Details

analyze366.0ms (9.7%)

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%	74.9%	25.1%	6
6.2%	68.6%	25.1%	7
9.4%	65.5%	25.1%	8
14%	35.9%	50.1%	9
21.1%	28.9%	50.1%	10
24.6%	25.4%	50.1%	11
28.7%	21.3%	50.1%	12
33.4%	16.5%	50.1%	13
35.8%	14.1%	50.1%	14

Compiler

Compiled 16 to 11 computations (31.3% saved)

sample1.1s (29%)

Results

1.0s	8255×	body	128	valid
4.0ms	39×	body	128	invalid
0.0ms	1×	body	256	valid

Compiler

Compiled 47 to 32 computations (31.9% saved)

simplify35.0ms (0.9%)

Algorithm

1×	egg-herbie

Rules

780×	`fma-neg_binary64`
402×	`fma-def_binary64`
312×	`cancel-sign-sub-inv_binary64`
267×	`sub-neg_binary64`
242×	`unsub-neg_binary64`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	11	18
1	25	18
2	77	16
3	312	16
4	947	16
5	2808	16
6	4404	16
7	4894	16

Stop Event

1×	node limit

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

0.1b

Counts

3 → 2

Alt Table

Status	Error	Program
	0.1b	(-.f64 (+.f64 (-.f64 x (*.f64 (+.f64 y 1/2) (log.f64 y))) y) z)
▶	0.1b	(+.f64 (fma.f64 (log.f64 y) (-.f64 -1/2 y) y) (-.f64 x z))

Compiler

Compiled 84 to 53 computations (36.9% saved)

localize7.0ms (0.2%)

Local error

Found 1 expressions with local error:

New	Error	Program
✓	0.1b	(fma.f64 (log.f64 y) (-.f64 -1/2 y) y)

series8.0ms (0.2%)

Counts

1 → 12

Calls

1 calls:

8.0ms

(fma.f64 (log.f64 y) (-.f64 -1/2 y) y)

rewrite39.0ms (1%)

Algorithm

1×	batch-egg-rewrite

Rules

641×	`log1p-expm1-u_binary64`
641×	`expm1-log1p-u_binary64`
278×	`log-prod_binary64`
119×	`expm1-udef_binary64`
119×	`log1p-udef_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	6	10
1	130	10
2	1636	10

Stop Event

1×	node limit

Counts

1 → 29

Calls

1 calls:

38.0ms

(fma.f64 (log.f64 y) (-.f64 -1/2 y) y)

simplify22.0ms (0.6%)

Algorithm

1×	egg-herbie

Rules

631×	`fma-neg_binary64`
356×	`distribute-rgt-in_binary64`
347×	`associate--r+_binary64`
304×	`fma-def_binary64`
292×	`distribute-lft-in_binary64`

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	35	136
1	92	132
2	246	132
3	667	114
4	2128	114

Stop Event

1×	node limit

Counts

41 → 37

prune35.0ms (0.9%)

Pruning

5 alts after pruning (4 fresh and 1 done)

	Pruned	Kept	Total
New	34	3	37
Fresh	0	1	1
Picked	0	1	1
Done	0	0	0
Total	34	5	39

Error

0.0b

Counts

39 → 5

Alt Table

Status	Error	Program
▶	0.1b	(-.f64 (+.f64 (-.f64 x (*.f64 (+.f64 y 1/2) (log.f64 y))) y) z)
	18.3b	(+.f64 (/.f64 (-.f64 (.f64 (.f64 (log.f64 y) (-.f64 -1/2 y)) (.f64 (log.f64 y) (-.f64 -1/2 y))) (.f64 y y)) (-.f64 (*.f64 (log.f64 y) (-.f64 -1/2 y)) y)) (-.f64 x z))
	24.3b	(+.f64 (/.f64 (+.f64 (pow.f64 (.f64 (log.f64 y) (-.f64 -1/2 y)) 3) (pow.f64 y 3)) (fma.f64 (.f64 (log.f64 y) (-.f64 -1/2 y)) (.f64 (log.f64 y) (-.f64 -1/2 y)) (-.f64 (.f64 y y) (.f64 (.f64 (log.f64 y) (-.f64 -1/2 y)) y)))) (-.f64 x z))
	0.5b	(+.f64 (*.f64 (cbrt.f64 (fma.f64 (log.f64 y) (-.f64 -1/2 y) y)) (pow.f64 (cbrt.f64 (fma.f64 (log.f64 y) (-.f64 -1/2 y) y)) 2)) (-.f64 x z))
✓	0.1b	(+.f64 (fma.f64 (log.f64 y) (-.f64 -1/2 y) y) (-.f64 x z))

