Details

analyze5.0ms (0.2%)

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)

sample123.0ms (4.6%)

Algorithm

1×

intervals

Results

37.0ms	131×	body	1024	valid
9.0ms	62×	body	512	valid
5.0ms	34×	body	256	valid
2.0ms	7×	body	2048	valid
1.0ms	22×	body	128	valid

Compiler

Compiled 20 to 16 computations (20% saved)

simplify62.0ms (2.3%)

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

3 alts after pruning (3 fresh and 0 done)

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

Error

57.3b

Counts

3 → 2

Alt Table

Status	Error	Program
	57.3b	(fma.f64 1/2 (exp.f64 x) (/.f64 -1/2 (exp.f64 x)))
▶	57.3b	(/.f64 (-.f64 (exp.f64 x) (exp.f64 (neg.f64 x))) 2)

Compiler

Compiled 53 to 37 computations (30.2% saved)

localize6.0ms (0.2%)

Local error

Found 1 expressions with local error:

New	Error	Program
✓	4.4b	(-.f64 (exp.f64 x) (exp.f64 (neg.f64 x)))

series2.0ms (0.1%)

Counts

1 → 8

Calls

1 calls:

2.0ms

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

rewrite7.0ms (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:

5.0ms

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

simplify78.0ms (2.9%)

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

prune27.0ms (1%)

Pruning

3 alts after pruning (3 fresh and 0 done)

	Pruned	Kept	Total
New	47	2	49
Fresh	0	1	1
Picked	1	0	1
Done	0	0	0
Total	48	3	51

Error

Counts

51 → 3

Alt Table

Status	Error	Program
	57.3b	(fma.f64 1/2 (exp.f64 x) (/.f64 -1/2 (exp.f64 x)))
▶	0.0b	(/.f64 (*.f64 2 (sinh.f64 x)) 2)
	1.2b	(/.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 1002 to 393 computations (60.8% saved)

localize3.0ms (0.1%)

Local error

Found 1 expressions with local error:

New	Error	Program
✓	0.0b	(sinh.f64 x)

series9.0ms (0.3%)

Counts

1 → 12

Calls

1 calls:

9.0ms

(sinh.f64 x)

rewrite1.0ms (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)

simplify59.0ms (2.2%)

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

prune14.0ms (0.5%)

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
	57.3b	(fma.f64 1/2 (exp.f64 x) (/.f64 -1/2 (exp.f64 x)))
▶	1.4b	(/.f64 (*.f64 2 (fma.f64 1/6 (pow.f64 x 3) x)) 2)
✓	0.0b	(/.f64 (*.f64 2 (sinh.f64 x)) 2)

Compiler

Compiled 282 to 210 computations (25.5% saved)

localize9.0ms (0.3%)

Local error

Found 1 expressions with local error:

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

series3.0ms (0.1%)

Counts

1 → 12

Calls

1 calls:

3.0ms

(fma.f64 1/6 (pow.f64 x 3) x)

rewrite1.0ms (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:

0.0ms

(fma.f64 1/6 (pow.f64 x 3) x)

simplify57.0ms (2.1%)

Algorithm

1×	egg-herbie

Rules

708×	`unswap-sqr_binary64`
638×	`distribute-rgt-in_binary64`
628×	`distribute-lft-in_binary64`
512×	`distribute-rgt-out_binary64`
310×	`*-commutative_binary64`

Counts

22 → 15

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	18	214
1	28	197
2	67	197
3	207	197
4	895	197
5	2743	197
6	3667	197
7	5070	197

prune10.0ms (0.4%)

Pruning

3 alts after pruning (1 fresh and 2 done)

	Pruned	Kept	Total
New	15	0	15
Fresh	0	1	1
Picked	0	1	1
Done	0	1	1
Total	15	3	18

Error

Counts

18 → 3

Alt Table

Status	Error	Program
▶	57.3b	(fma.f64 1/2 (exp.f64 x) (/.f64 -1/2 (exp.f64 x)))
✓	1.4b	(/.f64 (*.f64 2 (fma.f64 1/6 (pow.f64 x 3) x)) 2)
✓	0.0b	(/.f64 (*.f64 2 (sinh.f64 x)) 2)

