.f64 x 4))))

simplify29.0ms (0.9%)

Algorithm

1×	egg-herbie

Rules

657×	`times-frac_binary64`
389×	`fma-neg_binary64`
326×	`associate-/l/_binary64`
310×	`associate-*l/_binary64`
297×	`associate-/l*_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	25	291
1	65	273
2	170	273
3	425	273
4	1319	273

Stop Event

1×	node limit

Counts

149 → 135

prune116.0ms (3.6%)

Pruning

5 alts after pruning (4 fresh and 1 done)

	Pruned	Kept	Total
New	134	1	135
Fresh	0	3	3
Picked	0	1	1
Done	0	0	0
Total	134	5	139

Error

0.0b

Counts

139 → 5

Alt Table

Status	Error	Program
✓	29.5b	(+.f64 (/.f64 -1 (*.f64 x x)) (+.f64 (/.f64 -3 (pow.f64 x 3)) (+.f64 (/.f64 -3 x) (/.f64 -1 (pow.f64 x 4)))))
▶	31.3b	(/.f64 (-.f64 (.f64 (neg.f64 x) (/.f64 (+.f64 x -1) (+.f64 x 1))) (.f64 (fma.f64 -1 x -1) 1)) (*.f64 (fma.f64 -1 x -1) (/.f64 (+.f64 x -1) (+.f64 x 1))))
	45.1b	(+.f64 (/.f64 -1 (.f64 x x)) (.f64 (-.f64 (/.f64 9 (pow.f64 x 6)) (pow.f64 (fma.f64 -1 (pow.f64 x -4) (/.f64 -3 x)) 2)) (/.f64 1 (-.f64 (*.f64 -3 (pow.f64 x -3)) (fma.f64 -1 (pow.f64 x -4) (/.f64 -3 x))))))
	31.7b	(-.f64 (log.f64 (exp.f64 (/.f64 x (+.f64 x 1)))) (/.f64 (+.f64 x 1) (-.f64 x 1)))
	34.7b	(+.f64 1 (+.f64 (pow.f64 x 2) (+.f64 (.f64 3 x) (.f64 3 (pow.f64 x 3)))))

Compiler

Compiled 4105 to 3082 computations (24.9% saved)

localize13.0ms (0.4%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(*.f64 (fma.f64 -1 x -1) (/.f64 (+.f64 x -1) (+.f64 x 1)))
✓	0.0b	(*.f64 (neg.f64 x) (/.f64 (+.f64 x -1) (+.f64 x 1)))
✓	0.0b	(/.f64 (-.f64 (.f64 (neg.f64 x) (/.f64 (+.f64 x -1) (+.f64 x 1))) (.f64 (fma.f64 -1 x -1) 1)) (*.f64 (fma.f64 -1 x -1) (/.f64 (+.f64 x -1) (+.f64 x 1))))
✓	2.2b	(-.f64 (.f64 (neg.f64 x) (/.f64 (+.f64 x -1) (+.f64 x 1))) (.f64 (fma.f64 -1 x -1) 1))

series12.0ms (0.4%)

Counts

4 → 48

Calls

4 calls:

4.0ms	(*.f64 (fma.f64 -1 x -1) (/.f64 (+.f64 x -1) (+.f64 x 1)))
3.0ms	(/.f64 (-.f64 (.f64 (neg.f64 x) (/.f64 (+.f64 x -1) (+.f64 x 1))) (.f64 (fma.f64 -1 x -1) 1)) (*.f64 (fma.f64 -1 x -1) (/.f64 (+.f64 x -1) (+.f64 x 1))))
3.0ms	(-.f64 (.f64 (neg.f64 x) (/.f64 (+.f64 x -1) (+.f64 x 1))) (.f64 (fma.f64 -1 x -1) 1))
2.0ms	(*.f64 (neg.f64 x) (/.f64 (+.f64 x -1) (+.f64 x 1)))

rewrite47.0ms (1.5%)

Algorithm

1×	batch-egg-rewrite

Rules

179×	`egg-rr`
153×	`add-sqr-sqrt_binary64`
147×	`log1p-expm1-u_binary64`
147×	`expm1-log1p-u_binary64`
144×	`add-cbrt-cube_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	14	95
1	340	53

Stop Event

1×	node limit

Counts

4 → 179

Calls

4 calls:

