Details

analyze4.0ms (0.1%)

Algorithm

1×

Search

True	Other	False	Iter
0%	100%	0%	0
0%	100%	0%	1
0%	100%	0%	2
25%	75%	0%	3
62.5%	25%	12.5%	4
68.7%	12.5%	18.8%	5
71.8%	6.2%	21.9%	6
73.4%	3.1%	23.5%	7
74.2%	1.6%	24.3%	8
74.6%	0.8%	24.6%	9
75%	0.4%	24.6%	10
75.1%	0.2%	24.7%	11
75.1%	0.1%	24.8%	12
75.1%	0%	24.8%	13
75.2%	0%	24.8%	14

Compiler

Compiled 8 to 6 computations (25% saved)

sample2.3s (70.8%)

Results

1.4s	2760×	body	1024	valid
357.0ms	1408×	body	512	valid
290.0ms	3172×	body	128	valid
155.0ms	621×	body	256	valid
116.0ms	295×	body	2048	valid

Compiler

Compiled 23 to 17 computations (26.1% saved)

simplify18.0ms (0.5%)

Algorithm

1×	egg-herbie

Rules

95×	`fma-def_binary64`
80×	`fma-neg_binary64`
32×	`distribute-rgt-in_binary64`
27×	`cancel-sign-sub-inv_binary64`
26×	`distribute-lft-in_binary64`

Counts

1 → 2

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	6	6
1	15	6
2	18	6
3	22	6
4	30	6
5	38	6
6	57	6
7	86	6
8	113	6
9	154	6
10	224	6
11	261	6
12	297	6
13	300	6
14	263	6

prune3.0ms (0.1%)

Pruning

1 alts after pruning (1 fresh and 0 done)

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

Error

0.0b

Counts

3 → 1

Alt Table

Status	Error	Program
▶	0.0b	(/.f64 (expm1.f64 x) x)

Compiler

Compiled 21 to 13 computations (38.1% saved)

localize4.0ms (0.1%)

Local error

Found 1 expressions with local error:

New	Error	Program
✓	0.0b	(/.f64 (expm1.f64 x) x)

series3.0ms (0.1%)

Counts

1 → 12

Calls

1 calls:

3.0ms

(/.f64 (expm1.f64 x) x)

rewrite4.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

9×	`*-un-lft-identity_binary64`
9×	`times-frac_binary64`
9×	`add-sqr-sqrt_binary64`
9×	`add-cube-cbrt_binary64`
3×	`associate-/r*_binary64`

Counts

1 → 30

Calls

1 calls:

2.0ms

(/.f64 (expm1.f64 x) x)

simplify59.0ms (1.8%)

Algorithm

1×	egg-herbie

Rules

665×	`times-frac_binary64`
337×	`associate-/l*_binary64`
285×	`fma-def_binary64`
269×	`associate-l_binary64`
256×	`fma-neg_binary64`

Counts

42 → 42

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	76	468
1	144	440
2	345	437
3	884	430
4	4051	430
5	5063	430

prune28.0ms (0.8%)

Pruning

3 alts after pruning (3 fresh and 0 done)

	Pruned	Kept	Total
New	39	3	42
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	40	3	43

Error

Counts

43 → 3

Alt Table

Status	Error	Program
▶	0.0b	(/.f64 1 (/.f64 x (expm1.f64 x)))
	0.2b	(*.f64 (sqrt.f64 (/.f64 (expm1.f64 x) x)) (sqrt.f64 (/.f64 (expm1.f64 x) x)))
	24.2b	(fma.f64 x (fma.f64 x 1/6 1/2) 1)

Compiler

Compiled 456 to 184 computations (59.6% saved)

localize4.0ms (0.1%)

Local error

Found 2 expressions with local error:

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

series13.0ms (0.4%)

Counts

2 → 24

Calls

2 calls:

8.0ms	(/.f64 x (expm1.f64 x))
4.0ms	(/.f64 1 (/.f64 x (expm1.f64 x)))

rewrite14.0ms (0.4%)