Compiler

Compiled 882 to 488 computations (44.7% saved)

localize12.0ms (0.3%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.0b	(-.f64 x (*.f64 (+.f64 y 1/2) (log.f64 y)))
✓	0.1b	(+.f64 (-.f64 x (*.f64 (+.f64 y 1/2) (log.f64 y))) y)
✓	0.2b	(*.f64 (+.f64 y 1/2) (log.f64 y))

series152.0ms (4%)

Counts

3 → 60

Calls

3 calls:

76.0ms	(-.f64 x (*.f64 (+.f64 y 1/2) (log.f64 y)))
69.0ms	(+.f64 (-.f64 x (*.f64 (+.f64 y 1/2) (log.f64 y))) y)
7.0ms	(*.f64 (+.f64 y 1/2) (log.f64 y))

rewrite74.0ms (2%)

Algorithm

1×	batch-egg-rewrite

Rules

556×	`fma-def_binary64`
302×	`fma-neg_binary64`
199×	`expm1-udef_binary64`
199×	`log1p-udef_binary64`
183×	`egg-rr`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	9	36
1	212	36
2	3141	36

Stop Event

1×	node limit

Counts

3 → 183

Calls

3 calls:

70.0ms	(-.f64 x (*.f64 (+.f64 y 1/2) (log.f64 y)))
70.0ms	(+.f64 (-.f64 x (*.f64 (+.f64 y 1/2) (log.f64 y))) y)
70.0ms	(*.f64 (+.f64 y 1/2) (log.f64 y))

simplify53.0ms (1.4%)

Algorithm

1×	egg-herbie

Rules

738×	`fma-def_binary64`
651×	`sub-neg_binary64`
296×	`associate--l+_binary64`
252×	`fma-neg_binary64`
242×	`associate--r+_binary64`

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	53	676
1	173	672
2	535	658
3	1550	584
4	4376	584

Stop Event

1×	node limit

Counts

243 → 213

prune208.0ms (5.5%)

Pruning

8 alts after pruning (6 fresh and 2 done)

	Pruned	Kept	Total
New	209	4	213
Fresh	1	2	3
Picked	0	1	1
Done	0	1	1
Total	210	8	218

Error

0.0b

Counts

218 → 8

Alt Table

Status	Error	Program
✓	0.1b	(-.f64 (+.f64 (-.f64 x (*.f64 (+.f64 y 1/2) (log.f64 y))) y) z)
	31.5b	(-.f64 (+.f64 (fma.f64 (*.f64 (+.f64 (neg.f64 y) -1/2) (sqrt.f64 (log.f64 y))) (sqrt.f64 (log.f64 y)) x) y) z)
▶	0.5b	(-.f64 (+.f64 (fma.f64 (*.f64 (+.f64 (neg.f64 y) -1/2) (pow.f64 (cbrt.f64 (log.f64 y)) 2)) (cbrt.f64 (log.f64 y)) x) y) z)
	18.3b	(+.f64 (/.f64 (-.f64 (.f64 (.f64 (log.f64 y) (-.f64 -1/2 y)) (.f64 (log.f64 y) (-.f64 -1/2 y))) (.f64 y y)) (-.f64 (*.f64 (log.f64 y) (-.f64 -1/2 y)) y)) (-.f64 x z))
	0.5b	(+.f64 (*.f64 (cbrt.f64 (fma.f64 (log.f64 y) (-.f64 -1/2 y) y)) (pow.f64 (cbrt.f64 (fma.f64 (log.f64 y) (-.f64 -1/2 y) y)) 2)) (-.f64 x z))
	17.8b	(-.f64 (+.f64 (-.f64 x (/.f64 (*.f64 (fma.f64 y y -1/4) (log.f64 y)) (+.f64 y -1/2))) y) z)
	24.0b	(-.f64 (+.f64 (-.f64 x (/.f64 (.f64 (+.f64 1/8 (pow.f64 y 3)) (log.f64 y)) (-.f64 (fma.f64 y y 1/4) (.f64 y 1/2)))) y) z)
✓	0.1b	(+.f64 (fma.f64 (log.f64 y) (-.f64 -1/2 y) y) (-.f64 x z))

