Details

analyze367.0ms (7%)

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)

sample69.0ms (1.3%)

Algorithm

1×

intervals

Results

29.0ms	67×	body	1024	valid
16.0ms	41×	body	2048	valid
8.0ms	37×	body	512	valid
5.0ms	87×	body	128	valid
3.0ms	24×	body	256	valid

Compiler

Compiled 22 to 16 computations (27.3% 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

44.0b

Counts

3 → 1

Alt Table

Status	Error	Program
▶	44.0b	(log.f64 (+.f64 x (hypot.f64 1 x)))

Compiler

Compiled 30 to 21 computations (30% saved)

localize4.0ms (0.1%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.0b	(hypot.f64 1 x)
✓	0.8b	(+.f64 x (hypot.f64 1 x))
✓	5.1b	(log.f64 (+.f64 x (hypot.f64 1 x)))

series10.0ms (0.2%)

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 (0.1%)

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)

simplify72.0ms (1.4%)

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

prune60.0ms (1.1%)

Pruning

5 alts after pruning (4 fresh and 1 done)

	Pruned	Kept	Total
New	109	4	113
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	109	5	114

Error

0.0b

Counts

114 → 5

Alt Table

Status	Error	Program
▶	31.5b	(-.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))))
✓	44.0b	(log.f64 (+.f64 x (hypot.f64 1 x)))
	43.9b	(log.f64 (fma.f64 (*.f64 (cbrt.f64 x) (cbrt.f64 x)) (cbrt.f64 x) (hypot.f64 1 x)))
	60.4b	(log.f64 (log1p.f64 (expm1.f64 (+.f64 x (hypot.f64 1 x)))))
	48.7b	(log.f64 (/.f64 -1/2 x))

Compiler

Compiled 1617 to 1212 computations (25% 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	(*.f64 5/112 (pow.f64 x 7))
✓	0.1b	(fma.f64 1/6 (pow.f64 x 3) (*.f64 5/112 (pow.f64 x 7)))
✓	22.7b	(-.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 (0.3%)

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 (0.2%)

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)

simplify107.0ms (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

prune111.0ms (2.1%)

Pruning

5 alts after pruning (3 fresh and 2 done)

	Pruned	Kept	Total
New	122	0	122
Fresh	0	3	3
Picked	0	1	1
Done	0	1	1
Total	122	5	127

Error

0.0b

Counts

127 → 5

Alt Table

Status	Error	Program
✓	31.5b	(-.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))))
✓	44.0b	(log.f64 (+.f64 x (hypot.f64 1 x)))
▶	43.9b	(log.f64 (fma.f64 (*.f64 (cbrt.f64 x) (cbrt.f64 x)) (cbrt.f64 x) (hypot.f64 1 x)))
	60.4b	(log.f64 (log1p.f64 (expm1.f64 (+.f64 x (hypot.f64 1 x)))))
	48.7b	(log.f64 (/.f64 -1/2 x))

Compiler

Compiled 3513 to 2780 computations (20.9% saved)

localize10.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.5b	(*.f64 (cbrt.f64 x) (cbrt.f64 x))
✓	0.6b	(cbrt.f64 x)
✓	5.1b	(log.f64 (fma.f64 (*.f64 (cbrt.f64 x) (cbrt.f64 x)) (cbrt.f64 x) (hypot.f64 1 x)))
✓	14.2b	(fma.f64 (*.f64 (cbrt.f64 x) (cbrt.f64 x)) (cbrt.f64 x) (hypot.f64 1 x))

series98.0ms (1.9%)

Counts

4 → 48

Calls

4 calls:

38.0ms	(cbrt.f64 x)
35.0ms	(*.f64 (cbrt.f64 x) (cbrt.f64 x))
14.0ms	(log.f64 (fma.f64 (*.f64 (cbrt.f64 x) (cbrt.f64 x)) (cbrt.f64 x) (hypot.f64 1 x)))
10.0ms	(fma.f64 (*.f64 (cbrt.f64 x) (cbrt.f64 x)) (cbrt.f64 x) (hypot.f64 1 x))

rewrite9.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

22×	`add-sqr-sqrt_binary64`
19×	`cbrt-prod_binary64`
14×	`*-un-lft-identity_binary64`
14×	`add-cube-cbrt_binary64`
12×	`pow1_binary64`

Counts

4 → 79

Calls

4 calls:

4.0ms	(*.f64 (cbrt.f64 x) (cbrt.f64 x))
1.0ms	(log.f64 (fma.f64 (*.f64 (cbrt.f64 x) (cbrt.f64 x)) (cbrt.f64 x) (hypot.f64 1 x)))
1.0ms	(cbrt.f64 x)
0.0ms	(fma.f64 (*.f64 (cbrt.f64 x) (cbrt.f64 x)) (cbrt.f64 x) (hypot.f64 1 x))

simplify107.0ms (2%)

