Details

analyze347.0ms (7.4%)

Algorithm

1×

Search

True	Other	False	Iter
0%	100%	0%	0
0%	100%	0%	1
0%	100%	0%	2
25%	75%	0%	3
25%	50%	25%	4
25%	37.5%	37.5%	5
25%	31.2%	43.8%	6
25%	28.1%	46.9%	7
25%	26.5%	48.5%	8
25%	25.8%	49.2%	9
25%	25.4%	49.6%	10
25%	25.2%	49.8%	11
25%	25.1%	49.9%	12
25%	25%	50%	13
25%	25%	50%	14

Compiler

Compiled 11 to 8 computations (27.3% saved)

sample200.0ms (4.2%)

Algorithm

1×

intervals

Results

23.0ms	119×	body	2048	nan
15.0ms	256×	body	128	valid
9.0ms	62×	body	1024	nan
5.0ms	43×	body	512	nan
2.0ms	20×	body	256	nan
0.0ms	10×	body	128	nan

Compiler

Compiled 22 to 16 computations (27.3% saved)

simplify128.0ms (2.7%)

Algorithm

1×	egg-herbie

Rules

871×	`fma-neg_binary64`
804×	`unsub-neg_binary64`
461×	`distribute-neg-in_binary64`
434×	`sub-neg_binary64`
338×	`distribute-rgt-out_binary64`

Counts

1 → 2

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	8	12
1	18	12
2	22	12
3	37	12
4	64	12
5	113	12
6	247	12
7	500	12
8	1560	12
9	2513	12
10	3218	12
11	3602	12
12	3803	12
13	3974	12
14	4075	12
15	4392	12
16	4836	12
17	4898	12
18	4901	12

prune2.0ms (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

30.6b

Counts

3 → 1

Alt Table

Status	Error	Program
▶	30.6b	(log.f64 (+.f64 x (sqrt.f64 (fma.f64 x x -1))))

Compiler

Compiled 36 to 24 computations (33.3% saved)

localize6.0ms (0.1%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.0b	(+.f64 x (sqrt.f64 (fma.f64 x x -1)))
✓	0.5b	(log.f64 (+.f64 x (sqrt.f64 (fma.f64 x x -1))))
✓	28.5b	(sqrt.f64 (fma.f64 x x -1))

series13.0ms (0.3%)

Counts

3 → 36

Calls

3 calls:

6.0ms	(log.f64 (+.f64 x (sqrt.f64 (fma.f64 x x -1))))
4.0ms	(sqrt.f64 (fma.f64 x x -1))
3.0ms	(+.f64 x (sqrt.f64 (fma.f64 x x -1)))

rewrite11.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

10×	`*-un-lft-identity_binary64`
7×	`add-sqr-sqrt_binary64`
6×	`add-cube-cbrt_binary64`
5×	`add-log-exp_binary64`
5×	`pow1_binary64`

Counts

3 → 49

Calls

3 calls:

6.0ms	(+.f64 x (sqrt.f64 (fma.f64 x x -1)))
3.0ms	(log.f64 (+.f64 x (sqrt.f64 (fma.f64 x x -1))))
1.0ms	(sqrt.f64 (fma.f64 x x -1))

simplify81.0ms (1.7%)

Algorithm

1×	egg-herbie

Rules

583×	`fma-neg_binary64`
330×	`sub-neg_binary64`
301×	`fma-def_binary64`
254×	`distribute-neg-frac_binary64`
210×	`associate-+l+_binary64`

Counts

85 → 118

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	159	1395
1	401	1305
2	1052	1265
3	3424	1265
4	4773	1265
5	4915	1265

prune72.0ms (1.5%)

Pruning

3 alts after pruning (2 fresh and 1 done)

	Pruned	Kept	Total
New	116	2	118
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	116	3	119

Error

0.0b

Counts

119 → 3

Alt Table

Status	Error	Program
✓	30.6b	(log.f64 (+.f64 x (sqrt.f64 (fma.f64 x x -1))))
	0.6b	(log.f64 (fma.f64 x 2 (/.f64 -1/2 x)))
▶	0.5b	(+.f64 (log.f64 2) (log.f64 x))