Compiler

Compiled 4815 to 2976 computations (38.2% saved)

localize12.0ms (0.3%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.1b	(*.f64 (+.f64 (neg.f64 y) -1/2) (pow.f64 (cbrt.f64 (log.f64 y)) 2))
✓	0.2b	(fma.f64 (*.f64 (+.f64 (neg.f64 y) -1/2) (pow.f64 (cbrt.f64 (log.f64 y)) 2)) (cbrt.f64 (log.f64 y)) x)
✓	0.5b	(pow.f64 (cbrt.f64 (log.f64 y)) 2)
✓	0.5b	(cbrt.f64 (log.f64 y))

series345.0ms (9.1%)

Counts

4 → 60

Calls

4 calls:

163.0ms	(fma.f64 (*.f64 (+.f64 (neg.f64 y) -1/2) (pow.f64 (cbrt.f64 (log.f64 y)) 2)) (cbrt.f64 (log.f64 y)) x)
76.0ms	(pow.f64 (cbrt.f64 (log.f64 y)) 2)
75.0ms	(cbrt.f64 (log.f64 y))
31.0ms	(*.f64 (+.f64 (neg.f64 y) -1/2) (pow.f64 (cbrt.f64 (log.f64 y)) 2))

rewrite57.0ms (1.5%)

Algorithm

1×	batch-egg-rewrite

Rules

481×	`log-prod_binary64`
195×	`expm1-udef_binary64`
195×	`log1p-udef_binary64`
169×	`log-pow_binary64`
164×	`prod-diff_binary64`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	12	53
1	252	39
2	3052	37

Stop Event

1×	node limit

Counts

4 → 106

Calls

4 calls:

55.0ms	(*.f64 (+.f64 (neg.f64 y) -1/2) (pow.f64 (cbrt.f64 (log.f64 y)) 2))
55.0ms	(fma.f64 (*.f64 (+.f64 (neg.f64 y) -1/2) (pow.f64 (cbrt.f64 (log.f64 y)) 2)) (cbrt.f64 (log.f64 y)) x)
55.0ms	(pow.f64 (cbrt.f64 (log.f64 y)) 2)
55.0ms	(cbrt.f64 (log.f64 y))

simplify39.0ms (1%)

Algorithm

1×	egg-herbie

Rules

606×	`fma-def_binary64`
372×	`cancel-sign-sub-inv_binary64`
288×	`distribute-rgt-in_binary64`
243×	`distribute-lft-in_binary64`
203×	`fma-neg_binary64`

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	67	699
1	212	687
2	611	643
3	2015	611

Stop Event

1×	node limit

Counts

166 → 137

prune210.0ms (5.5%)

Pruning

8 alts after pruning (7 fresh and 1 done)

	Pruned	Kept	Total
New	164	3	167
Fresh	1	4	5
Picked	1	0	1
Done	1	1	2
Total	167	8	175

