Details

analyze412.0ms (11.4%)

Algorithm

1×

Search

True	Other	False	Iter
0%	100%	0%	0
0%	100%	0%	1
50%	50%	0%	2
50%	50%	0%	3
62.5%	37.5%	0%	4
68.7%	31.2%	0%	5
71.8%	28.1%	0%	6
73.4%	26.5%	0%	7
74.2%	25.8%	0%	8
74.6%	25.4%	0%	9
74.8%	25.2%	0%	10
74.9%	25.1%	0%	11
74.9%	25%	0%	12
74.9%	25%	0%	13
75%	25%	0%	14

Compiler

Compiled 11 to 8 computations (27.3% saved)

sample92.0ms (2.5%)

Algorithm

1×

intervals

Results

42.0ms	97×	body	1024	valid
10.0ms	28×	body	2048	valid
8.0ms	36×	body	512	valid
4.0ms	71×	body	128	valid
3.0ms	22×	body	256	valid
1.0ms	2×	body	4096	valid

Compiler

Compiled 22 to 16 computations (27.3% saved)

simplify7.0ms (0.2%)

Algorithm

1×	egg-herbie

Rules

2×	`+-commutative_binary64`
1×	`1-exp_binary64`
1×	`hypot-1-def_binary64`
1×	`fma-def_binary64`

Counts

1 → 2

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	8	12
1	13	9
2	14	9
3	13	9

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

46.1b

Counts

3 → 1

Alt Table

Status	Error	Program
▶	46.1b	(log.f64 (+.f64 x (hypot.f64 1 x)))

Compiler

Compiled 30 to 21 computations (30% saved)

localize5.0ms (0.1%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.0b	(hypot.f64 1 x)
✓	0.5b	(+.f64 x (hypot.f64 1 x))
✓	2.4b	(log.f64 (+.f64 x (hypot.f64 1 x)))

series10.0ms (0.3%)

Counts

3 → 36

Calls

3 calls:

4.0ms	(log.f64 (+.f64 x (hypot.f64 1 x)))
3.0ms	(+.f64 x (hypot.f64 1 x))
3.0ms	(hypot.f64 1 x)

rewrite6.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

9×	`*-un-lft-identity_binary64`
5×	`add-log-exp_binary64`
5×	`add-sqr-sqrt_binary64`
5×	`add-cube-cbrt_binary64`
4×	`add-exp-log_binary64`

Counts

3 → 44

Calls

3 calls:

2.0ms	(+.f64 x (hypot.f64 1 x))
2.0ms	(log.f64 (+.f64 x (hypot.f64 1 x)))
0.0ms	(hypot.f64 1 x)

simplify78.0ms (2.2%)

Algorithm

1×	egg-herbie

Rules

910×	`fma-neg_binary64`
469×	`cancel-sign-sub-inv_binary64`
426×	`associate-/r*_binary64`
376×	`fma-def_binary64`
361×	`sub-neg_binary64`

Counts

80 → 113

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	148	1089
1	394	1025
2	959	1013
3	2675	1013
4	4999	1013
5	5338	1013

prune69.0ms (1.9%)

Pruning

4 alts after pruning (4 fresh and 0 done)

	Pruned	Kept	Total
New	109	4	113
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	110	4	114

Error

Counts

114 → 4

Alt Table

Status	Error	Program
	49.5b	(log.f64 (/.f64 -1/2 x))
	61.1b	(log.f64 (/.f64 (-.f64 (.f64 x x) (.f64 (hypot.f64 1 x) (hypot.f64 1 x))) (-.f64 x (hypot.f64 1 x))))
	46.1b	(log.f64 (expm1.f64 (log1p.f64 (+.f64 x (hypot.f64 1 x)))))
▶	28.0b	x

Compiler

Compiled 1590 to 1193 computations (25% saved)

localize1.0ms (0%)

prune4.0ms (0.1%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Kept	Total
New	0	0
Fresh	3	3
Picked	1	1
Done	0	0
Total	4	4

Error

Counts

4 → 4

Alt Table

Status	Error	Program
	49.5b	(log.f64 (/.f64 -1/2 x))
	61.1b	(log.f64 (/.f64 (-.f64 (.f64 x x) (.f64 (hypot.f64 1 x) (hypot.f64 1 x))) (-.f64 x (hypot.f64 1 x))))
▶	46.1b	(log.f64 (expm1.f64 (log1p.f64 (+.f64 x (hypot.f64 1 x)))))
✓	28.0b	x

Compiler

Compiled 68 to 49 computations (27.9% saved)

localize9.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.0b	(hypot.f64 1 x)
	0.5b	(+.f64 x (hypot.f64 1 x))
✓	1.3b	(expm1.f64 (log1p.f64 (+.f64 x (hypot.f64 1 x))))
✓	32.7b	(log.f64 (expm1.f64 (log1p.f64 (+.f64 x (hypot.f64 1 x)))))

series7.0ms (0.2%)

Counts

2 → 24

Calls

2 calls:

4.0ms	(log.f64 (expm1.f64 (log1p.f64 (+.f64 x (hypot.f64 1 x)))))
3.0ms	(expm1.f64 (log1p.f64 (+.f64 x (hypot.f64 1 x))))

rewrite3.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

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

Counts

2 → 25

Calls

2 calls:

1.0ms	(log.f64 (expm1.f64 (log1p.f64 (+.f64 x (hypot.f64 1 x)))))
0.0ms	(expm1.f64 (log1p.f64 (+.f64 x (hypot.f64 1 x))))

simplify62.0ms (1.7%)

Algorithm

1×	egg-herbie

Rules

754×	`fma-neg_binary64`
426×	`associate-/r*_binary64`
417×	`associate-l_binary64`
364×	`cancel-sign-sub-inv_binary64`
277×	`sub-neg_binary64`

Counts

49 → 86

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	112	732
1	282	676
2	734	670
3	2057	670
4	4330	670
5	4907	670

prune92.0ms (2.5%)

Pruning

4 alts after pruning (2 fresh and 2 done)

	Pruned	Kept	Total
New	158	0	158
Fresh	0	2	2
Picked	0	1	1
Done	0	1	1
Total	158	4	162

Error

Counts

162 → 4

Alt Table

Status	Error	Program
▶	49.5b	(log.f64 (/.f64 -1/2 x))
	61.1b	(log.f64 (/.f64 (-.f64 (.f64 x x) (.f64 (hypot.f64 1 x) (hypot.f64 1 x))) (-.f64 x (hypot.f64 1 x))))
✓	46.1b	(log.f64 (expm1.f64 (log1p.f64 (+.f64 x (hypot.f64 1 x)))))
✓	28.0b	x

Compiler

Compiled 2284 to 1782 computations (22% saved)

localize3.0ms (0.1%)

Local error

Found 1 expressions with local error:

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

series31.0ms (0.9%)

Counts

1 → 12

Calls

1 calls:

31.0ms

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

rewrite3.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

13×	`log-prod_binary64`
9×	`times-frac_binary64`
8×	`*-un-lft-identity_binary64`
8×	`add-sqr-sqrt_binary64`
8×	`add-cube-cbrt_binary64`

Counts

1 → 26

Calls

1 calls:

2.0ms

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

simplify124.0ms (3.4%)

Algorithm

1×	egg-herbie

Rules

935×	`unsub-neg_binary64`
616×	`fma-def_binary64`
451×	`fma-neg_binary64`
429×	`sub-neg_binary64`
423×	`distribute-neg-out_binary64`

Counts

38 → 36

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	72	424
1	114	406
2	227	395
3	415	393
4	975	391
5	2148	391
6	3642	391
7	4491	391
8	4900	391
9	4996	391
10	4892	391

prune15.0ms (0.4%)

Pruning

4 alts after pruning (1 fresh and 3 done)

	Pruned	Kept	Total
New	36	0	36
Fresh	0	1	1
Picked	0	1	1
Done	0	2	2
Total	36	4	40

Error

Counts

40 → 4

Alt Table

Status	Error	Program
✓	49.5b	(log.f64 (/.f64 -1/2 x))
	61.1b	(log.f64 (/.f64 (-.f64 (.f64 x x) (.f64 (hypot.f64 1 x) (hypot.f64 1 x))) (-.f64 x (hypot.f64 1 x))))
✓	46.1b	(log.f64 (expm1.f64 (log1p.f64 (+.f64 x (hypot.f64 1 x)))))
✓	28.0b	x

Compiler

Compiled 405 to 312 computations (23% saved)

regimes108.0ms (3%)

Accuracy

Total 0.1b remaining (49%)

Threshold costs 0.1b (49%)

Counts

27 → 3

Compiler

Compiled 960 to 742 computations (22.7% saved)

bsearch34.0ms (0.9%)

Steps

Iters	Range		Point
10	1.2469161381373078e-8	120367609.9304264	9.494981790915549e-6
7	-46.58916388319284	-0.3479609702528069	-0.8443812609077854

Compiler

Compiled 2 to 1 computations (50% saved)

simplify6.0ms (0.2%)

Algorithm

1×	egg-herbie

Rules

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

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	33	60
1	41	60
2	48	60
3	62	60
4	67	60
5	69	60
6	66	60

end1.0ms (0%)

Compiler: Compiled 41 to 31 computations (24.4% saved)

sample2.4s (67.2%)

Algorithm

1×

intervals

Results

1.1s	2494×	body	1024	valid
478.0ms	1189×	body	2048	valid
303.0ms	1237×	body	512	valid
138.0ms	2400×	body	128	valid
92.0ms	637×	body	256	valid
21.0ms	43×	body	4096	valid

Compiler

Compiled 88 to 65 computations (26.1% saved)

Details

analyze412.0ms (11.4%)

sample92.0ms (2.5%)

simplify7.0ms (0.2%)

prune3.0ms (0.1%)

localize5.0ms (0.1%)

series10.0ms (0.3%)

rewrite6.0ms (0.2%)

simplify78.0ms (2.2%)

prune69.0ms (1.9%)

localize1.0ms (0%)

prune4.0ms (0.1%)

localize9.0ms (0.2%)

series7.0ms (0.2%)

rewrite3.0ms (0.1%)

simplify62.0ms (1.7%)

prune92.0ms (2.5%)

localize3.0ms (0.1%)

series31.0ms (0.9%)

rewrite3.0ms (0.1%)

simplify124.0ms (3.4%)

prune15.0ms (0.4%)

regimes108.0ms (3%)

bsearch34.0ms (0.9%)

simplify6.0ms (0.2%)

end1.0ms (0%)

sample2.4s (67.2%)

Profiling