Algorithm

1×	rewrite-expression-head

Rules

84×	`times-frac_binary64`
52×	`*-un-lft-identity_binary64`
52×	`add-sqr-sqrt_binary64`
52×	`add-cube-cbrt_binary64`
16×	`associate-/r*_binary64`

Counts

2 → 107

Calls

2 calls:

4.0ms	(/.f64 1 (/.f64 x (expm1.f64 x)))
2.0ms	(/.f64 x (expm1.f64 x))

simplify101.0ms (3%)

Algorithm

1×	egg-herbie

Rules

475×	`fma-def_binary64`
424×	`associate-/l/_binary64`
353×	`distribute-rgt-in_binary64`
343×	`distribute-lft-in_binary64`
257×	`fma-neg_binary64`

Counts

131 → 153

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	131	1825
1	254	1614
2	662	1580
3	1739	1565
4	4503	1565
5	4942	1565

prune76.0ms (2.3%)

Pruning

3 alts after pruning (2 fresh and 1 done)

	Pruned	Kept	Total
New	153	0	153
Fresh	0	2	2
Picked	0	1	1
Done	0	0	0
Total	153	3	156

Error

Counts

156 → 3

Alt Table

Status	Error	Program
✓	0.0b	(/.f64 1 (/.f64 x (expm1.f64 x)))
▶	0.2b	(*.f64 (sqrt.f64 (/.f64 (expm1.f64 x) x)) (sqrt.f64 (/.f64 (expm1.f64 x) x)))
	24.2b	(fma.f64 x (fma.f64 x 1/6 1/2) 1)

Compiler

Compiled 2084 to 861 computations (58.7% saved)

localize6.0ms (0.2%)

Local error

Found 3 expressions with local error:

New	Error	Program
	0.0b	(/.f64 (expm1.f64 x) x)
✓	0.0b	(sqrt.f64 (/.f64 (expm1.f64 x) x))
✓	0.2b	(*.f64 (sqrt.f64 (/.f64 (expm1.f64 x) x)) (sqrt.f64 (/.f64 (expm1.f64 x) x)))

series84.0ms (2.5%)

Counts

2 → 12

Calls

2 calls:

51.0ms	(sqrt.f64 (/.f64 (expm1.f64 x) x))
32.0ms	(*.f64 (sqrt.f64 (/.f64 (expm1.f64 x) x)) (sqrt.f64 (/.f64 (expm1.f64 x) x)))

rewrite29.0ms (0.9%)

Algorithm

1×	rewrite-expression-head

Rules

90×	`add-sqr-sqrt_binary64`
79×	`sqrt-prod_binary64`
58×	`times-frac_binary64`
41×	`*-un-lft-identity_binary64`
41×	`add-cube-cbrt_binary64`

Counts

2 → 122

Calls

2 calls:

14.0ms	(*.f64 (sqrt.f64 (/.f64 (expm1.f64 x) x)) (sqrt.f64 (/.f64 (expm1.f64 x) x)))
2.0ms	(sqrt.f64 (/.f64 (expm1.f64 x) x))

simplify138.0ms (4.2%)

Algorithm

1×	egg-herbie

Rules

516×	`associate-/r/_binary64`
364×	`fma-def_binary64`
251×	`unswap-sqr_binary64`
232×	`distribute-rgt-in_binary64`
226×	`distribute-lft-in_binary64`

Counts

134 → 170

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	161	1751
1	263	1648
2	840	1611
3	1886	1544
4	4332	1544
5	5006	1544

prune131.0ms (4%)

Pruning

3 alts after pruning (1 fresh and 2 done)

	Pruned	Kept	Total
New	293	0	293
Fresh	0	1	1
Picked	0	1	1
Done	0	1	1
Total	293	3	296

Error

Counts

296 → 3

Alt Table

Status	Error	Program
✓	0.0b	(/.f64 1 (/.f64 x (expm1.f64 x)))
✓	0.2b	(*.f64 (sqrt.f64 (/.f64 (expm1.f64 x) x)) (sqrt.f64 (/.f64 (expm1.f64 x) x)))
▶	24.2b	(fma.f64 x (fma.f64 x 1/6 1/2) 1)