43.0ms	(*.f64 (fma.f64 -1 x -1) (/.f64 (+.f64 x -1) (+.f64 x 1)))
43.0ms	(*.f64 (neg.f64 x) (/.f64 (+.f64 x -1) (+.f64 x 1)))
43.0ms	(/.f64 (-.f64 (.f64 (neg.f64 x) (/.f64 (+.f64 x -1) (+.f64 x 1))) (.f64 (fma.f64 -1 x -1) 1)) (*.f64 (fma.f64 -1 x -1) (/.f64 (+.f64 x -1) (+.f64 x 1))))
43.0ms	(-.f64 (.f64 (neg.f64 x) (/.f64 (+.f64 x -1) (+.f64 x 1))) (.f64 (fma.f64 -1 x -1) 1))

simplify31.0ms (1%)

Algorithm

1×	egg-herbie

Rules

415×	`fma-neg_binary64`
351×	`cancel-sign-sub-inv_binary64`
288×	`fma-def_binary64`
270×	`associate-l_binary64`
241×	`associate-r_binary64`

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	62	502
1	201	475
2	595	457
3	1871	456

Stop Event

1×	node limit

Counts

227 → 220

prune178.0ms (5.5%)

Pruning

5 alts after pruning (3 fresh and 2 done)

	Pruned	Kept	Total
New	220	0	220
Fresh	0	3	3
Picked	0	1	1
Done	0	1	1
Total	220	5	225

Error

0.0b

Counts

225 → 5

Alt Table

Status	Error	Program
✓	29.5b	(+.f64 (/.f64 -1 (*.f64 x x)) (+.f64 (/.f64 -3 (pow.f64 x 3)) (+.f64 (/.f64 -3 x) (/.f64 -1 (pow.f64 x 4)))))
✓	31.3b	(/.f64 (-.f64 (.f64 (neg.f64 x) (/.f64 (+.f64 x -1) (+.f64 x 1))) (.f64 (fma.f64 -1 x -1) 1)) (*.f64 (fma.f64 -1 x -1) (/.f64 (+.f64 x -1) (+.f64 x 1))))
	45.1b	(+.f64 (/.f64 -1 (.f64 x x)) (.f64 (-.f64 (/.f64 9 (pow.f64 x 6)) (pow.f64 (fma.f64 -1 (pow.f64 x -4) (/.f64 -3 x)) 2)) (/.f64 1 (-.f64 (*.f64 -3 (pow.f64 x -3)) (fma.f64 -1 (pow.f64 x -4) (/.f64 -3 x))))))
▶	31.7b	(-.f64 (log.f64 (exp.f64 (/.f64 x (+.f64 x 1)))) (/.f64 (+.f64 x 1) (-.f64 x 1)))
	34.7b	(+.f64 1 (+.f64 (pow.f64 x 2) (+.f64 (.f64 3 x) (.f64 3 (pow.f64 x 3)))))

Compiler

Compiled 6419 to 4703 computations (26.7% saved)

localize9.0ms (0.3%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(exp.f64 (/.f64 x (+.f64 x 1)))
	0.0b	(/.f64 (+.f64 x 1) (-.f64 x 1))
✓	2.7b	(-.f64 (log.f64 (exp.f64 (/.f64 x (+.f64 x 1)))) (/.f64 (+.f64 x 1) (-.f64 x 1)))
✓	2.8b	(log.f64 (exp.f64 (/.f64 x (+.f64 x 1))))

series11.0ms (0.3%)

Counts

3 → 36

Calls

3 calls:

6.0ms	(exp.f64 (/.f64 x (+.f64 x 1)))
3.0ms	(-.f64 (log.f64 (exp.f64 (/.f64 x (+.f64 x 1)))) (/.f64 (+.f64 x 1) (-.f64 x 1)))
2.0ms	(log.f64 (exp.f64 (/.f64 x (+.f64 x 1))))

rewrite70.0ms (2.2%)

Algorithm

1×	batch-egg-rewrite

Rules

427×	`fma-def_binary64`
281×	`fma-neg_binary64`
242×	`log-div_binary64`
203×	`egg-rr`
184×	`expm1-udef_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	10	35
1	213	35
2	3197	35

Stop Event

1×	node limit

Counts

3 → 203

Calls

3 calls:

