Details

analyze6.0ms (0.1%)

Algorithm

1×

Search

True	Other	False	Iter
0%	100%	0%	0
0%	100%	0%	1
0%	100%	0%	2
0%	50%	50%	3
25%	25%	50%	4
37.5%	12.5%	50%	5
43.7%	6.2%	50%	6
46.9%	3.1%	50%	7
48.4%	1.6%	50%	8
49.2%	0.8%	50%	9
49.6%	0.4%	50%	10
49.8%	0.2%	50%	11
49.9%	0.1%	50%	12
49.9%	0%	50%	13
49.9%	0%	50%	14

Compiler

Compiled 14 to 12 computations (14.3% saved)

sample564.0ms (10.4%)

Algorithm

1×

intervals

Results

51.0ms	121×	body	1024	valid
17.0ms	60×	body	512	valid
11.0ms	19×	body	2048	valid
6.0ms	38×	body	256	valid
1.0ms	18×	body	128	valid

Compiler

Compiled 28 to 24 computations (14.3% saved)

simplify463.0ms (8.5%)

Algorithm

1×	egg-herbie

Rules

7982×	`fma-neg_binary64`
642×	`unsub-neg_binary64`
573×	`distribute-neg-in_binary64`
572×	`distribute-rgt-in_binary64`
535×	`distribute-rgt-out--_binary64`

Counts

1 → 2

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	11	15
1	20	13
2	28	13
3	43	13
4	67	13
5	95	13
6	136	13
7	234	13
8	429	13
9	636	13
10	827	13
11	918	13
12	1093	13
13	1183	13
14	1272	13
15	1630	13
16	2135	13
17	2217	13
18	2418	13
19	2438	13
20	2558	13
21	2558	13
22	2954	13
23	3004	13
24	3130	13
25	3162	13
26	3210	13
27	3230	13
28	3238	13
29	3238	13
30	3238	13
31	3574	13
32	3558	13
33	3856	13
34	4014	13
35	4100	13
36	4126	13
37	4142	13
38	4154	13
39	4190	13
40	4202	13
41	4206	13
42	4206	13
43	11004	13

prune4.0ms (0.1%)

Pruning

1 alts after pruning (1 fresh and 0 done)

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

Error

0.0b

Counts

3 → 1

Alt Table

Status	Error	Program
▶	0.0b	(*.f64 1/2 (-.f64 (log1p.f64 x) (log1p.f64 (neg.f64 x))))

Compiler

Compiled 39 to 31 computations (20.5% saved)

localize5.0ms (0.1%)

Local error

Found 1 expressions with local error:

New	Error	Program
✓	0.0b	(-.f64 (log1p.f64 x) (log1p.f64 (neg.f64 x)))

series4.0ms (0.1%)

Counts

1 → 12

Calls

1 calls:

4.0ms

(-.f64 (log1p.f64 x) (log1p.f64 (neg.f64 x)))

rewrite5.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

11×	`*-un-lft-identity_binary64`
11×	`add-sqr-sqrt_binary64`
9×	`prod-diff_binary64`
9×	`add-cube-cbrt_binary64`
5×	`add-log-exp_binary64`

Counts

1 → 33

Calls

1 calls:

3.0ms

(-.f64 (log1p.f64 x) (log1p.f64 (neg.f64 x)))

simplify111.0ms (2%)

Algorithm

1×	egg-herbie

Rules

424×	`unsub-neg_binary64`
332×	`unswap-sqr_binary64`
325×	`times-frac_binary64`
317×	`sqr-pow_binary64`
315×	`distribute-rgt-in_binary64`

Counts

45 → 63

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	104	900
1	223	663
2	571	600
3	1725	600
4	3147	600
5	4384	600
6	4805	600
7	4516	600
8	4840	600

prune35.0ms (0.6%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	60	3	63
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	60	4	64