Algorithm

1×	egg-herbie

Rules

540×	`fma-neg_binary64`
494×	`associate-/r*_binary64`
355×	`times-frac_binary64`
343×	`fma-def_binary64`
295×	`associate-/l*_binary64`

Counts

127 → 164

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	155	1371
1	343	1213
2	1070	1142
3	4115	1127
4	4819	1127
5	4995	1127
6	4906	1127

prune82.0ms (1.5%)

Pruning

5 alts after pruning (2 fresh and 3 done)

	Pruned	Kept	Total
New	200	0	200
Fresh	0	2	2
Picked	0	1	1
Done	0	2	2
Total	200	5	205

Error

0.0b

Counts

205 → 5

Alt Table

Status	Error	Program
✓	31.5b	(-.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))))
✓	44.0b	(log.f64 (+.f64 x (hypot.f64 1 x)))
✓	43.9b	(log.f64 (fma.f64 (*.f64 (cbrt.f64 x) (cbrt.f64 x)) (cbrt.f64 x) (hypot.f64 1 x)))
	60.4b	(log.f64 (log1p.f64 (expm1.f64 (+.f64 x (hypot.f64 1 x)))))
▶	48.7b	(log.f64 (/.f64 -1/2 x))

Compiler

Compiled 3142 to 1581 computations (49.7% saved)

localize3.0ms (0.1%)

prune3.0ms (0.1%)

Pruning

5 alts after pruning (1 fresh and 4 done)

	Kept	Total
New	0	0
Fresh	1	1
Picked	1	1
Done	3	3
Total	5	5

Error

0.0b

Counts

5 → 5

Alt Table

Status	Error	Program
✓	31.5b	(-.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))))
✓	44.0b	(log.f64 (+.f64 x (hypot.f64 1 x)))
✓	43.9b	(log.f64 (fma.f64 (*.f64 (cbrt.f64 x) (cbrt.f64 x)) (cbrt.f64 x) (hypot.f64 1 x)))
	60.4b	(log.f64 (log1p.f64 (expm1.f64 (+.f64 x (hypot.f64 1 x)))))
✓	48.7b	(log.f64 (/.f64 -1/2 x))

Compiler

Compiled 52 to 37 computations (28.8% saved)

regimes94.0ms (1.8%)

Accuracy

Total 0.1b remaining (52.3%)

Threshold costs 0.1b (52.3%)

Counts

24 → 3

Compiler

Compiled 873 to 664 computations (23.9% saved)

bsearch34.0ms (0.6%)

Steps

Iters	Range		Point
11	5.136032267515115e-5	6592503494772929000.0	0.023563724942838992
7	-32.35992716534212	-0.9873232282890734	-0.9971603401393445

Compiler

Compiled 2 to 1 computations (50% saved)

simplify5.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

10×	`+-commutative_binary64`
6×	`sub-neg_binary64`
5×	`*-commutative_binary64`
4×	`neg-sub0_binary64`
4×	`neg-mul-1_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	46	83
1	57	83
2	67	83
3	83	83
4	89	83
5	91	83
6	88	83

end1.0ms (0%)

Compiler: Compiled 57 to 44 computations (22.8% saved)

sample4.0s (75.3%)

Algorithm

1×

intervals

Results

1.7s	2466×	body	1024	valid
769.0ms	1184×	body	2048	valid
535.0ms	1317×	body	512	valid
239.0ms	2378×	body	128	valid
141.0ms	608×	body	256	valid
40.0ms	47×	body	4096	valid

Compiler

Compiled 121 to 90 computations (25.6% saved)

Details

analyze367.0ms (7%)

sample69.0ms (1.3%)

simplify6.0ms (0.1%)

prune3.0ms (0.1%)

localize4.0ms (0.1%)

series10.0ms (0.2%)

rewrite6.0ms (0.1%)

simplify72.0ms (1.4%)

prune60.0ms (1.1%)

localize10.0ms (0.2%)

series16.0ms (0.3%)

rewrite13.0ms (0.2%)

simplify107.0ms (2%)

prune111.0ms (2.1%)

localize10.0ms (0.2%)

series98.0ms (1.9%)

rewrite9.0ms (0.2%)

simplify107.0ms (2%)

prune82.0ms (1.5%)

localize3.0ms (0.1%)

prune3.0ms (0.1%)

regimes94.0ms (1.8%)

bsearch34.0ms (0.6%)

simplify5.0ms (0.1%)

end1.0ms (0%)

sample4.0s (75.3%)

Profiling