Details

analyze367.0ms (8.9%)

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)

sample88.0ms (2.1%)

Algorithm

1×

intervals

Results

30.0ms	74×	body	1024	valid
14.0ms	43×	body	2048	valid
13.0ms	43×	body	512	valid
6.0ms	17×	body	256	valid
4.0ms	78×	body	128	valid
0.0ms	1×	body	4096	valid

Compiler

Compiled 22 to 16 computations (27.3% saved)

simplify10.0ms (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

45.0b

Counts

3 → 1

Alt Table

Status	Error	Program
▶	45.0b	(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
✓	1.2b	(+.f64 x (hypot.f64 1 x))
✓	2.8b	(log.f64 (+.f64 x (hypot.f64 1 x)))

series7.0ms (0.2%)

Counts

2 → 24

Calls

2 calls:

4.0ms	(log.f64 (+.f64 x (hypot.f64 1 x)))
3.0ms	(+.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 (1.9%)

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

prune45.0ms (1.1%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	78	3	81
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	78	4	82

Error

0.0b

Counts

82 → 4

Alt Table

Status	Error	Program
✓	45.0b	(log.f64 (+.f64 x (hypot.f64 1 x)))
▶	34.1b	(-.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))))
	45.4b	(.f64 (.f64 (cbrt.f64 (log.f64 (+.f64 x (hypot.f64 1 x)))) (cbrt.f64 (log.f64 (+.f64 x (hypot.f64 1 x))))) (cbrt.f64 (log.f64 (+.f64 x (hypot.f64 1 x)))))
	45.4b	(log.f64 (/.f64 -1/2 x))

Compiler

Compiled 1207 to 914 computations (24.3% saved)

localize10.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(fma.f64 3/40 (pow.f64 x 5) x)
✓	0.1b	(fma.f64 1/6 (pow.f64 x 3) (*.f64 5/112 (pow.f64 x 7)))
✓	0.1b	(*.f64 5/112 (pow.f64 x 7))
✓	23.6b	(-.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))))

series16.0ms (0.4%)

Counts

4 → 36

Calls

4 calls:

5.0ms	(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))))
4.0ms	(*.f64 5/112 (pow.f64 x 7))
3.0ms	(fma.f64 3/40 (pow.f64 x 5) x)

rewrite13.0ms (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:

5.0ms	(-.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))))
4.0ms	(*.f64 5/112 (pow.f64 x 7))
0.0ms	(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)

simplify103.0ms (2.5%)

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

prune117.0ms (2.8%)

Pruning

4 alts after pruning (2 fresh and 2 done)

	Pruned	Kept	Total
New	122	0	122
Fresh	0	2	2
Picked	0	1	1
Done	0	1	1
Total	122	4	126

Error

0.0b

Counts

126 → 4

Alt Table

Status	Error	Program
✓	45.0b	(log.f64 (+.f64 x (hypot.f64 1 x)))
✓	34.1b	(-.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))))
▶	45.4b	(.f64 (.f64 (cbrt.f64 (log.f64 (+.f64 x (hypot.f64 1 x)))) (cbrt.f64 (log.f64 (+.f64 x (hypot.f64 1 x))))) (cbrt.f64 (log.f64 (+.f64 x (hypot.f64 1 x)))))
	45.4b	(log.f64 (/.f64 -1/2 x))

Compiler

Compiled 3517 to 2788 computations (20.7% saved)

localize7.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.2b	(*.f64 (cbrt.f64 (log.f64 (+.f64 x (hypot.f64 1 x)))) (cbrt.f64 (log.f64 (+.f64 x (hypot.f64 1 x)))))
✓	0.2b	(cbrt.f64 (log.f64 (+.f64 x (hypot.f64 1 x))))
	1.2b	(+.f64 x (hypot.f64 1 x))
	2.8b	(log.f64 (+.f64 x (hypot.f64 1 x)))

series155.0ms (3.7%)

Counts

2 → 24

Calls

2 calls:

124.0ms	(*.f64 (cbrt.f64 (log.f64 (+.f64 x (hypot.f64 1 x)))) (cbrt.f64 (log.f64 (+.f64 x (hypot.f64 1 x)))))
31.0ms	(cbrt.f64 (log.f64 (+.f64 x (hypot.f64 1 x))))

rewrite10.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

28×	`cbrt-prod_binary64`
19×	`add-sqr-sqrt_binary64`
16×	`pow1_binary64`
13×	`*-un-lft-identity_binary64`
11×	`add-cube-cbrt_binary64`

Counts

2 → 61

Calls

2 calls:

5.0ms	(*.f64 (cbrt.f64 (log.f64 (+.f64 x (hypot.f64 1 x)))) (cbrt.f64 (log.f64 (+.f64 x (hypot.f64 1 x)))))
1.0ms	(cbrt.f64 (log.f64 (+.f64 x (hypot.f64 1 x))))

simplify106.0ms (2.6%)