Error

Counts

64 → 4

Alt Table

Status	Error	Program
✓	0.0b	(*.f64 1/2 (-.f64 (log1p.f64 x) (log1p.f64 (neg.f64 x))))
	1.0b	(.f64 1/2 (+.f64 (log1p.f64 x) (.f64 (neg.f64 (*.f64 (cbrt.f64 (log1p.f64 (neg.f64 x))) (cbrt.f64 (log1p.f64 (neg.f64 x))))) (cbrt.f64 (log1p.f64 (neg.f64 x))))))
	35.4b	(*.f64 1/2 (fma.f64 (sqrt.f64 (log1p.f64 x)) (sqrt.f64 (log1p.f64 x)) (neg.f64 (log1p.f64 (neg.f64 x)))))
▶	0.3b	(.f64 1/2 (fma.f64 2 x (.f64 2/3 (pow.f64 x 3))))

Compiler

Compiled 1250 to 578 computations (53.8% saved)

localize6.0ms (0.1%)

Local error

Found 1 expressions with local error:

New	Error	Program
✓	0.2b	(*.f64 2/3 (pow.f64 x 3))

series3.0ms (0.1%)

Counts

1 → 0

Calls

1 calls:

3.0ms

(*.f64 2/3 (pow.f64 x 3))

rewrite6.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

12×	`associate-r_binary64`
12×	`add-sqr-sqrt_binary64`
6×	`add-exp-log_binary64`
5×	`*-un-lft-identity_binary64`
5×	`add-cube-cbrt_binary64`

Counts

1 → 33

Calls

1 calls:

5.0ms

(*.f64 2/3 (pow.f64 x 3))

simplify82.0ms (1.5%)

Algorithm

1×	egg-herbie

Rules

513×	`associate-l_binary64`
478×	`associate-r_binary64`
457×	`fma-def_binary64`
349×	`log-prod_binary64`
311×	`cube-prod_binary64`

Counts

33 → 38

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	58	354
1	108	314
2	300	314
3	1642	314
4	2725	284
5	4358	284
6	4937	284
7	4923	284

prune32.0ms (0.6%)

Pruning

4 alts after pruning (2 fresh and 2 done)

	Pruned	Kept	Total
New	38	0	38
Fresh	0	2	2
Picked	0	1	1
Done	0	1	1
Total	38	4	42

Error

Counts

42 → 4

Alt Table

Status	Error	Program
✓	0.0b	(*.f64 1/2 (-.f64 (log1p.f64 x) (log1p.f64 (neg.f64 x))))
▶	1.0b	(.f64 1/2 (+.f64 (log1p.f64 x) (.f64 (neg.f64 (*.f64 (cbrt.f64 (log1p.f64 (neg.f64 x))) (cbrt.f64 (log1p.f64 (neg.f64 x))))) (cbrt.f64 (log1p.f64 (neg.f64 x))))))
	35.4b	(*.f64 1/2 (fma.f64 (sqrt.f64 (log1p.f64 x)) (sqrt.f64 (log1p.f64 x)) (neg.f64 (log1p.f64 (neg.f64 x)))))
✓	0.3b	(.f64 1/2 (fma.f64 2 x (.f64 2/3 (pow.f64 x 3))))

Compiler

Compiled 683 to 529 computations (22.5% saved)

localize11.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(+.f64 (log1p.f64 x) (.f64 (neg.f64 (.f64 (cbrt.f64 (log1p.f64 (neg.f64 x))) (cbrt.f64 (log1p.f64 (neg.f64 x))))) (cbrt.f64 (log1p.f64 (neg.f64 x)))))
✓	0.3b	(.f64 (neg.f64 (.f64 (cbrt.f64 (log1p.f64 (neg.f64 x))) (cbrt.f64 (log1p.f64 (neg.f64 x))))) (cbrt.f64 (log1p.f64 (neg.f64 x))))
✓	0.5b	(*.f64 (cbrt.f64 (log1p.f64 (neg.f64 x))) (cbrt.f64 (log1p.f64 (neg.f64 x))))
✓	0.7b	(cbrt.f64 (log1p.f64 (neg.f64 x)))

series84.0ms (1.5%)

Counts

4 → 48

Calls

4 calls:

59.0ms	(*.f64 (cbrt.f64 (log1p.f64 (neg.f64 x))) (cbrt.f64 (log1p.f64 (neg.f64 x))))
18.0ms	(cbrt.f64 (log1p.f64 (neg.f64 x)))
4.0ms	(+.f64 (log1p.f64 x) (.f64 (neg.f64 (.f64 (cbrt.f64 (log1p.f64 (neg.f64 x))) (cbrt.f64 (log1p.f64 (neg.f64 x))))) (cbrt.f64 (log1p.f64 (neg.f64 x)))))
3.0ms	(.f64 (neg.f64 (.f64 (cbrt.f64 (log1p.f64 (neg.f64 x))) (cbrt.f64 (log1p.f64 (neg.f64 x))))) (cbrt.f64 (log1p.f64 (neg.f64 x))))

rewrite18.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

29×	`add-sqr-sqrt_binary64`
23×	`cbrt-prod_binary64`
17×	`*-un-lft-identity_binary64`
17×	`add-cube-cbrt_binary64`
13×	`pow1_binary64`

Counts

4 → 101

Calls

4 calls:

5.0ms	(*.f64 (cbrt.f64 (log1p.f64 (neg.f64 x))) (cbrt.f64 (log1p.f64 (neg.f64 x))))
5.0ms	(.f64 (neg.f64 (.f64 (cbrt.f64 (log1p.f64 (neg.f64 x))) (cbrt.f64 (log1p.f64 (neg.f64 x))))) (cbrt.f64 (log1p.f64 (neg.f64 x))))
2.0ms	(+.f64 (log1p.f64 x) (.f64 (neg.f64 (.f64 (cbrt.f64 (log1p.f64 (neg.f64 x))) (cbrt.f64 (log1p.f64 (neg.f64 x))))) (cbrt.f64 (log1p.f64 (neg.f64 x)))))
1.0ms	(cbrt.f64 (log1p.f64 (neg.f64 x)))

simplify119.0ms (2.2%)

Algorithm

1×	egg-herbie

Rules

411×	`fma-def_binary64`
309×	`associate-r_binary64`
292×	`associate-l_binary64`
247×	`*-commutative_binary64`
223×	`associate-+r+_binary64`

Counts

149 → 238

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	417	4397
1	1267	3983
2	4479	3797
3	4970	3797

prune202.0ms (3.7%)

Pruning

4 alts after pruning (1 fresh and 3 done)

	Pruned	Kept	Total
New	316	0	316
Fresh	0	1	1
Picked	0	1	1
Done	0	2	2
Total	316	4	320

Error

Counts

320 → 4

Alt Table

Status	Error	Program
✓	0.0b	(*.f64 1/2 (-.f64 (log1p.f64 x) (log1p.f64 (neg.f64 x))))
✓	1.0b	(.f64 1/2 (+.f64 (log1p.f64 x) (.f64 (neg.f64 (*.f64 (cbrt.f64 (log1p.f64 (neg.f64 x))) (cbrt.f64 (log1p.f64 (neg.f64 x))))) (cbrt.f64 (log1p.f64 (neg.f64 x))))))
▶	35.4b	(*.f64 1/2 (fma.f64 (sqrt.f64 (log1p.f64 x)) (sqrt.f64 (log1p.f64 x)) (neg.f64 (log1p.f64 (neg.f64 x)))))
✓	0.3b	(.f64 1/2 (fma.f64 2 x (.f64 2/3 (pow.f64 x 3))))

Compiler

Compiled 11664 to 6354 computations (45.5% saved)

localize8.0ms (0.1%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.0b	(sqrt.f64 (log1p.f64 x))
✓	0.0b	(fma.f64 (sqrt.f64 (log1p.f64 x)) (sqrt.f64 (log1p.f64 x)) (neg.f64 (log1p.f64 (neg.f64 x))))

series51.0ms (0.9%)

Counts

2 → 17

Calls

2 calls:

38.0ms	(fma.f64 (sqrt.f64 (log1p.f64 x)) (sqrt.f64 (log1p.f64 x)) (neg.f64 (log1p.f64 (neg.f64 x))))
13.0ms	(sqrt.f64 (log1p.f64 x))

rewrite2.0ms (0%)

