Details

analyze101.0ms (3.1%)

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%	1.6%	48.5%	9
50.4%	1.2%	48.5%	10
50.4%	1.2%	48.5%	11
50.4%	1.1%	48.6%	12
50.4%	1%	48.6%	13
50.5%	0.9%	48.6%	14

Compiler

Compiled 15 to 8 computations (46.7% saved)

sample64.0ms (1.9%)

Algorithm

1×

intervals

Results

37.0ms	123×	body	1024	valid
11.0ms	59×	body	512	valid
4.0ms	41×	body	256	valid
2.0ms	6×	body	2048	valid
1.0ms	27×	body	128	valid

Compiler

Compiled 30 to 16 computations (46.7% saved)

simplify76.0ms (2.3%)

Algorithm

1×	egg-herbie

Rules

720×	`fma-def_binary64`
658×	`unswap-sqr_binary64`
478×	`fma-neg_binary64`
464×	`times-frac_binary64`
388×	`associate-/r/_binary64`

Counts

1 → 1

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	8	22
1	20	22
2	34	22
3	58	22
4	125	22
5	288	22
6	624	22
7	1577	22
8	3798	22
9	4553	22
10	5023	22

prune2.0ms (0.1%)

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

58.1b

Counts

2 → 1

Alt Table

Status	Error	Program
▶	58.1b	(/.f64 (-.f64 (exp.f64 x) (exp.f64 (neg.f64 x))) (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x))))

Compiler

Compiled 42 to 21 computations (50% saved)

localize7.0ms (0.2%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.5b	(/.f64 (-.f64 (exp.f64 x) (exp.f64 (neg.f64 x))) (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x))))
✓	7.2b	(-.f64 (exp.f64 x) (exp.f64 (neg.f64 x)))

rewrite18.0ms (0.6%)

Algorithm

1×	rewrite-expression-head

Rules

51×	`*-un-lft-identity_binary64`
37×	`add-sqr-sqrt_binary64`
30×	`times-frac_binary64`
23×	`add-cube-cbrt_binary64`
9×	`prod-diff_binary64`

Counts

2 → 92

Calls

2 calls:

9.0ms	(/.f64 (-.f64 (exp.f64 x) (exp.f64 (neg.f64 x))) (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x))))
4.0ms	(-.f64 (exp.f64 x) (exp.f64 (neg.f64 x)))

series26.0ms (0.8%)

Counts

2 → 16

Calls

2 calls:

22.0ms	(/.f64 (-.f64 (exp.f64 x) (exp.f64 (neg.f64 x))) (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x))))
4.0ms	(-.f64 (exp.f64 x) (exp.f64 (neg.f64 x)))

simplify130.0ms (3.9%)

Algorithm

1×	egg-herbie

Rules

436×	`fma-def_binary64`
418×	`associate-l_binary64`
364×	`associate-r_binary64`
322×	`times-frac_binary64`
220×	`fma-neg_binary64`

Counts

108 → 174

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	172	2760
1	382	2556
2	1145	2481
3	4347	2481
4	4881	2481

prune59.0ms (1.8%)

Pruning

3 alts after pruning (3 fresh and 0 done)

	Pruned	Kept	Total
New	171	3	174
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	172	3	175

Error

Counts

175 → 3

Alt Table

Status	Error	Program
	1.5b	(-.f64 (fma.f64 (pow.f64 x 5) 2/15 x) (fma.f64 1/3 (pow.f64 x 3) (*.f64 (pow.f64 x 7) 17/315)))
	0.5b	(/.f64 (sinh.f64 x) (cosh.f64 x))
▶	0.0b	(tanh.f64 x)

Compiler

Compiled 2849 to 618 computations (78.3% saved)

localize2.0ms (0%)

Local error

Found 1 expressions with local error:

New	Error	Program
✓	0.0b	(tanh.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 → 12

Calls

1 calls:

1.0ms

(tanh.f64 x)

series18.0ms (0.5%)

Counts

1 → 12

Calls

1 calls:

17.0ms

(tanh.f64 x)

simplify43.0ms (1.3%)

Algorithm

1×	egg-herbie

Rules

761×	`times-frac_binary64`
520×	`fma-neg_binary64`
330×	`fma-def_binary64`
234×	`distribute-rgt-in_binary64`
232×	`distribute-lft-in_binary64`

Counts

24 → 38

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	46	189
1	111	182
2	264	178
3	747	175
4	3029	175
5	5001	175

prune17.0ms (0.5%)

Pruning

2 alts after pruning (2 fresh and 0 done)

	Pruned	Kept	Total
New	36	2	38
Fresh	2	0	2
Picked	1	0	1
Done	0	0	0
Total	39	2	41

Error

Counts

41 → 2

Alt Table

Status	Error	Program
	0.5b	(/.f64 (expm1.f64 (+.f64 x x)) (+.f64 1 (exp.f64 (+.f64 x x))))
▶	0.3b	(/.f64 (neg.f64 (expm1.f64 (.f64 x -2))) (+.f64 1 (exp.f64 (.f64 x -2))))

Compiler

Compiled 244 to 159 computations (34.8% saved)

localize8.0ms (0.3%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.0b	(expm1.f64 (*.f64 x -2))
✓	0.0b	(+.f64 1 (exp.f64 (*.f64 x -2)))
✓	0.3b	(/.f64 (neg.f64 (expm1.f64 (.f64 x -2))) (+.f64 1 (exp.f64 (.f64 x -2))))

rewrite14.0ms (0.4%)

Algorithm

1×	rewrite-expression-head

Rules

54×	`*-un-lft-identity_binary64`
40×	`times-frac_binary64`
30×	`add-sqr-sqrt_binary64`
30×	`add-cube-cbrt_binary64`
15×	`distribute-lft-neg-in_binary64`

Counts

3 → 100

Calls

3 calls:

5.0ms	(/.f64 (neg.f64 (expm1.f64 (.f64 x -2))) (+.f64 1 (exp.f64 (.f64 x -2))))
2.0ms	(+.f64 1 (exp.f64 (*.f64 x -2)))
0.0ms	(expm1.f64 (*.f64 x -2))

series27.0ms (0.8%)

Counts

3 → 36

Calls

3 calls:

24.0ms	(/.f64 (neg.f64 (expm1.f64 (.f64 x -2))) (+.f64 1 (exp.f64 (.f64 x -2))))
2.0ms	(expm1.f64 (*.f64 x -2))
2.0ms	(+.f64 1 (exp.f64 (*.f64 x -2)))

simplify119.0ms (3.6%)

Algorithm

1×	egg-herbie

Rules

685×	`div-sub_binary64`
614×	`fma-neg_binary64`
361×	`times-frac_binary64`
257×	`associate-/l*_binary64`
227×	`fma-def_binary64`

Counts

136 → 253

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	167	3028
1	375	2898
2	1013	2832
3	3402	2802
4	5217	2802

prune113.0ms (3.4%)

Pruning

2 alts after pruning (1 fresh and 1 done)

	Pruned	Kept	Total
New	253	0	253
Fresh	0	1	1
Picked	0	1	1
Done	0	0	0
Total	253	2	255

Error

Counts

255 → 2

Alt Table

Status	Error	Program
▶	0.5b	(/.f64 (expm1.f64 (+.f64 x x)) (+.f64 1 (exp.f64 (+.f64 x x))))
✓	0.3b	(/.f64 (neg.f64 (expm1.f64 (.f64 x -2))) (+.f64 1 (exp.f64 (.f64 x -2))))

Compiler

Compiled 3574 to 2985 computations (16.5% saved)

localize6.0ms (0.2%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.0b	(expm1.f64 (+.f64 x x))
✓	0.0b	(+.f64 1 (exp.f64 (+.f64 x x)))
✓	0.5b	(/.f64 (expm1.f64 (+.f64 x x)) (+.f64 1 (exp.f64 (+.f64 x x))))

rewrite14.0ms (0.4%)