Compiler

Compiled 5016 to 1119 computations (77.7% saved)

localize4.0ms (0.1%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.0b	(fma.f64 x (fma.f64 x 1/6 1/2) 1)
✓	0.1b	(fma.f64 x 1/6 1/2)

series8.0ms (0.2%)

Counts

2 → 24

Calls

2 calls:

6.0ms	(fma.f64 x (fma.f64 x 1/6 1/2) 1)
2.0ms	(fma.f64 x 1/6 1/2)

rewrite1.0ms (0%)

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:

0.0ms	(fma.f64 x (fma.f64 x 1/6 1/2) 1)
0.0ms	(fma.f64 x 1/6 1/2)

simplify100.0ms (3%)

Algorithm

1×	egg-herbie

Rules

590×	`distribute-rgt-out_binary64`
503×	`sqr-pow_binary64`
365×	`*-commutative_binary64`
298×	`distribute-rgt-in_binary64`
294×	`distribute-lft-in_binary64`

Counts

44 → 49

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	36	413
1	55	342
2	110	341
3	337	341
4	1484	341
5	2130	341
6	2811	341
7	3949	341
8	4978	341
9	4992	341
10	4895	341

prune34.0ms (1%)

Pruning

3 alts after pruning (0 fresh and 3 done)

	Pruned	Kept	Total
New	49	0	49
Fresh	0	0	0
Picked	0	1	1
Done	0	2	2
Total	49	3	52

Error

Counts

52 → 3

Alt Table

Status	Error	Program
✓	0.0b	(/.f64 1 (/.f64 x (expm1.f64 x)))
✓	0.2b	(*.f64 (sqrt.f64 (/.f64 (expm1.f64 x) x)) (sqrt.f64 (/.f64 (expm1.f64 x) x)))
✓	24.2b	(fma.f64 x (fma.f64 x 1/6 1/2) 1)

Compiler

Compiled 533 to 406 computations (23.8% saved)

regimes54.0ms (1.6%)

Accuracy

Total 0.0b remaining (75.7%)

Threshold costs 0.0b (75.7%)

Counts

27 → 1

Compiler

Compiled 443 to 317 computations (28.4% saved)

simplify3.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

1×	`1-exp_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	6	9
1	8	9
2	7	9

end46.0ms (1.4%)

Compiler: Compiled 41 to 26 computations (36.6% saved)

Iter	Nodes	Cost
0	6	6
1	15	6
2	18	6
3	22	6
4	30	6
5	38	6
6	57	6
7	86	6
8	113	6
9	154	6
10	224	6
11	261	6
12	297	6
13	300	6
14	263	6

Iter	Nodes	Cost
0	6	6
1	15	6
2	18	6
3	22	6
4	30	6
5	38	6
6	57	6
7	86	6
8	113	6
9	154	6
10	224	6
11	261	6
12	297	6
13	300	6
14	263	6

Details

analyze4.0ms (0.1%)

sample2.3s (70.8%)

simplify18.0ms (0.5%)

prune3.0ms (0.1%)

localize4.0ms (0.1%)

series3.0ms (0.1%)

rewrite4.0ms (0.1%)

simplify59.0ms (1.8%)

prune28.0ms (0.8%)

localize4.0ms (0.1%)

series13.0ms (0.4%)

rewrite14.0ms (0.4%)

simplify101.0ms (3%)

prune76.0ms (2.3%)

localize6.0ms (0.2%)

series84.0ms (2.5%)

rewrite29.0ms (0.9%)

simplify138.0ms (4.2%)

prune131.0ms (4%)

localize4.0ms (0.1%)

series8.0ms (0.2%)

rewrite1.0ms (0%)

simplify100.0ms (3%)

prune34.0ms (1%)

regimes54.0ms (1.6%)

simplify3.0ms (0.1%)

end46.0ms (1.4%)

Profiling

Iter	Nodes	Cost
0	6	6
1	15	6
2	18	6
3	22	6
4	30	6
5	38	6
6	57	6
7	86	6
8	113	6
9	154	6
10	224	6
11	261	6
12	297	6
13	300	6
14	263	6