Algorithm

1×	rewrite-expression-head

Rules

4×	`add-sqr-sqrt_binary64`
3×	`sqrt-prod_binary64`
3×	`*-un-lft-identity_binary64`
3×	`add-cube-cbrt_binary64`
3×	`pow1_binary64`

Counts

2 → 25

Calls

2 calls:

1.0ms	(sqrt.f64 (log1p.f64 x))
0.0ms	(fma.f64 (sqrt.f64 (log1p.f64 x)) (sqrt.f64 (log1p.f64 x)) (neg.f64 (log1p.f64 (neg.f64 x))))

simplify62.0ms (1.1%)

Algorithm

1×	egg-herbie

Rules

683×	`fma-neg_binary64`
383×	`associate-+l+_binary64`
351×	`fma-def_binary64`
284×	`associate-/r*_binary64`
279×	`sub-neg_binary64`

Counts

42 → 65

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	135	1056
1	352	871
2	1093	714
3	4131	707
4	5062	707

prune54.0ms (1%)

Pruning

4 alts after pruning (0 fresh and 4 done)

	Pruned	Kept	Total
New	96	0	96
Fresh	0	0	0
Picked	0	1	1
Done	0	3	3
Total	96	4	100

Error

Counts

100 → 4

Alt Table

Status	Error	Program
✓	0.0b	(*.f64 1/2 (-.f64 (log1p.f64 x) (log1p.f64 (neg.f64 x))))
✓	1.0b	(.f64 1/2 (+.f64 (log1p.f64 x) (.f64 (neg.f64 (*.f64 (cbrt.f64 (log1p.f64 (neg.f64 x))) (cbrt.f64 (log1p.f64 (neg.f64 x))))) (cbrt.f64 (log1p.f64 (neg.f64 x))))))
✓	35.4b	(*.f64 1/2 (fma.f64 (sqrt.f64 (log1p.f64 x)) (sqrt.f64 (log1p.f64 x)) (neg.f64 (log1p.f64 (neg.f64 x)))))
✓	0.3b	(.f64 1/2 (fma.f64 2 x (.f64 2/3 (pow.f64 x 3))))

Compiler

Compiled 2719 to 1528 computations (43.8% saved)

regimes67.0ms (1.2%)

Accuracy

Total 0.0b remaining (77.8%)

Threshold costs 0.0b (77.8%)

Counts

20 → 1

Compiler

Compiled 1664 to 938 computations (43.6% saved)

simplify3.0ms (0%)

Algorithm

1×	egg-herbie

Rules

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

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	8	13
1	15	13
2	20	13
3	23	13
4	24	13
5	24	13

end0.0ms (0%)

Compiler: Compiled 9 to 7 computations (22.2% saved)

sample3.4s (63.2%)

Algorithm

1×

intervals

Results

2.2s	4081×	body	1024	valid
522.0ms	1993×	body	512	valid
242.0ms	394×	body	2048	valid
141.0ms	949×	body	256	valid
42.0ms	583×	body	128	valid

Compiler

Compiled 79 to 56 computations (29.1% saved)

Details

analyze6.0ms (0.1%)

sample564.0ms (10.4%)

simplify463.0ms (8.5%)

prune4.0ms (0.1%)

localize5.0ms (0.1%)

series4.0ms (0.1%)

rewrite5.0ms (0.1%)

simplify111.0ms (2%)

prune35.0ms (0.6%)

localize6.0ms (0.1%)

series3.0ms (0.1%)

rewrite6.0ms (0.1%)

simplify82.0ms (1.5%)

prune32.0ms (0.6%)

localize11.0ms (0.2%)

series84.0ms (1.5%)

rewrite18.0ms (0.3%)

simplify119.0ms (2.2%)

prune202.0ms (3.7%)

localize8.0ms (0.1%)

series51.0ms (0.9%)

rewrite2.0ms (0%)

simplify62.0ms (1.1%)

prune54.0ms (1%)

regimes67.0ms (1.2%)

simplify3.0ms (0%)

end0.0ms (0%)

sample3.4s (63.2%)

Profiling