Algorithm

1×	rewrite-expression-head

Rules

23×	`*-un-lft-identity_binary64`
13×	`add-sqr-sqrt_binary64`
13×	`add-cube-cbrt_binary64`
12×	`times-frac_binary64`
5×	`distribute-lft-out_binary64`

Counts

3 → 64

Calls

3 calls:

7.0ms	(/.f64 (expm1.f64 (+.f64 x x)) (+.f64 1 (exp.f64 (+.f64 x x))))
4.0ms	(+.f64 1 (exp.f64 (+.f64 x x)))
0.0ms	(expm1.f64 (+.f64 x x))

series23.0ms (0.7%)

Counts

3 → 36

Calls

3 calls:

19.0ms	(/.f64 (expm1.f64 (+.f64 x x)) (+.f64 1 (exp.f64 (+.f64 x x))))
3.0ms	(expm1.f64 (+.f64 x x))
2.0ms	(+.f64 1 (exp.f64 (+.f64 x x)))

simplify119.0ms (3.6%)

Algorithm

1×	egg-herbie

Rules

490×	`fma-neg_binary64`
362×	`distribute-rgt-in_binary64`
316×	`fma-def_binary64`
300×	`distribute-lft-in_binary64`
221×	`cancel-sign-sub-inv_binary64`

Counts

100 → 181

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	117	1701
1	269	1520
2	709	1508
3	2162	1505
4	4690	1505
5	4991	1505
6	4931	1505

prune60.0ms (1.8%)

Pruning

2 alts after pruning (0 fresh and 2 done)

	Pruned	Kept	Total
New	181	0	181
Fresh	0	0	0
Picked	0	1	1
Done	0	1	1
Total	181	2	183

Error

Counts

183 → 2

Alt Table

Status	Error	Program
✓	0.5b	(/.f64 (expm1.f64 (+.f64 x x)) (+.f64 1 (exp.f64 (+.f64 x x))))
✓	0.3b	(/.f64 (neg.f64 (expm1.f64 (.f64 x -2))) (+.f64 1 (exp.f64 (.f64 x -2))))

Compiler

Compiled 2231 to 906 computations (59.4% saved)

regimes110.0ms (3.3%)

Accuracy

Total 0.0b remaining (35.5%)

Threshold costs 0.0b (35.5%)

Compiler

Compiled 2360 to 1343 computations (43.1% saved)

simplify3.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

1×	`*-commutative_binary64`
1×	`*-lft-identity_binary64`
1×	`1-exp_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	5	3
1	8	3
2	7	3

end0.0ms (0%)

Compiler: Compiled 3 to 2 computations (33.3% saved)

sample2.1s (64.4%)

Algorithm

1×

intervals

Results

1.2s	3901×	body	1024	valid
340.0ms	1918×	body	512	valid
152.0ms	442×	body	2048	valid
111.0ms	963×	body	256	valid
45.0ms	776×	body	128	valid

Compiler

Compiled 44 to 29 computations (34.1% saved)

Details

analyze101.0ms (3.1%)

sample64.0ms (1.9%)

simplify76.0ms (2.3%)

prune2.0ms (0.1%)

localize7.0ms (0.2%)

rewrite18.0ms (0.6%)

series26.0ms (0.8%)

simplify130.0ms (3.9%)

prune59.0ms (1.8%)

localize2.0ms (0%)

rewrite1.0ms (0%)

series18.0ms (0.5%)

simplify43.0ms (1.3%)

prune17.0ms (0.5%)

localize8.0ms (0.3%)

rewrite14.0ms (0.4%)

series27.0ms (0.8%)

simplify119.0ms (3.6%)

prune113.0ms (3.4%)

localize6.0ms (0.2%)

rewrite14.0ms (0.4%)

series23.0ms (0.7%)

simplify119.0ms (3.6%)

prune60.0ms (1.8%)

regimes110.0ms (3.3%)

simplify3.0ms (0.1%)

end0.0ms (0%)

sample2.1s (64.4%)

Profiling