Compiler

Compiled 239 to 192 computations (19.7% saved)

localize4.0ms (0.2%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.0b	(/.f64 -1/2 (exp.f64 x))
✓	4.4b	(fma.f64 1/2 (exp.f64 x) (/.f64 -1/2 (exp.f64 x)))

series15.0ms (0.6%)

Counts

2 → 16

Calls

2 calls:

9.0ms	(fma.f64 1/2 (exp.f64 x) (/.f64 -1/2 (exp.f64 x)))
6.0ms	(/.f64 -1/2 (exp.f64 x))

rewrite4.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

10×	`*-un-lft-identity_binary64`
10×	`add-sqr-sqrt_binary64`
10×	`add-cube-cbrt_binary64`
9×	`times-frac_binary64`
4×	`add-cbrt-cube_binary64`

Counts

2 → 39

Calls

2 calls:

3.0ms	(/.f64 -1/2 (exp.f64 x))
0.0ms	(fma.f64 1/2 (exp.f64 x) (/.f64 -1/2 (exp.f64 x)))

simplify91.0ms (3.4%)

Algorithm

1×	egg-herbie

Rules

622×	`associate-l_binary64`
537×	`fma-neg_binary64`
481×	`associate-r_binary64`
467×	`fma-def_binary64`
387×	`cancel-sign-sub-inv_binary64`

Counts

55 → 61

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	95	729
1	196	668
2	411	666
3	1095	660
4	3465	659
5	4949	659
6	4974	659
7	4885	659

prune27.0ms (1%)

Pruning

3 alts after pruning (0 fresh and 3 done)

	Pruned	Kept	Total
New	61	0	61
Fresh	0	0	0
Picked	0	1	1
Done	0	2	2
Total	61	3	64

Error

Counts

64 → 3

Alt Table

Status	Error	Program
✓	57.3b	(fma.f64 1/2 (exp.f64 x) (/.f64 -1/2 (exp.f64 x)))
✓	1.4b	(/.f64 (*.f64 2 (fma.f64 1/6 (pow.f64 x 3) x)) 2)
✓	0.0b	(/.f64 (*.f64 2 (sinh.f64 x)) 2)

Compiler

Compiled 823 to 507 computations (38.4% saved)

regimes37.0ms (1.4%)

Accuracy

Total 0.0b remaining (62.7%)

Threshold costs 0.0b (62.7%)

Counts

15 → 1

Compiler

Compiled 501 to 401 computations (20% saved)

simplify2.0ms (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

end0.0ms (0%)

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

sample2.0s (75.3%)

Algorithm

1×

intervals

Results

1.2s	3917×	body	1024	valid
306.0ms	2037×	body	512	valid
135.0ms	972×	body	256	valid
116.0ms	405×	body	2048	valid
31.0ms	669×	body	128	valid
0.0ms	1×	body	128	invalid

Compiler

Compiled 45 to 36 computations (20% saved)

Details

analyze5.0ms (0.2%)

sample123.0ms (4.6%)

simplify62.0ms (2.3%)

prune4.0ms (0.1%)

localize6.0ms (0.2%)

series2.0ms (0.1%)

rewrite7.0ms (0.3%)

simplify78.0ms (2.9%)

prune27.0ms (1%)

localize3.0ms (0.1%)

series9.0ms (0.3%)

rewrite1.0ms (0%)

simplify59.0ms (2.2%)

prune14.0ms (0.5%)

localize9.0ms (0.3%)

series3.0ms (0.1%)

rewrite1.0ms (0%)

simplify57.0ms (2.1%)

prune10.0ms (0.4%)

localize4.0ms (0.2%)

series15.0ms (0.6%)

rewrite4.0ms (0.2%)

simplify91.0ms (3.4%)

prune27.0ms (1%)

regimes37.0ms (1.4%)

simplify2.0ms (0.1%)

end0.0ms (0%)

sample2.0s (75.3%)

Profiling