Details

analyze113.0ms (2.4%)

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)

sample112.0ms (2.3%)

Algorithm

1×

intervals

Results

67.0ms	126×	body	1024	valid
15.0ms	55×	body	512	valid
8.0ms	14×	body	2048	valid
6.0ms	39×	body	256	valid
2.0ms	22×	body	128	valid

Compiler

Compiled 20 to 16 computations (20% saved)

simplify73.0ms (1.5%)

Algorithm

1×	egg-herbie

Rules

618×	`fma-neg_binary64`
579×	`fma-def_binary64`
510×	`associate-/l*_binary64`
467×	`div-sub_binary64`
425×	`times-frac_binary64`

Counts

1 → 2

Iterations

Useful iterations: 8 (0.0ms)

Iter	Nodes	Cost
0	8	13
1	19	13
2	33	13
3	57	13
4	112	13
5	224	13
6	514	13
7	1303	13
8	3047	12
9	4469	12
10	4859	12

prune4.0ms (0.1%)

Pruning

2 alts after pruning (2 fresh and 0 done)

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

Error

57.5b

Counts

3 → 1

Alt Table

Status	Error	Program
▶	57.5b	(/.f64 (-.f64 (exp.f64 x) (exp.f64 (neg.f64 x))) 2)

Compiler

Compiled 35 to 25 computations (28.6% saved)

localize11.0ms (0.2%)

Local error

Found 1 expressions with local error:

New	Error	Program
✓	7.2b	(-.f64 (exp.f64 x) (exp.f64 (neg.f64 x)))

series5.0ms (0.1%)

Counts

1 → 8

Calls

1 calls:

4.0ms

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

rewrite14.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

11×	`*-un-lft-identity_binary64`
11×	`add-sqr-sqrt_binary64`
9×	`prod-diff_binary64`
9×	`add-cube-cbrt_binary64`
3×	`cancel-sign-sub-inv_binary64`

Counts

1 → 31

Calls

1 calls:

10.0ms

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

simplify97.0ms (2%)

Algorithm

1×	egg-herbie

Rules

608×	`fma-neg_binary64`
326×	`unsub-neg_binary64`
325×	`distribute-rgt-in_binary64`
287×	`associate-/r*_binary64`
265×	`associate-l_binary64`

Counts

39 → 49

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	86	629
1	175	535
2	491	470
3	1944	470
4	3994	468
5	4786	468
6	4810	468

prune57.0ms (1.2%)

Pruning

3 alts after pruning (3 fresh and 0 done)

	Pruned	Kept	Total
New	46	3	49
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	47	3	50

Error

Counts

50 → 3

Alt Table

Status	Error	Program
▶	0.0b	(/.f64 (*.f64 2 (sinh.f64 x)) 2)
	57.5b	(/.f64 (fma.f64 (sqrt.f64 (exp.f64 x)) (sqrt.f64 (exp.f64 x)) (neg.f64 (exp.f64 (neg.f64 x)))) 2)
	0.9b	(/.f64 (fma.f64 1/60 (pow.f64 x 5) (fma.f64 1/2520 (pow.f64 x 7) (fma.f64 2 x (*.f64 1/3 (pow.f64 x 3))))) 2)

Compiler

Compiled 1012 to 399 computations (60.6% saved)

localize7.0ms (0.2%)

Local error

Found 1 expressions with local error:

New	Error	Program
✓	0.0b	(sinh.f64 x)

series18.0ms (0.4%)

Counts

1 → 12

Calls

1 calls:

17.0ms

(sinh.f64 x)

rewrite2.0ms (0%)

Algorithm

1×	rewrite-expression-head

Rules

1×	`*-un-lft-identity_binary64`
1×	`add-sqr-sqrt_binary64`
1×	`add-cube-cbrt_binary64`
1×	`add-cbrt-cube_binary64`
1×	`add-exp-log_binary64`

Counts

1 → 10

Calls

1 calls:

1.0ms

(sinh.f64 x)

simplify72.0ms (1.5%)

Algorithm

1×	egg-herbie

Rules

738×	`div-sub_binary64`
465×	`times-frac_binary64`
453×	`associate-l_binary64`
349×	`fma-def_binary64`
331×	`associate-r_binary64`

Counts

22 → 20

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	37	220
1	79	213
2	179	205
3	396	205
4	843	205
5	2533	205
6	4634	205
7	5567	205

prune32.0ms (0.7%)

Pruning

3 alts after pruning (2 fresh and 1 done)

	Pruned	Kept	Total
New	19	1	20
Fresh	1	1	2
Picked	0	1	1
Done	0	0	0
Total	20	3	23

Error

Counts

23 → 3

Alt Table

Status	Error	Program
▶	1.1b	(/.f64 (*.f64 2 (fma.f64 1/120 (pow.f64 x 5) (fma.f64 1/6 (pow.f64 x 3) x))) 2)
✓	0.0b	(/.f64 (*.f64 2 (sinh.f64 x)) 2)
	57.5b	(/.f64 (fma.f64 (sqrt.f64 (exp.f64 x)) (sqrt.f64 (exp.f64 x)) (neg.f64 (exp.f64 (neg.f64 x)))) 2)

Compiler

Compiled 302 to 224 computations (25.8% saved)

localize18.0ms (0.4%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.0b	(fma.f64 1/120 (pow.f64 x 5) (fma.f64 1/6 (pow.f64 x 3) x))
✓	0.0b	(fma.f64 1/6 (pow.f64 x 3) x)

series14.0ms (0.3%)

Counts

2 → 24

Calls

2 calls:

7.0ms	(fma.f64 1/120 (pow.f64 x 5) (fma.f64 1/6 (pow.f64 x 3) x))
7.0ms	(fma.f64 1/6 (pow.f64 x 3) x)

rewrite3.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

2×	`*-un-lft-identity_binary64`
2×	`add-sqr-sqrt_binary64`
2×	`add-cube-cbrt_binary64`
2×	`add-cbrt-cube_binary64`
2×	`add-exp-log_binary64`

Counts

2 → 20

Calls

2 calls:

1.0ms	(fma.f64 1/6 (pow.f64 x 3) x)
1.0ms	(fma.f64 1/120 (pow.f64 x 5) (fma.f64 1/6 (pow.f64 x 3) x))

simplify119.0ms (2.5%)

Algorithm

1×	egg-herbie

Rules

622×	`distribute-rgt-in_binary64`
618×	`distribute-lft-in_binary64`
484×	`associate-l_binary64`
426×	`associate-r_binary64`
400×	`unswap-sqr_binary64`

Counts

44 → 31

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	34	566
1	54	518
2	146	518
3	554	518
4	3054	518
5	3713	518
6	4901	518
7	4974	518
8	4863	518

prune46.0ms (1%)

Pruning

3 alts after pruning (1 fresh and 2 done)

	Pruned	Kept	Total
New	31	0	31
Fresh	0	1	1
Picked	0	1	1
Done	0	1	1
Total	31	3	34

Error

Counts

34 → 3

Alt Table

Status	Error	Program
✓	1.1b	(/.f64 (*.f64 2 (fma.f64 1/120 (pow.f64 x 5) (fma.f64 1/6 (pow.f64 x 3) x))) 2)
✓	0.0b	(/.f64 (*.f64 2 (sinh.f64 x)) 2)
▶	57.5b	(/.f64 (fma.f64 (sqrt.f64 (exp.f64 x)) (sqrt.f64 (exp.f64 x)) (neg.f64 (exp.f64 (neg.f64 x)))) 2)

Compiler

Compiled 646 to 520 computations (19.5% saved)

localize16.0ms (0.3%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.0b	(sqrt.f64 (exp.f64 x))
✓	7.2b	(fma.f64 (sqrt.f64 (exp.f64 x)) (sqrt.f64 (exp.f64 x)) (neg.f64 (exp.f64 (neg.f64 x))))

series18.0ms (0.4%)

