Details

analyze1.1s (21.5%)

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)

sample3.4s (67%)

Results

1.6s	2612×	body	1024	valid
794.0ms	1251×	body	2048	valid
475.0ms	1243×	body	512	valid
271.0ms	2439×	body	128	valid
161.0ms	675×	body	256	valid
28.0ms	36×	body	4096	valid

Compiler

Compiled 32 to 23 computations (28.1% saved)

simplify6.0ms (0.1%)

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

43.9b

Counts

3 → 1

Alt Table

Status	Error	Program
▶	43.9b	(log.f64 (+.f64 x (hypot.f64 1 x)))

Compiler

Compiled 30 to 21 computations (30% saved)

localize4.0ms (0.1%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	1.0b	(+.f64 x (hypot.f64 1 x))
✓	2.9b	(log.f64 (+.f64 x (hypot.f64 1 x)))

series11.0ms (0.2%)

Counts

2 → 24

Calls

2 calls:

7.0ms	(+.f64 x (hypot.f64 1 x))
4.0ms	(log.f64 (+.f64 x (hypot.f64 1 x)))

rewrite6.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

8×	`*-un-lft-identity_binary64`
4×	`add-log-exp_binary64`
4×	`add-sqr-sqrt_binary64`
4×	`log-prod_binary64`
4×	`add-cube-cbrt_binary64`

Counts

2 → 34

Calls

2 calls:

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

simplify77.0ms (1.5%)

Algorithm

1×	egg-herbie

Rules

665×	`fma-neg_binary64`
426×	`associate-/r*_binary64`
386×	`cancel-sign-sub-inv_binary64`
299×	`sub-neg_binary64`
286×	`fma-def_binary64`

Counts

58 → 81

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	125	861
1	334	805
2	827	799
3	2288	799
4	4460	799
5	4998	799
6	4887	799

prune46.0ms (0.9%)

Pruning

3 alts after pruning (2 fresh and 1 done)

	Pruned	Kept	Total
New	79	2	81
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	79	3	82

Error

Counts

82 → 3

Alt Table

Status	Error	Program
▶	31.8b	(-.f64 (fma.f64 3/40 (pow.f64 x 5) x) (fma.f64 1/6 (pow.f64 x 3) (*.f64 5/112 (pow.f64 x 7))))
✓	43.9b	(log.f64 (+.f64 x (hypot.f64 1 x)))
	48.4b	(log.f64 (/.f64 -1/2 x))

Compiler

Compiled 1159 to 878 computations (24.2% saved)

localize11.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(fma.f64 3/40 (pow.f64 x 5) x)
✓	0.0b	(*.f64 5/112 (pow.f64 x 7))
✓	0.1b	(fma.f64 1/6 (pow.f64 x 3) (*.f64 5/112 (pow.f64 x 7)))
✓	24.5b	(-.f64 (fma.f64 3/40 (pow.f64 x 5) x) (fma.f64 1/6 (pow.f64 x 3) (*.f64 5/112 (pow.f64 x 7))))

series15.0ms (0.3%)

Counts

4 → 36

Calls

4 calls:

4.0ms	(fma.f64 1/6 (pow.f64 x 3) (*.f64 5/112 (pow.f64 x 7)))
4.0ms	(-.f64 (fma.f64 3/40 (pow.f64 x 5) x) (fma.f64 1/6 (pow.f64 x 3) (*.f64 5/112 (pow.f64 x 7))))
3.0ms	(*.f64 5/112 (pow.f64 x 7))
3.0ms	(fma.f64 3/40 (pow.f64 x 5) x)

rewrite14.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

22×	`add-sqr-sqrt_binary64`
17×	`*-un-lft-identity_binary64`
15×	`add-cube-cbrt_binary64`
9×	`add-exp-log_binary64`
9×	`prod-diff_binary64`

Counts

4 → 79

Calls

4 calls:

6.0ms	(*.f64 5/112 (pow.f64 x 7))
3.0ms	(-.f64 (fma.f64 3/40 (pow.f64 x 5) x) (fma.f64 1/6 (pow.f64 x 3) (*.f64 5/112 (pow.f64 x 7))))
0.0ms	(fma.f64 3/40 (pow.f64 x 5) x)
0.0ms	(fma.f64 1/6 (pow.f64 x 3) (*.f64 5/112 (pow.f64 x 7)))

simplify103.0ms (2%)

Algorithm

1×	egg-herbie

Rules

874×	`fma-neg_binary64`
633×	`times-frac_binary64`
600×	`associate-r_binary64`
389×	`fma-def_binary64`
339×	`distribute-lft-in_binary64`

Counts

115 → 122

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	142	2229
1	264	2018
2	793	1831
3	3426	1774
4	4426	1759
5	5632	1759

prune97.0ms (1.9%)

Pruning

3 alts after pruning (1 fresh and 2 done)

	Pruned	Kept	Total
New	122	0	122
Fresh	0	1	1
Picked	0	1	1
Done	0	1	1
Total	122	3	125

Error

Counts

125 → 3

Alt Table

Status	Error	Program
✓	31.8b	(-.f64 (fma.f64 3/40 (pow.f64 x 5) x) (fma.f64 1/6 (pow.f64 x 3) (*.f64 5/112 (pow.f64 x 7))))
✓	43.9b	(log.f64 (+.f64 x (hypot.f64 1 x)))
▶	48.4b	(log.f64 (/.f64 -1/2 x))

Compiler

Compiled 3469 to 2752 computations (20.7% saved)

localize3.0ms (0.1%)

prune2.0ms (0%)

Pruning

3 alts after pruning (0 fresh and 3 done)

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

Error

Counts

3 → 3

Alt Table

Status	Error	Program
✓	31.8b	(-.f64 (fma.f64 3/40 (pow.f64 x 5) x) (fma.f64 1/6 (pow.f64 x 3) (*.f64 5/112 (pow.f64 x 7))))
✓	43.9b	(log.f64 (+.f64 x (hypot.f64 1 x)))
✓	48.4b	(log.f64 (/.f64 -1/2 x))

Compiler

Compiled 30 to 23 computations (23.3% saved)

regimes66.0ms (1.3%)

Accuracy

Total 0.1b remaining (50.1%)

Threshold costs 0.1b (50.1%)

Counts

17 → 3

Compiler

Compiled 552 to 421 computations (23.7% saved)

bsearch34.0ms (0.7%)

Steps

Iters	Range		Point
7	0.007609009331524822	0.200053827669209	0.02445914869640051
10	-956451461.9024228	-5.5425954250658755e-5	-1.2637896809849636

Compiler

Compiled 2 to 1 computations (50% saved)

simplify3.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

1×	`+-commutative_binary64`
1×	`1-exp_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	28	49
1	31	49
2	30	49

end84.0ms (1.7%)

Compiler: Compiled 100 to 75 computations (25% saved)

Details

analyze1.1s (21.5%)

sample3.4s (67%)

simplify6.0ms (0.1%)

prune3.0ms (0.1%)

localize4.0ms (0.1%)

series11.0ms (0.2%)

rewrite6.0ms (0.1%)

simplify77.0ms (1.5%)

prune46.0ms (0.9%)

localize11.0ms (0.2%)

series15.0ms (0.3%)

rewrite14.0ms (0.3%)

simplify103.0ms (2%)

prune97.0ms (1.9%)

localize3.0ms (0.1%)

prune2.0ms (0%)

regimes66.0ms (1.3%)

bsearch34.0ms (0.7%)

simplify3.0ms (0.1%)

end84.0ms (1.7%)

Profiling