Compiler

Compiled 1902 to 1421 computations (25.3% saved)

localize5.0ms (0.1%)

Local error

Found 1 expressions with local error:

New	Error	Program
✓	0.2b	(+.f64 (log.f64 2) (log.f64 x))

series40.0ms (0.8%)

Counts

1 → 12

Calls

1 calls:

40.0ms

(+.f64 (log.f64 2) (log.f64 x))

rewrite4.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

8×	`*-un-lft-identity_binary64`
6×	`log-prod_binary64`
6×	`pow1_binary64`
5×	`log-pow_binary64`
4×	`distribute-lft-out_binary64`

Counts

1 → 27

Calls

1 calls:

3.0ms

(+.f64 (log.f64 2) (log.f64 x))

simplify75.0ms (1.6%)

Algorithm

1×	egg-herbie

Rules

539×	`sub-neg_binary64`
476×	`fma-def_binary64`
458×	`distribute-neg-in_binary64`
398×	`fma-neg_binary64`
397×	`unsub-neg_binary64`

Counts

39 → 38

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	54	363
1	120	344
2	274	342
3	660	342
4	2248	342
5	3872	342
6	4273	342
7	4971	342

prune24.0ms (0.5%)

Pruning

3 alts after pruning (2 fresh and 1 done)

	Pruned	Kept	Total
New	37	1	38
Fresh	0	1	1
Picked	1	0	1
Done	0	1	1
Total	38	3	41

Error

Counts

41 → 3

Alt Table

Status	Error	Program
✓	30.6b	(log.f64 (+.f64 x (sqrt.f64 (fma.f64 x x -1))))
	0.8b	(cbrt.f64 (pow.f64 (+.f64 (log.f64 x) (log.f64 2)) 3))
▶	0.6b	(log.f64 (fma.f64 x 2 (/.f64 -1/2 x)))

Compiler

Compiled 440 to 318 computations (27.7% saved)

localize5.0ms (0.1%)

Local error

Found 1 expressions with local error:

New	Error	Program
✓	0.5b	(log.f64 (fma.f64 x 2 (/.f64 -1/2 x)))

series4.0ms (0.1%)

Counts

1 → 12

Calls

1 calls:

4.0ms

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

rewrite1.0ms (0%)

Algorithm

1×	rewrite-expression-head

Rules

3×	`log-prod_binary64`
2×	`add-exp-log_binary64`
2×	`*-un-lft-identity_binary64`
2×	`add-sqr-sqrt_binary64`
2×	`add-cube-cbrt_binary64`

Counts

1 → 14

Calls

1 calls:

1.0ms

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

simplify85.0ms (1.8%)

Algorithm

1×	egg-herbie

Rules

732×	`fma-def_binary64`
535×	`times-frac_binary64`
409×	`cancel-sign-sub-inv_binary64`
345×	`sub-neg_binary64`
309×	`fma-neg_binary64`

Counts

26 → 38

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	79	493
1	184	449
2	525	449
3	1696	449
4	4117	449
5	4962	449
6	4996	449
7	4927	449

prune21.0ms (0.5%)

Pruning

3 alts after pruning (1 fresh and 2 done)

	Pruned	Kept	Total
New	38	0	38
Fresh	0	1	1
Picked	0	1	1
Done	0	1	1
Total	38	3	41

Error

Counts

41 → 3

Alt Table

Status	Error	Program
✓	30.6b	(log.f64 (+.f64 x (sqrt.f64 (fma.f64 x x -1))))
▶	0.8b	(cbrt.f64 (pow.f64 (+.f64 (log.f64 x) (log.f64 2)) 3))
✓	0.6b	(log.f64 (fma.f64 x 2 (/.f64 -1/2 x)))

Compiler

Compiled 620 to 478 computations (22.9% saved)

localize7.0ms (0.1%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.2b	(+.f64 (log.f64 x) (log.f64 2))
✓	0.5b	(cbrt.f64 (pow.f64 (+.f64 (log.f64 x) (log.f64 2)) 3))
✓	0.7b	(pow.f64 (+.f64 (log.f64 x) (log.f64 2)) 3)

series112.0ms (2.4%)