Counts

2 → 16

Calls

2 calls:

12.0ms	(fma.f64 (sqrt.f64 (exp.f64 x)) (sqrt.f64 (exp.f64 x)) (neg.f64 (exp.f64 (neg.f64 x))))
6.0ms	(sqrt.f64 (exp.f64 x))

rewrite6.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

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

Counts

2 → 28

Calls

2 calls:

3.0ms	(sqrt.f64 (exp.f64 x))
1.0ms	(fma.f64 (sqrt.f64 (exp.f64 x)) (sqrt.f64 (exp.f64 x)) (neg.f64 (exp.f64 (neg.f64 x))))

simplify89.0ms (1.9%)

Algorithm

1×	egg-herbie

Rules

570×	`distribute-rgt-in_binary64`
527×	`distribute-lft-in_binary64`
495×	`fma-def_binary64`
433×	`fma-neg_binary64`
275×	`associate-l_binary64`

Counts

44 → 54

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	74	454
1	137	429
2	289	426
3	719	419
4	1971	419
5	4463	419
6	4890	419

prune57.0ms (1.2%)

Pruning

3 alts after pruning (0 fresh and 3 done)

	Pruned	Kept	Total
New	80	0	80
Fresh	0	0	0
Picked	0	1	1
Done	0	2	2
Total	80	3	83

Error

Counts

83 → 3

Alt Table

Status	Error	Program
✓	1.1b	(/.f64 (*.f64 2 (fma.f64 1/120 (pow.f64 x 5) (fma.f64 1/6 (pow.f64 x 3) x))) 2)
✓	0.0b	(/.f64 (*.f64 2 (sinh.f64 x)) 2)
✓	57.5b	(/.f64 (fma.f64 (sqrt.f64 (exp.f64 x)) (sqrt.f64 (exp.f64 x)) (neg.f64 (exp.f64 (neg.f64 x)))) 2)

Compiler

Compiled 1382 to 532 computations (61.5% saved)

regimes128.0ms (2.7%)

Accuracy

Total 0.0b remaining (55.1%)

Threshold costs 0.0b (55.1%)

Counts

26 → 1

Compiler

Compiled 1392 to 917 computations (34.1% saved)

simplify4.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

1×	`*-commutative_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	6	9
1	7	9
2	7	9

end1.0ms (0%)

Compiler: Compiled 7 to 6 computations (14.3% saved)

sample3.7s (76.4%)

Algorithm

1×

intervals

Results

2.2s	4002×	body	1024	valid
588.0ms	2009×	body	512	valid
248.0ms	415×	body	2048	valid
166.0ms	955×	body	256	valid
55.0ms	619×	body	128	valid

Compiler

Compiled 55 to 43 computations (21.8% saved)

Details

analyze113.0ms (2.4%)

sample112.0ms (2.3%)

simplify73.0ms (1.5%)

prune4.0ms (0.1%)

localize11.0ms (0.2%)

series5.0ms (0.1%)

rewrite14.0ms (0.3%)

simplify97.0ms (2%)

prune57.0ms (1.2%)

localize7.0ms (0.2%)

series18.0ms (0.4%)

rewrite2.0ms (0%)

simplify72.0ms (1.5%)

prune32.0ms (0.7%)

localize18.0ms (0.4%)

series14.0ms (0.3%)

rewrite3.0ms (0.1%)

simplify119.0ms (2.5%)

prune46.0ms (1%)

localize16.0ms (0.3%)

series18.0ms (0.4%)

rewrite6.0ms (0.1%)

simplify89.0ms (1.9%)

prune57.0ms (1.2%)

regimes128.0ms (2.7%)

simplify4.0ms (0.1%)

end1.0ms (0%)

sample3.7s (76.4%)

Profiling