Details

analyze100.0ms (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%	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 (1.2%)

Algorithm

1×

intervals

Results

35.0ms	112×	body	1024	valid
10.0ms	63×	body	512	valid
4.0ms	14×	body	2048	valid
4.0ms	38×	body	256	valid
2.0ms	29×	body	128	valid

Compiler

Compiled 30 to 16 computations (46.7% saved)

simplify66.0ms (1.2%)

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%)

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

57.2b

Counts

2 → 1

Alt Table

Status	Error	Program
▶	57.2b	(/.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 (0.1%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.0b	(+.f64 (exp.f64 x) (exp.f64 (neg.f64 x)))
✓	1.3b	(/.f64 (-.f64 (exp.f64 x) (exp.f64 (neg.f64 x))) (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x))))
✓	7.5b	(-.f64 (exp.f64 x) (exp.f64 (neg.f64 x)))

series21.0ms (0.4%)

Counts

3 → 24

Calls

3 calls:

14.0ms	(/.f64 (-.f64 (exp.f64 x) (exp.f64 (neg.f64 x))) (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x))))
5.0ms	(+.f64 (exp.f64 x) (exp.f64 (neg.f64 x)))
3.0ms	(-.f64 (exp.f64 x) (exp.f64 (neg.f64 x)))

rewrite24.0ms (0.4%)

Algorithm

1×	rewrite-expression-head

Rules

55×	`*-un-lft-identity_binary64`
39×	`add-sqr-sqrt_binary64`
30×	`times-frac_binary64`
25×	`add-cube-cbrt_binary64`
9×	`prod-diff_binary64`

Counts

3 → 110

Calls

3 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)))
3.0ms	(+.f64 (exp.f64 x) (exp.f64 (neg.f64 x)))

simplify114.0ms (2.1%)

Algorithm

1×	egg-herbie

Rules

508×	`fma-def_binary64`
473×	`associate-l_binary64`
370×	`fma-neg_binary64`
327×	`times-frac_binary64`
203×	`associate-/l*_binary64`

Counts

134 → 152

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	192	3081
1	434	2840
2	1282	2757
3	4252	2757
4	4850	2757

prune66.0ms (1.2%)

Pruning

4 alts after pruning (4 fresh and 0 done)

	Pruned	Kept	Total
New	148	4	152
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	149	4	153

Error

Counts

153 → 4

Alt Table

Status	Error	Program
	1.3b	(/.f64 (sinh.f64 x) (cosh.f64 x))
	2.5b	(fma.f64 (pow.f64 x 3) -1/3 (fma.f64 (pow.f64 x 5) 2/15 x))
	2.3b	(*.f64 (/.f64 2 (sqrt.f64 (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x))))) (/.f64 (sinh.f64 x) (sqrt.f64 (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x))))))
▶	0.0b	(tanh.f64 x)

Compiler

Compiled 3420 to 758 computations (77.8% saved)

localize1.0ms (0%)

Local error

Found 1 expressions with local error:

New	Error	Program
✓	0.0b	(tanh.f64 x)

series21.0ms (0.4%)

Counts

1 → 12

Calls

1 calls:

21.0ms

(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)

simplify52.0ms (0.9%)

Algorithm

1×	egg-herbie

Rules

748×	`times-frac_binary64`
602×	`fma-neg_binary64`
330×	`fma-def_binary64`
236×	`distribute-rgt-in_binary64`
234×	`distribute-lft-in_binary64`

Counts

24 → 24

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	49	189
1	111	182
2	266	178
3	751	175
4	3049	175
5	4950	175
6	5000	175

prune18.0ms (0.3%)

Pruning

3 alts after pruning (3 fresh and 0 done)

	Pruned	Kept	Total
New	22	2	24
Fresh	2	1	3
Picked	1	0	1
Done	0	0	0
Total	25	3	28

Error

Counts

28 → 3

Alt Table

Status	Error	Program
	2.5b	(fma.f64 (pow.f64 x 3) -1/3 (fma.f64 (pow.f64 x 5) 2/15 x))
▶	0.5b	(/.f64 (expm1.f64 (+.f64 x x)) (+.f64 1 (pow.f64 (exp.f64 x) 2)))
	0.8b	(/.f64 (neg.f64 (expm1.f64 (*.f64 x -2))) (+.f64 1 (pow.f64 (exp.f64 x) -2)))

Compiler

Compiled 283 to 188 computations (33.6% saved)

localize8.0ms (0.2%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.0b	(+.f64 1 (pow.f64 (exp.f64 x) 2))
✓	0.0b	(pow.f64 (exp.f64 x) 2)
✓	0.5b	(/.f64 (expm1.f64 (+.f64 x x)) (+.f64 1 (pow.f64 (exp.f64 x) 2)))

series39.0ms (0.7%)

Counts

3 → 20

Calls

3 calls:

32.0ms	(/.f64 (expm1.f64 (+.f64 x x)) (+.f64 1 (pow.f64 (exp.f64 x) 2)))
3.0ms	(+.f64 1 (pow.f64 (exp.f64 x) 2))
3.0ms	(pow.f64 (exp.f64 x) 2)

rewrite14.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

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

Counts

3 → 76

Calls

3 calls:

5.0ms	(/.f64 (expm1.f64 (+.f64 x x)) (+.f64 1 (pow.f64 (exp.f64 x) 2)))
4.0ms	(+.f64 1 (pow.f64 (exp.f64 x) 2))
2.0ms	(pow.f64 (exp.f64 x) 2)

simplify113.0ms (2%)