Error

0.0b

Counts

175 → 8

Alt Table

Status	Error	Program
	18.3b	(+.f64 (/.f64 (-.f64 (.f64 (.f64 (log.f64 y) (-.f64 -1/2 y)) (.f64 (log.f64 y) (-.f64 -1/2 y))) (.f64 y y)) (-.f64 (*.f64 (log.f64 y) (-.f64 -1/2 y)) y)) (-.f64 x z))
	31.6b	(-.f64 (+.f64 (fma.f64 (*.f64 (+.f64 (neg.f64 y) -1/2) (pow.f64 (cbrt.f64 (log.f64 y)) 2)) (expm1.f64 (log1p.f64 (cbrt.f64 (log.f64 y)))) x) y) z)
	31.5b	(-.f64 (+.f64 (fma.f64 (*.f64 (+.f64 (neg.f64 y) -1/2) (sqrt.f64 (log.f64 y))) (sqrt.f64 (log.f64 y)) x) y) z)
	0.5b	(-.f64 (+.f64 (fma.f64 (.f64 (+.f64 (neg.f64 y) -1/2) (+.f64 (log.f64 (.f64 (cbrt.f64 (exp.f64 (pow.f64 (cbrt.f64 (log.f64 y)) 2))) (cbrt.f64 (exp.f64 (pow.f64 (cbrt.f64 (log.f64 y)) 2))))) (log.f64 (cbrt.f64 (exp.f64 (pow.f64 (cbrt.f64 (log.f64 y)) 2)))))) (cbrt.f64 (log.f64 y)) x) y) z)
	0.5b	(+.f64 (*.f64 (cbrt.f64 (fma.f64 (log.f64 y) (-.f64 -1/2 y) y)) (pow.f64 (cbrt.f64 (fma.f64 (log.f64 y) (-.f64 -1/2 y) y)) 2)) (-.f64 x z))
▶	0.3b	(-.f64 (+.f64 (fma.f64 (*.f64 (cbrt.f64 (pow.f64 (log.f64 y) 2)) (-.f64 -1/2 y)) (cbrt.f64 (log.f64 y)) x) y) z)
	17.8b	(-.f64 (+.f64 (-.f64 x (/.f64 (*.f64 (fma.f64 y y -1/4) (log.f64 y)) (+.f64 y -1/2))) y) z)
✓	0.1b	(+.f64 (fma.f64 (log.f64 y) (-.f64 -1/2 y) y) (-.f64 x z))

Compiler

Compiled 4007 to 2098 computations (47.6% saved)

localize15.0ms (0.4%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.2b	(fma.f64 (*.f64 (cbrt.f64 (pow.f64 (log.f64 y) 2)) (-.f64 -1/2 y)) (cbrt.f64 (log.f64 y)) x)
✓	0.5b	(pow.f64 (log.f64 y) 2)
✓	0.5b	(cbrt.f64 (pow.f64 (log.f64 y) 2))
	0.5b	(cbrt.f64 (log.f64 y))

series236.0ms (6.2%)

Counts

3 → 44

Calls

3 calls:

157.0ms	(fma.f64 (*.f64 (cbrt.f64 (pow.f64 (log.f64 y) 2)) (-.f64 -1/2 y)) (cbrt.f64 (log.f64 y)) x)
52.0ms	(cbrt.f64 (pow.f64 (log.f64 y) 2))
27.0ms	(pow.f64 (log.f64 y) 2)

rewrite51.0ms (1.4%)

Algorithm

1×	batch-egg-rewrite

Rules

503×	`log-prod_binary64`
203×	`expm1-udef_binary64`
203×	`log1p-udef_binary64`
181×	`log-pow_binary64`
127×	`prod-diff_binary64`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	12	36
1	247	26
2	2864	24

Stop Event

1×	node limit

Counts

3 → 80

Calls

3 calls:

50.0ms	(fma.f64 (*.f64 (cbrt.f64 (pow.f64 (log.f64 y) 2)) (-.f64 -1/2 y)) (cbrt.f64 (log.f64 y)) x)
50.0ms	(pow.f64 (log.f64 y) 2)
50.0ms	(cbrt.f64 (pow.f64 (log.f64 y) 2))

simplify29.0ms (0.8%)

