Details

analyze76.0ms (1.8%)

Algorithm

1×

Search

True	Other	False	Iter
0%	100%	0%	0
0%	100%	0%	1
0%	100%	0%	2
50%	50%	0%	3
50%	25%	25%	4
50%	12.5%	37.5%	5
50%	6.2%	43.8%	6
50%	3.1%	46.9%	7
50%	1.6%	48.5%	8
50%	0.8%	49.2%	9
50.4%	0.4%	49.2%	10
50.4%	0.2%	49.4%	11
50.4%	0.1%	49.5%	12
50.4%	0%	49.6%	13
50.4%	0%	49.6%	14

Compiler

Compiled 10 to 8 computations (20% saved)

sample106.0ms (2.6%)

Algorithm

1×

intervals

Results

78.0ms	145×	body	2048	valid
14.0ms	57×	body	1024	valid
3.0ms	25×	body	512	valid
2.0ms	22×	body	256	valid
0.0ms	7×	body	128	valid

Compiler

Compiled 20 to 16 computations (20% saved)

simplify65.0ms (1.6%)

Algorithm

1×	egg-herbie

Rules

819×	`div-sub_binary64`
801×	`associate-/l*_binary64`
624×	`fma-def_binary64`
581×	`fma-neg_binary64`
548×	`unswap-sqr_binary64`

Counts

1 → 1

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	8	13
1	20	13
2	35	13
3	57	13
4	112	13
5	223	13
6	481	13
7	890	13
8	1570	13
9	4778	13
10	5815	13

prune2.0ms (0%)

Pruning

2 alts after pruning (2 fresh and 0 done)

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

Error

27.6b

Counts

2 → 1

Alt Table

Status	Error	Program
▶	27.6b	(+.f64 (-.f64 (exp.f64 x) 2) (exp.f64 (neg.f64 x)))

Compiler

Compiled 27 to 21 computations (22.2% saved)

localize5.0ms (0.1%)

Local error

Found 1 expressions with local error:

New	Error	Program
✓	4.1b	(+.f64 (-.f64 (exp.f64 x) 2) (exp.f64 (neg.f64 x)))

rewrite11.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

16×	`*-un-lft-identity_binary64`
13×	`associate-+l+_binary64`
11×	`add-sqr-sqrt_binary64`
9×	`prod-diff_binary64`
9×	`add-cube-cbrt_binary64`

Counts

1 → 39

Calls

1 calls:

8.0ms

(+.f64 (-.f64 (exp.f64 x) 2) (exp.f64 (neg.f64 x)))

series8.0ms (0.2%)

Counts

1 → 12

Calls

1 calls:

8.0ms

(+.f64 (-.f64 (exp.f64 x) 2) (exp.f64 (neg.f64 x)))

simplify98.0ms (2.4%)

Algorithm

1×	egg-herbie

Rules

359×	`div-sub_binary64`
337×	`sub-neg_binary64`
330×	`distribute-rgt-in_binary64`
315×	`distribute-lft-in_binary64`
313×	`+-commutative_binary64`

Counts

51 → 89

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	111	905
1	247	700
2	624	685
3	2245	676
4	3585	676
5	4863	676
6	4832	676

prune42.0ms (1%)

Pruning

2 alts after pruning (1 fresh and 1 done)

	Pruned	Kept	Total
New	88	1	89
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	88	2	90

Error

0.0b

Counts

90 → 2

Alt Table

Status	Error	Program
✓	27.6b	(+.f64 (-.f64 (exp.f64 x) 2) (exp.f64 (neg.f64 x)))
▶	0.5b	(fma.f64 1/12 (pow.f64 x 4) (fma.f64 x x (*.f64 1/360 (pow.f64 x 6))))

Compiler

Compiled 1289 to 736 computations (42.9% saved)

localize7.0ms (0.2%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.0b	(fma.f64 1/12 (pow.f64 x 4) (fma.f64 x x (*.f64 1/360 (pow.f64 x 6))))
✓	0.1b	(*.f64 1/360 (pow.f64 x 6))

rewrite6.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

10×	`add-sqr-sqrt_binary64`
7×	`associate-r_binary64`
7×	`add-exp-log_binary64`
5×	`*-un-lft-identity_binary64`
5×	`add-cube-cbrt_binary64`

Counts

2 → 37

Calls

2 calls:

4.0ms	(*.f64 1/360 (pow.f64 x 6))
0.0ms	(fma.f64 1/12 (pow.f64 x 4) (fma.f64 x x (*.f64 1/360 (pow.f64 x 6))))

series32.0ms (0.8%)

Counts

2 → 12

Calls

2 calls:

18.0ms	(*.f64 1/360 (pow.f64 x 6))
14.0ms	(fma.f64 1/12 (pow.f64 x 4) (fma.f64 x x (*.f64 1/360 (pow.f64 x 6))))

simplify71.0ms (1.7%)

Algorithm

1×	egg-herbie

Rules

562×	`distribute-rgt-in_binary64`
557×	`distribute-lft-in_binary64`
385×	`fma-def_binary64`
384×	`unswap-sqr_binary64`
350×	`log-prod_binary64`

Counts

49 → 77

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	75	702
1	135	653
2	330	621
3	1413	621
4	4726	621
5	5066	621

prune41.0ms (1%)