66.0ms	(exp.f64 (/.f64 x (+.f64 x 1)))
66.0ms	(-.f64 (log.f64 (exp.f64 (/.f64 x (+.f64 x 1)))) (/.f64 (+.f64 x 1) (-.f64 x 1)))
66.0ms	(log.f64 (exp.f64 (/.f64 x (+.f64 x 1))))

simplify36.0ms (1.1%)

Algorithm

1×	egg-herbie

Rules

325×	`fma-neg_binary64`
311×	`cancel-sign-sub-inv_binary64`
233×	`associate-l_binary64`
216×	`associate-/r*_binary64`
212×	`fma-def_binary64`

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	64	502
1	186	471
2	563	448
3	1833	443

Stop Event

1×	node limit

Counts

239 → 244

prune203.0ms (6.4%)

Pruning

5 alts after pruning (2 fresh and 3 done)

	Pruned	Kept	Total
New	290	1	291
Fresh	1	1	2
Picked	0	1	1
Done	0	2	2
Total	291	5	296

Error

0.0b

Counts

296 → 5

Alt Table

Status	Error	Program
	34.7b	(fma.f64 x (+.f64 x 3) (fma.f64 3 (pow.f64 x 3) 1))
✓	29.5b	(+.f64 (/.f64 -1 (*.f64 x x)) (+.f64 (/.f64 -3 (pow.f64 x 3)) (+.f64 (/.f64 -3 x) (/.f64 -1 (pow.f64 x 4)))))
✓	31.3b	(/.f64 (-.f64 (.f64 (neg.f64 x) (/.f64 (+.f64 x -1) (+.f64 x 1))) (.f64 (fma.f64 -1 x -1) 1)) (*.f64 (fma.f64 -1 x -1) (/.f64 (+.f64 x -1) (+.f64 x 1))))
	45.1b	(+.f64 (/.f64 -1 (.f64 x x)) (.f64 (-.f64 (/.f64 9 (pow.f64 x 6)) (pow.f64 (fma.f64 -1 (pow.f64 x -4) (/.f64 -3 x)) 2)) (/.f64 1 (-.f64 (*.f64 -3 (pow.f64 x -3)) (fma.f64 -1 (pow.f64 x -4) (/.f64 -3 x))))))
✓	31.7b	(-.f64 (log.f64 (exp.f64 (/.f64 x (+.f64 x 1)))) (/.f64 (+.f64 x 1) (-.f64 x 1)))

Compiler

Compiled 6904 to 5144 computations (25.5% saved)

regimes197.0ms (6.2%)

Accuracy

Total 0.0b remaining (33.5%)

Threshold costs 0.0b (33.5%)

Counts

70 → 3

Compiler

Compiled 2566 to 1934 computations (24.6% saved)

bsearch38.0ms (1.2%)

Steps

Iters	Range		Point
8	51.30456041676415	34216.05202029802	2060.25424106069
10	-467743497.6302302	-0.00010000226361996492	-2722.4750697981704

Compiler

Compiled 2 to 1 computations (50% saved)

simplify5.0ms (0.2%)

Algorithm

1×	egg-herbie

Rules

16×	`+-commutative_binary64`
10×	`*-commutative_binary64`
10×	`sub-neg_binary64`
8×	`neg-sub0_binary64`
8×	`neg-mul-1_binary64`

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	34	96
1	56	96
2	75	96
3	93	94
4	105	94
5	111	94
6	113	94

Stop Event

1×

saturated

end140.0ms (4.4%)

Compiler: Compiled 251 to 188 computations (25.1% saved)

Details

analyze6.0ms (0.2%)

sample1.6s (49.4%)

simplify62.0ms (1.9%)

prune2.0ms (0.1%)

localize6.0ms (0.2%)

series7.0ms (0.2%)

rewrite74.0ms (2.3%)

simplify33.0ms (1%)

prune223.0ms (7%)

localize13.0ms (0.4%)

series11.0ms (0.3%)

rewrite46.0ms (1.4%)

simplify29.0ms (0.9%)

prune116.0ms (3.6%)

localize13.0ms (0.4%)

series12.0ms (0.4%)

rewrite47.0ms (1.5%)

simplify31.0ms (1%)

prune178.0ms (5.5%)

localize9.0ms (0.3%)

series11.0ms (0.3%)

rewrite70.0ms (2.2%)

simplify36.0ms (1.1%)

prune203.0ms (6.4%)

regimes197.0ms (6.2%)

bsearch38.0ms (1.2%)

simplify5.0ms (0.2%)

end140.0ms (4.4%)

Profiling