Algorithm

1×	egg-herbie

Rules

487×	`fma-def_binary64`
454×	`associate-l_binary64`
376×	`associate-r_binary64`
269×	`cancel-sign-sub-inv_binary64`
255×	`distribute-rgt-in_binary64`

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	45	450
1	142	434
2	392	408
3	1259	376

Stop Event

1×	node limit

Counts

124 → 100

prune145.0ms (3.8%)

Pruning

7 alts after pruning (5 fresh and 2 done)

	Pruned	Kept	Total
New	128	2	130
Fresh	3	3	6
Picked	0	1	1
Done	0	1	1
Total	131	7	138

Error

0.0b

Counts

138 → 7

Alt Table

Status	Error	Program
	0.4b	(-.f64 (+.f64 (fma.f64 (*.f64 (cbrt.f64 (cbrt.f64 (pow.f64 (pow.f64 (log.f64 y) 2) 3))) (-.f64 -1/2 y)) (cbrt.f64 (log.f64 y)) x) y) z)
	31.5b	(-.f64 (+.f64 (fma.f64 (*.f64 (+.f64 (neg.f64 y) -1/2) (sqrt.f64 (log.f64 y))) (sqrt.f64 (log.f64 y)) x) y) z)
	0.8b	(-.f64 (+.f64 (pow.f64 (cbrt.f64 (fma.f64 (-.f64 -1/2 y) (log.f64 y) x)) 3) y) z)
✓	0.3b	(-.f64 (+.f64 (fma.f64 (*.f64 (cbrt.f64 (pow.f64 (log.f64 y) 2)) (-.f64 -1/2 y)) (cbrt.f64 (log.f64 y)) x) y) z)
	31.6b	(-.f64 (+.f64 (fma.f64 (*.f64 (+.f64 (neg.f64 y) -1/2) (pow.f64 (cbrt.f64 (log.f64 y)) 2)) (expm1.f64 (log1p.f64 (cbrt.f64 (log.f64 y)))) x) y) z)
	0.5b	(+.f64 (*.f64 (cbrt.f64 (fma.f64 (log.f64 y) (-.f64 -1/2 y) y)) (pow.f64 (cbrt.f64 (fma.f64 (log.f64 y) (-.f64 -1/2 y) y)) 2)) (-.f64 x z))
✓	0.1b	(+.f64 (fma.f64 (log.f64 y) (-.f64 -1/2 y) y) (-.f64 x z))

Compiler

Compiled 2812 to 1526 computations (45.7% saved)

regimes403.0ms (10.7%)

Accuracy

Total 0.1b remaining (71.6%)

Threshold costs 0.1b (71.6%)

Counts

77 → 1

Compiler

Compiled 7635 to 5116 computations (33% saved)

simplify3.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

5×	`+-commutative_binary64`
4×	`sub-neg_binary64`
2×	`*-commutative_binary64`
2×	`neg-sub0_binary64`
2×	`neg-mul-1_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	10	16
1	15	16
2	23	16
3	27	16
4	29	16

Stop Event

1×

saturated

end124.0ms (3.3%)

Compiler: Compiled 174 to 115 computations (33.9% saved)

Details

analyze366.0ms (9.7%)

sample1.1s (29%)

simplify35.0ms (0.9%)

prune3.0ms (0.1%)

localize7.0ms (0.2%)

series8.0ms (0.2%)

rewrite39.0ms (1%)

simplify22.0ms (0.6%)

prune35.0ms (0.9%)

localize12.0ms (0.3%)

series152.0ms (4%)

rewrite74.0ms (2%)

simplify53.0ms (1.4%)

prune208.0ms (5.5%)

localize12.0ms (0.3%)

series345.0ms (9.1%)

rewrite57.0ms (1.5%)

simplify39.0ms (1%)

prune210.0ms (5.5%)

localize15.0ms (0.4%)

series236.0ms (6.2%)

rewrite51.0ms (1.4%)

simplify29.0ms (0.8%)

prune145.0ms (3.8%)

regimes403.0ms (10.7%)

simplify3.0ms (0.1%)

end124.0ms (3.3%)

Profiling