Details

analyze225.0ms (5%)

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
25%	74.9%	0.1%	5
43.7%	43.7%	12.6%	6
53.1%	31.2%	15.7%	7
59.3%	18.7%	22%	8
62.4%	14%	23.5%	9
64.8%	8.6%	26.6%	10
66%	6.6%	27.4%	11
66.9%	4.1%	29%	12
67.4%	3.2%	29.4%	13
67.9%	2%	30.1%	14

Compiler

Compiled 12 to 9 computations (25% saved)

sample30.0ms (0.7%)

Algorithm

1×

intervals

Results

13.0ms	232×	body	128	valid
4.0ms	10×	body	1024	valid
2.0ms	7×	body	512	valid
1.0ms	7×	body	256	valid
0.0ms	2×	body	128	invalid

Compiler

Compiled 25 to 19 computations (24% saved)

simplify101.0ms (2.3%)

Algorithm

1×	egg-herbie

Rules

837×	`fma-def_binary64`
741×	`fabs-mul_binary64`
531×	`fabs-div_binary64`
469×	`swap-sqr_binary64`
420×	`fma-neg_binary64`

Counts

1 → 2

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	9	11
1	19	11
2	28	11
3	45	11
4	59	11
5	89	11
6	120	11
7	148	11
8	188	11
9	201	11
10	231	11
11	257	11
12	336	11
13	544	11
14	967	11
15	2930	11
16	3463	11
17	3600	11
18	3896	11
19	4820	11
20	4969	11

prune3.0ms (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

0.3b

Counts

3 → 1

Alt Table

Status	Error	Program
▶	0.3b	(-.f64 (log1p.f64 (exp.f64 x)) (*.f64 x y))

Compiler

Compiled 36 to 22 computations (38.9% saved)

localize5.0ms (0.1%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.0b	(-.f64 (log1p.f64 (exp.f64 x)) (*.f64 x y))
✓	0.3b	(log1p.f64 (exp.f64 x))

series323.0ms (7.2%)

Counts

2 → 36

Calls

2 calls:

203.0ms	(log1p.f64 (exp.f64 x))
120.0ms	(-.f64 (log1p.f64 (exp.f64 x)) (*.f64 x y))

rewrite4.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

5×	`add-log-exp_binary64`
4×	`*-un-lft-identity_binary64`
4×	`add-sqr-sqrt_binary64`
4×	`add-cube-cbrt_binary64`
3×	`fma-neg_binary64`

Counts

2 → 32

Calls

2 calls:

2.0ms	(-.f64 (log1p.f64 (exp.f64 x)) (*.f64 x y))
0.0ms	(log1p.f64 (exp.f64 x))

simplify79.0ms (1.8%)

Algorithm

1×	egg-herbie

Rules

620×	`cancel-sign-sub-inv_binary64`
339×	`unswap-sqr_binary64`
285×	`*-commutative_binary64`
285×	`unsub-neg_binary64`
252×	`distribute-rgt-in_binary64`

Counts

68 → 56

Iterations

Useful iterations: 5 (0.0ms)

Iter	Nodes	Cost
0	73	789
1	167	742
2	426	710
3	1507	707
4	3171	707
5	4588	701
6	4872	701

prune28.0ms (0.6%)

Pruning

2 alts after pruning (1 fresh and 1 done)

	Pruned	Kept	Total
New	55	1	56
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	55	2	57

Error

0.2b

Counts

57 → 2

Alt Table

Status	Error	Program
▶	13.2b	(fma.f64 x (-.f64 1/2 y) (log.f64 2))
✓	0.3b	(-.f64 (log1p.f64 (exp.f64 x)) (*.f64 x y))

Compiler

Compiled 773 to 278 computations (64% saved)

localize6.0ms (0.1%)

Local error

Found 1 expressions with local error:

New	Error	Program
✓	0.0b	(fma.f64 x (-.f64 1/2 y) (log.f64 2))

series11.0ms (0.2%)

Counts

1 → 24

Calls

1 calls:

11.0ms

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

rewrite1.0ms (0%)

Algorithm

1×	rewrite-expression-head

Rules

1×	`*-un-lft-identity_binary64`
1×	`add-sqr-sqrt_binary64`
1×	`add-cube-cbrt_binary64`
1×	`add-cbrt-cube_binary64`
1×	`add-exp-log_binary64`

Counts

1 → 10

Calls

1 calls:

0.0ms

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

simplify67.0ms (1.5%)

Algorithm

1×	egg-herbie

Rules

855×	`fma-neg_binary64`
478×	`neg-sub0_binary64`
433×	`neg-mul-1_binary64`
375×	`*-commutative_binary64`
362×	`distribute-rgt-in_binary64`