Algorithm

1×	egg-herbie

Rules

406×	`fma-def_binary64`
277×	`associate-r_binary64`
246×	`associate-+r+_binary64`
244×	`*-commutative_binary64`
239×	`associate-l_binary64`

Counts

85 → 120

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	397	4639
1	1203	4233
2	4524	4038
3	5079	4038

prune421.0ms (10.2%)

Pruning

4 alts after pruning (2 fresh and 2 done)

	Pruned	Kept	Total
New	440	1	441
Fresh	0	1	1
Picked	1	0	1
Done	0	2	2
Total	441	4	445

Error

0.0b

Counts

445 → 4

Alt Table

Status	Error	Program
✓	45.0b	(log.f64 (+.f64 x (hypot.f64 1 x)))
✓	34.1b	(-.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))))
	45.5b	(.f64 (.f64 (pow.f64 (cbrt.f64 (cbrt.f64 (log.f64 (+.f64 x (hypot.f64 1 x))))) 4) (*.f64 (cbrt.f64 (cbrt.f64 (log.f64 (+.f64 x (hypot.f64 1 x))))) (cbrt.f64 (cbrt.f64 (log.f64 (+.f64 x (hypot.f64 1 x))))))) (cbrt.f64 (log.f64 (+.f64 x (hypot.f64 1 x)))))
▶	45.4b	(log.f64 (/.f64 -1/2 x))

Compiler

Compiled 18098 to 14345 computations (20.7% saved)

localize3.0ms (0.1%)

prune3.0ms (0.1%)

Pruning

4 alts after pruning (1 fresh and 3 done)

	Kept	Total
New	0	0
Fresh	1	1
Picked	1	1
Done	2	2
Total	4	4

Error

0.0b

Counts

4 → 4

Alt Table

Status	Error	Program
✓	45.0b	(log.f64 (+.f64 x (hypot.f64 1 x)))
✓	34.1b	(-.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))))
	45.5b	(.f64 (.f64 (pow.f64 (cbrt.f64 (cbrt.f64 (log.f64 (+.f64 x (hypot.f64 1 x))))) 4) (*.f64 (cbrt.f64 (cbrt.f64 (log.f64 (+.f64 x (hypot.f64 1 x))))) (cbrt.f64 (cbrt.f64 (log.f64 (+.f64 x (hypot.f64 1 x))))))) (cbrt.f64 (log.f64 (+.f64 x (hypot.f64 1 x)))))
✓	45.4b	(log.f64 (/.f64 -1/2 x))

Compiler

Compiled 67 to 52 computations (22.4% saved)

regimes117.0ms (2.8%)

Accuracy

Total 0.1b remaining (62.1%)

Threshold costs 0.1b (62.1%)

Counts

25 → 3

Compiler

Compiled 1503 to 1162 computations (22.7% saved)

bsearch34.0ms (0.8%)

Steps

Iters	Range		Point
8	6.976199906176216e-5	0.02598030036546575	0.023640278768881973
10	-941544012471358.0	-0.0111165616554553	-1.2618603046466388

Compiler

Compiled 2 to 1 computations (50% saved)

simplify4.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

9×	`+-commutative_binary64`
8×	`*-commutative_binary64`
6×	`sub-neg_binary64`
5×	`neg-sub0_binary64`
5×	`neg-mul-1_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	31	55
1	41	55
2	49	55
3	71	55
4	80	55
5	86	55
6	88	55
7	85	55

end1.0ms (0%)

Compiler: Compiled 38 to 29 computations (23.7% saved)

sample2.4s (58.2%)

Algorithm

1×

intervals

Results

1.0s	2488×	body	1024	valid
460.0ms	1220×	body	2048	valid
312.0ms	1279×	body	512	valid
146.0ms	2380×	body	128	valid
83.0ms	593×	body	256	valid
19.0ms	40×	body	4096	valid

Compiler

Compiled 117 to 90 computations (23.1% saved)

Details

analyze367.0ms (8.9%)

sample88.0ms (2.1%)

simplify10.0ms (0.2%)

prune3.0ms (0.1%)

localize4.0ms (0.1%)

series7.0ms (0.2%)

rewrite6.0ms (0.1%)

simplify77.0ms (1.9%)

prune45.0ms (1.1%)

localize10.0ms (0.2%)

series16.0ms (0.4%)

rewrite13.0ms (0.3%)

simplify103.0ms (2.5%)

prune117.0ms (2.8%)

localize7.0ms (0.2%)

series155.0ms (3.7%)

rewrite10.0ms (0.2%)

simplify106.0ms (2.6%)

prune421.0ms (10.2%)

localize3.0ms (0.1%)

prune3.0ms (0.1%)

regimes117.0ms (2.8%)

bsearch34.0ms (0.8%)

simplify4.0ms (0.1%)

end1.0ms (0%)

sample2.4s (58.2%)

Profiling