Pruning

3 alts after pruning (1 fresh and 2 done)

	Pruned	Kept	Total
New	76	1	77
Fresh	0	0	0
Picked	0	1	1
Done	0	1	1
Total	76	3	79

Error

Counts

79 → 3

Alt Table

Status	Error	Program
✓	27.6b	(+.f64 (-.f64 (exp.f64 x) 2) (exp.f64 (neg.f64 x)))
✓	0.5b	(fma.f64 1/12 (pow.f64 x 4) (fma.f64 x x (*.f64 1/360 (pow.f64 x 6))))
▶	0.5b	(.f64 (sqrt.f64 (fma.f64 1/12 (pow.f64 x 4) (fma.f64 x x (.f64 1/360 (pow.f64 x 6))))) (sqrt.f64 (fma.f64 1/12 (pow.f64 x 4) (fma.f64 x x (*.f64 1/360 (pow.f64 x 6))))))

Compiler

Compiled 1042 to 770 computations (26.1% saved)

localize10.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.1b	(*.f64 1/360 (pow.f64 x 6))
	0.1b	(*.f64 1/360 (pow.f64 x 6))
	31.0b	(sqrt.f64 (fma.f64 1/12 (pow.f64 x 4) (fma.f64 x x (*.f64 1/360 (pow.f64 x 6)))))
✓	31.0b	(sqrt.f64 (fma.f64 1/12 (pow.f64 x 4) (fma.f64 x x (*.f64 1/360 (pow.f64 x 6)))))

rewrite2.0ms (0%)

Algorithm

1×	rewrite-expression-head

Rules

3×	`sqrt-prod_binary64`
3×	`add-sqr-sqrt_binary64`
2×	`*-un-lft-identity_binary64`
2×	`add-cube-cbrt_binary64`
2×	`pow1_binary64`

Counts

1 → 15

Calls

1 calls:

1.0ms

(sqrt.f64 (fma.f64 1/12 (pow.f64 x 4) (fma.f64 x x (*.f64 1/360 (pow.f64 x 6)))))

series10.0ms (0.2%)

Counts

1 → 12

Calls

1 calls:

10.0ms

(sqrt.f64 (fma.f64 1/12 (pow.f64 x 4) (fma.f64 x x (*.f64 1/360 (pow.f64 x 6)))))

simplify68.0ms (1.7%)

Algorithm

1×	egg-herbie

Rules

463×	`unswap-sqr_binary64`
436×	`cancel-sign-sub-inv_binary64`
416×	`fma-neg_binary64`
267×	`associate-*r/_binary64`
262×	`sub-neg_binary64`

Counts

27 → 42

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	77	696
1	201	675
2	643	651
3	2241	647
4	4510	647
5	5155	647

prune177.0ms (4.3%)

Pruning

3 alts after pruning (0 fresh and 3 done)

	Pruned	Kept	Total
New	216	0	216
Fresh	0	0	0
Picked	0	1	1
Done	0	2	2
Total	216	3	219

Error

Counts

219 → 3

Alt Table

Status	Error	Program
✓	27.6b	(+.f64 (-.f64 (exp.f64 x) 2) (exp.f64 (neg.f64 x)))
✓	0.5b	(fma.f64 1/12 (pow.f64 x 4) (fma.f64 x x (*.f64 1/360 (pow.f64 x 6))))
✓	0.5b	(.f64 (sqrt.f64 (fma.f64 1/12 (pow.f64 x 4) (fma.f64 x x (.f64 1/360 (pow.f64 x 6))))) (sqrt.f64 (fma.f64 1/12 (pow.f64 x 4) (fma.f64 x x (*.f64 1/360 (pow.f64 x 6))))))

Compiler

Compiled 5335 to 4052 computations (24% saved)

regimes18.0ms (0.4%)

Accuracy

Total 0.5b remaining (94.2%)

Threshold costs 0.5b (94.2%)

Compiler

Compiled 226 to 168 computations (25.7% saved)

simplify3.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

1×	`*-commutative_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	11	18
1	12	18
2	12	18

end1.0ms (0%)

Compiler: Compiled 14 to 10 computations (28.6% saved)

sample3.2s (79%)

Algorithm

1×

intervals

Results

2.2s	4157×	body	2048	valid
491.0ms	2030×	body	1024	valid
133.0ms	943×	body	512	valid
50.0ms	525×	body	256	valid
15.0ms	345×	body	128	valid
0.0ms	2×	body	128	invalid

Compiler

Compiled 78 to 58 computations (25.6% saved)

Details

analyze76.0ms (1.8%)

sample106.0ms (2.6%)

simplify65.0ms (1.6%)

prune2.0ms (0%)

localize5.0ms (0.1%)

rewrite11.0ms (0.3%)

series8.0ms (0.2%)

simplify98.0ms (2.4%)

prune42.0ms (1%)

localize7.0ms (0.2%)

rewrite6.0ms (0.1%)

series32.0ms (0.8%)

simplify71.0ms (1.7%)

prune41.0ms (1%)

localize10.0ms (0.2%)

rewrite2.0ms (0%)

series10.0ms (0.2%)

simplify68.0ms (1.7%)

prune177.0ms (4.3%)

regimes18.0ms (0.4%)

simplify3.0ms (0.1%)

end1.0ms (0%)

sample3.2s (79%)

Profiling