Counts

3 → 36

Calls

3 calls:

43.0ms	(pow.f64 (+.f64 (log.f64 x) (log.f64 2)) 3)
34.0ms	(cbrt.f64 (pow.f64 (+.f64 (log.f64 x) (log.f64 2)) 3))
34.0ms	(+.f64 (log.f64 x) (log.f64 2))

rewrite16.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

32×	`*-un-lft-identity_binary64`
25×	`pow1_binary64`
21×	`log-pow_binary64`
20×	`cbrt-prod_binary64`
20×	`distribute-lft-out_binary64`

Counts

3 → 95

Calls

3 calls:

4.0ms	(cbrt.f64 (pow.f64 (+.f64 (log.f64 x) (log.f64 2)) 3))
4.0ms	(pow.f64 (+.f64 (log.f64 x) (log.f64 2)) 3)
3.0ms	(+.f64 (log.f64 x) (log.f64 2))

simplify99.0ms (2.1%)

Algorithm

1×	egg-herbie

Rules

672×	`associate-l_binary64`
522×	`associate-r_binary64`
406×	`distribute-rgt-in_binary64`
374×	`exp-prod_binary64`
369×	`distribute-lft-in_binary64`

Counts

131 → 99

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	107	1544
1	223	1514
2	695	1496
3	3642	1496
4	4938	1496
5	5017	1496

prune52.0ms (1.1%)

Pruning

3 alts after pruning (0 fresh and 3 done)

	Pruned	Kept	Total
New	99	0	99
Fresh	0	0	0
Picked	0	1	1
Done	0	2	2
Total	99	3	102

Error

Counts

102 → 3

Alt Table

Status	Error	Program
✓	30.6b	(log.f64 (+.f64 x (sqrt.f64 (fma.f64 x x -1))))
✓	0.8b	(cbrt.f64 (pow.f64 (+.f64 (log.f64 x) (log.f64 2)) 3))
✓	0.6b	(log.f64 (fma.f64 x 2 (/.f64 -1/2 x)))

Compiler

Compiled 1445 to 1098 computations (24% saved)

regimes55.0ms (1.2%)

Accuracy

Total 0.8b remaining (99.7%)

Threshold costs 0.8b (99.7%)

Counts

15 → 1

Compiler

Compiled 456 to 352 computations (22.8% saved)

simplify4.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

1×	`+-commutative_binary64`
1×	`*-commutative_binary64`
1×	`*-lft-identity_binary64`
1×	`1-exp_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	8	8
1	12	8
2	11	8

end0.0ms (0%)

Compiler: Compiled 6 to 5 computations (16.7% saved)

sample3.2s (68.8%)

Algorithm

1×

intervals

Results

942.0ms	8000×	body	128	valid
851.0ms	3933×	body	2048	nan
482.0ms	1906×	body	1024	nan
111.0ms	942×	body	512	nan
41.0ms	526×	body	256	nan
21.0ms	509×	body	128	nan
2.0ms	10×	body	4096	nan

Compiler

Compiled 44 to 34 computations (22.7% saved)

Details

analyze347.0ms (7.4%)

sample200.0ms (4.2%)

simplify128.0ms (2.7%)

prune2.0ms (0.1%)

localize6.0ms (0.1%)

series13.0ms (0.3%)

rewrite11.0ms (0.2%)

simplify81.0ms (1.7%)

prune72.0ms (1.5%)

localize5.0ms (0.1%)

series40.0ms (0.8%)

rewrite4.0ms (0.1%)

simplify75.0ms (1.6%)

prune24.0ms (0.5%)

localize5.0ms (0.1%)

series4.0ms (0.1%)

rewrite1.0ms (0%)

simplify85.0ms (1.8%)

prune21.0ms (0.5%)

localize7.0ms (0.1%)

series112.0ms (2.4%)

rewrite16.0ms (0.3%)

simplify99.0ms (2.1%)

prune52.0ms (1.1%)

regimes55.0ms (1.2%)

simplify4.0ms (0.1%)

end0.0ms (0%)

sample3.2s (68.8%)

Profiling