Counts

34 → 22

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	28	459
1	52	346
2	104	346
3	328	346
4	1670	346
5	2981	346
6	4467	346
7	4969	346

prune15.0ms (0.3%)

Pruning

3 alts after pruning (1 fresh and 2 done)

	Pruned	Kept	Total
New	21	1	22
Fresh	0	0	0
Picked	0	1	1
Done	0	1	1
Total	21	3	24

Error

0.2b

Counts

24 → 3

Alt Table

Status	Error	Program
▶	14.6b	(.f64 (.f64 (cbrt.f64 (fma.f64 x (-.f64 1/2 y) (log.f64 2))) (cbrt.f64 (fma.f64 x (-.f64 1/2 y) (log.f64 2)))) (cbrt.f64 (fma.f64 x (-.f64 1/2 y) (log.f64 2))))
✓	13.2b	(fma.f64 x (-.f64 1/2 y) (log.f64 2))
✓	0.3b	(-.f64 (log1p.f64 (exp.f64 x)) (*.f64 x y))

Compiler

Compiled 280 to 211 computations (24.6% saved)

localize10.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.0b	(fma.f64 x (-.f64 1/2 y) (log.f64 2))
✓	0.3b	(*.f64 (cbrt.f64 (fma.f64 x (-.f64 1/2 y) (log.f64 2))) (cbrt.f64 (fma.f64 x (-.f64 1/2 y) (log.f64 2))))
✓	0.7b	(.f64 (.f64 (cbrt.f64 (fma.f64 x (-.f64 1/2 y) (log.f64 2))) (cbrt.f64 (fma.f64 x (-.f64 1/2 y) (log.f64 2)))) (cbrt.f64 (fma.f64 x (-.f64 1/2 y) (log.f64 2))))
✓	1.1b	(cbrt.f64 (fma.f64 x (-.f64 1/2 y) (log.f64 2)))

series200.0ms (4.5%)

Counts

3 → 72

Calls

3 calls:

137.0ms

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

50.0ms

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

12.0ms

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

rewrite20.0ms (0.4%)

Algorithm

1×	rewrite-expression-head

Rules

29×	`pow1_binary64`
24×	`add-sqr-sqrt_binary64`
23×	`cbrt-prod_binary64`
16×	`pow1/3_binary64`
14×	`*-un-lft-identity_binary64`

Counts

3 → 93

Calls

3 calls:

7.0ms

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

4.0ms

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

1.0ms

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

simplify155.0ms (3.5%)

Algorithm

1×	egg-herbie

Rules

734×	`times-frac_binary64`
597×	`fma-def_binary64`
506×	`associate-/l*_binary64`
250×	`*-commutative_binary64`
137×	`+-commutative_binary64`

Counts

165 → 207

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	669	9535
1	2330	8681
2	5361	8681

prune517.0ms (11.6%)

Pruning

3 alts after pruning (1 fresh and 2 done)

	Pruned	Kept	Total
New	392	1	393
Fresh	0	0	0
Picked	1	0	1
Done	0	2	2
Total	393	3	396

Error

0.2b

Counts

396 → 3

Alt Table

Status	Error	Program
▶	60.8b	(.f64 (.f64 (cbrt.f64 (fma.f64 x (-.f64 1/2 y) (log.f64 2))) (cbrt.f64 (fma.f64 x (-.f64 1/2 y) (log.f64 2)))) (fma.f64 1/3 (/.f64 (pow.f64 (exp.f64 1/3) (+.f64 (log.f64 (-.f64 1/2 y)) (log.f64 x))) (/.f64 (-.f64 1/2 y) (/.f64 (log.f64 2) x))) (pow.f64 (exp.f64 1/3) (+.f64 (log.f64 (-.f64 1/2 y)) (log.f64 x)))))
✓	13.2b	(fma.f64 x (-.f64 1/2 y) (log.f64 2))
✓	0.3b	(-.f64 (log1p.f64 (exp.f64 x)) (*.f64 x y))

Compiler

Compiled 24196 to 18843 computations (22.1% saved)

localize22.0ms (0.5%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.3b	(*.f64 (cbrt.f64 (fma.f64 x (-.f64 1/2 y) (log.f64 2))) (cbrt.f64 (fma.f64 x (-.f64 1/2 y) (log.f64 2))))
✓	0.5b	(/.f64 (-.f64 1/2 y) (/.f64 (log.f64 2) x))
	1.1b	(cbrt.f64 (fma.f64 x (-.f64 1/2 y) (log.f64 2)))
✓	1.3b	(pow.f64 (exp.f64 1/3) (+.f64 (log.f64 (-.f64 1/2 y)) (log.f64 x)))

series506.0ms (11.3%)

Counts

2 → 48

Calls

2 calls:

463.0ms	(pow.f64 (exp.f64 1/3) (+.f64 (log.f64 (-.f64 1/2 y)) (log.f64 x)))
42.0ms	(/.f64 (-.f64 1/2 y) (/.f64 (log.f64 2) x))

rewrite26.0ms (0.6%)

Algorithm

1×	rewrite-expression-head

Rules

152×	`times-frac_binary64`
108×	`*-un-lft-identity_binary64`
104×	`add-sqr-sqrt_binary64`
70×	`add-cube-cbrt_binary64`
25×	`pow1_binary64`

Counts

2 → 150

Calls

2 calls:

8.0ms	(/.f64 (-.f64 1/2 y) (/.f64 (log.f64 2) x))
5.0ms	(pow.f64 (exp.f64 1/3) (+.f64 (log.f64 (-.f64 1/2 y)) (log.f64 x)))

simplify179.0ms (4%)

Algorithm

1×	egg-herbie

Rules

352×	`times-frac_binary64`
334×	`fma-def_binary64`
298×	`fma-neg_binary64`
222×	`associate-/r/_binary64`
167×	`distribute-rgt-in_binary64`

Counts

198 → 218

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	321	5032
1	861	4641
2	2376	4381
3	4465	4071
4	4929	4071
5	4952	4071

prune832.0ms (18.7%)

Pruning

3 alts after pruning (1 fresh and 2 done)

	Pruned	Kept	Total
New	503	1	504
Fresh	0	0	0
Picked	1	0	1
Done	0	2	2
Total	504	3	507

Error

0.2b

Counts

507 → 3

Alt Table

Status	Error	Program
	61.2b	(.f64 (.f64 (cbrt.f64 (fma.f64 x (-.f64 1/2 y) (log.f64 2))) (fma.f64 1/3 (/.f64 (pow.f64 (exp.f64 1/3) (+.f64 (log.f64 (-.f64 1/2 y)) (log.f64 x))) (/.f64 (-.f64 1/2 y) (/.f64 (log.f64 2) x))) (pow.f64 (exp.f64 1/3) (+.f64 (log.f64 (-.f64 1/2 y)) (log.f64 x))))) (fma.f64 1/3 (/.f64 (pow.f64 (exp.f64 1/3) (+.f64 (log.f64 (-.f64 1/2 y)) (log.f64 x))) (/.f64 (-.f64 1/2 y) (/.f64 (log.f64 2) x))) (pow.f64 (exp.f64 1/3) (+.f64 (log.f64 (-.f64 1/2 y)) (log.f64 x)))))
✓	13.2b	(fma.f64 x (-.f64 1/2 y) (log.f64 2))
✓	0.3b	(-.f64 (log1p.f64 (exp.f64 x)) (*.f64 x y))

Compiler

Compiled 38775 to 29712 computations (23.4% saved)

regimes115.0ms (2.6%)

Accuracy

Total 0.2b remaining (49.4%)

Threshold costs 0.2b (49.4%)

Counts

28 → 1

Compiler

Compiled 2249 to 1771 computations (21.3% saved)

simplify3.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

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

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	7	11
1	13	11
2	23	11
3	29	11
4	33	11
5	34	11
6	34	11

end0.0ms (0%)

Compiler: Compiled 9 to 6 computations (33.3% saved)

sample978.0ms (21.9%)

Algorithm

1×

intervals

Results

458.0ms	7396×	body	128	valid
106.0ms	222×	body	1024	valid
59.0ms	229×	body	512	valid
22.0ms	153×	body	256	valid
3.0ms	44×	body	128	invalid
0.0ms	7×	body	128	overflowed

Compiler

Compiled 115 to 87 computations (24.3% saved)

Details

analyze225.0ms (5%)

sample30.0ms (0.7%)

simplify101.0ms (2.3%)

prune3.0ms (0.1%)

localize5.0ms (0.1%)

series323.0ms (7.2%)

rewrite4.0ms (0.1%)

simplify79.0ms (1.8%)

prune28.0ms (0.6%)

localize6.0ms (0.1%)

series11.0ms (0.2%)

rewrite1.0ms (0%)

simplify67.0ms (1.5%)

prune15.0ms (0.3%)

localize10.0ms (0.2%)

series200.0ms (4.5%)

rewrite20.0ms (0.4%)

simplify155.0ms (3.5%)

prune517.0ms (11.6%)

localize22.0ms (0.5%)

series506.0ms (11.3%)

rewrite26.0ms (0.6%)

simplify179.0ms (4%)

prune832.0ms (18.7%)

regimes115.0ms (2.6%)

simplify3.0ms (0.1%)

end0.0ms (0%)

sample978.0ms (21.9%)

Profiling