Algorithm

1×	egg-herbie

Rules

613×	`unswap-sqr_binary64`
500×	`fma-neg_binary64`
333×	`fma-def_binary64`
307×	`exp-prod_binary64`
294×	`log-prod_binary64`

Counts

96 → 142

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	140	1647
1	301	1452
2	759	1435
3	2742	1433
4	4279	1433
5	4745	1433
6	4899	1433

prune88.0ms (1.6%)

Pruning

3 alts after pruning (2 fresh and 1 done)

	Pruned	Kept	Total
New	142	0	142
Fresh	0	2	2
Picked	0	1	1
Done	0	0	0
Total	142	3	145

Error

Counts

145 → 3

Alt Table

Status	Error	Program
	2.5b	(fma.f64 (pow.f64 x 3) -1/3 (fma.f64 (pow.f64 x 5) 2/15 x))
✓	0.5b	(/.f64 (expm1.f64 (+.f64 x x)) (+.f64 1 (pow.f64 (exp.f64 x) 2)))
▶	0.8b	(/.f64 (neg.f64 (expm1.f64 (*.f64 x -2))) (+.f64 1 (pow.f64 (exp.f64 x) -2)))

Compiler

Compiled 2585 to 1294 computations (49.9% saved)

localize8.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(+.f64 1 (pow.f64 (exp.f64 x) -2))
✓	0.0b	(expm1.f64 (*.f64 x -2))
✓	0.0b	(pow.f64 (exp.f64 x) -2)
✓	0.8b	(/.f64 (neg.f64 (expm1.f64 (*.f64 x -2))) (+.f64 1 (pow.f64 (exp.f64 x) -2)))

series65.0ms (1.2%)

Counts

4 → 48

Calls

4 calls:

46.0ms	(/.f64 (neg.f64 (expm1.f64 (*.f64 x -2))) (+.f64 1 (pow.f64 (exp.f64 x) -2)))
9.0ms	(+.f64 1 (pow.f64 (exp.f64 x) -2))
8.0ms	(pow.f64 (exp.f64 x) -2)
2.0ms	(expm1.f64 (*.f64 x -2))

rewrite19.0ms (0.4%)

Algorithm

1×	rewrite-expression-head

Rules

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

Counts

4 → 122

Calls

4 calls:

6.0ms	(/.f64 (neg.f64 (expm1.f64 (*.f64 x -2))) (+.f64 1 (pow.f64 (exp.f64 x) -2)))
4.0ms	(+.f64 1 (pow.f64 (exp.f64 x) -2))
2.0ms	(pow.f64 (exp.f64 x) -2)
0.0ms	(expm1.f64 (*.f64 x -2))

simplify117.0ms (2.1%)

Algorithm

1×	egg-herbie

Rules

497×	`fma-neg_binary64`
372×	`times-frac_binary64`
311×	`fma-def_binary64`
289×	`associate-/l*_binary64`
264×	`associate-r_binary64`

Counts

170 → 210

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	204	3390
1	446	3202
2	1188	3069
3	4016	3060
4	4909	3060

prune274.0ms (5%)

Pruning

3 alts after pruning (1 fresh and 2 done)

	Pruned	Kept	Total
New	210	0	210
Fresh	0	1	1
Picked	0	1	1
Done	0	1	1
Total	210	3	213

Error

Counts

213 → 3

Alt Table

Status	Error	Program
	2.5b	(fma.f64 (pow.f64 x 3) -1/3 (fma.f64 (pow.f64 x 5) 2/15 x))
✓	0.5b	(/.f64 (expm1.f64 (+.f64 x x)) (+.f64 1 (pow.f64 (exp.f64 x) 2)))
✓	0.8b	(/.f64 (neg.f64 (expm1.f64 (*.f64 x -2))) (+.f64 1 (pow.f64 (exp.f64 x) -2)))

Compiler

Compiled 4274 to 3372 computations (21.1% saved)

regimes253.0ms (4.6%)

Accuracy

Total 0.0b remaining (82.6%)

Threshold costs 0.0b (82.6%)

Counts

53 → 1

Compiler

Compiled 1606 to 1028 computations (36% saved)

simplify4.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

1×	`1-exp_binary64`
1×	`unpow1_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	5	3
1	7	3
2	6	3

end1.0ms (0%)

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

sample3.9s (71.7%)

Algorithm

1×

intervals

Results

2.3s	3906×	body	1024	valid
683.0ms	1939×	body	512	valid
263.0ms	410×	body	2048	valid
186.0ms	975×	body	256	valid
71.0ms	770×	body	128	valid

Compiler

Compiled 56 to 40 computations (28.6% saved)

Details

analyze100.0ms (1.8%)

sample64.0ms (1.2%)

simplify66.0ms (1.2%)

prune2.0ms (0%)

localize7.0ms (0.1%)

series21.0ms (0.4%)

rewrite24.0ms (0.4%)

simplify114.0ms (2.1%)

prune66.0ms (1.2%)

localize1.0ms (0%)

series21.0ms (0.4%)

rewrite1.0ms (0%)

simplify52.0ms (0.9%)

prune18.0ms (0.3%)

localize8.0ms (0.2%)

series39.0ms (0.7%)

rewrite14.0ms (0.3%)

simplify113.0ms (2%)

prune88.0ms (1.6%)

localize8.0ms (0.2%)

series65.0ms (1.2%)

rewrite19.0ms (0.4%)

simplify117.0ms (2.1%)

prune274.0ms (5%)

regimes253.0ms (4.6%)

simplify4.0ms (0.1%)

end1.0ms (0%)

sample3.9s (71.7%)

Profiling