Details

analyze61.0ms (0.5%)

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)

sample9.7s (76.3%)

Results

6.0s	3979×	body	1024	valid
1.9s	1995×	body	512	valid
650.0ms	1021×	body	256	valid
632.0ms	440×	body	2048	valid
293.0ms	821×	body	128	valid

Compiler

Compiled 44 to 23 computations (47.7% saved)

simplify160.0ms (1.3%)

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

prune10.0ms (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

57.9b

Counts

2 → 1

Alt Table

Status	Error	Program
▶	57.9b	(/.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)

localize29.0ms (0.2%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	1.2b	(/.f64 (-.f64 (exp.f64 x) (exp.f64 (neg.f64 x))) (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x))))
✓	7.1b	(-.f64 (exp.f64 x) (exp.f64 (neg.f64 x)))

series47.0ms (0.4%)

Counts

2 → 16

Calls

2 calls:

43.0ms	(/.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)))

rewrite69.0ms (0.5%)

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:

25.0ms	(/.f64 (-.f64 (exp.f64 x) (exp.f64 (neg.f64 x))) (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x))))
8.0ms	(-.f64 (exp.f64 x) (exp.f64 (neg.f64 x)))

simplify318.0ms (2.5%)

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 → 123

Iterations

Useful iterations: 2 (0.0ms)

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

prune164.0ms (1.3%)

Pruning

3 alts after pruning (3 fresh and 0 done)

	Pruned	Kept	Total
New	120	3	123
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	121	3	124

Error

Counts

124 → 3

Alt Table

Status	Error	Program
▶	0.0b	(tanh.f64 x)
	2.1b	(/.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))))) (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x))))
	1.3b	(/.f64 (sinh.f64 x) (cosh.f64 x))

Compiler

Compiled 2878 to 630 computations (78.1% saved)

localize3.0ms (0%)

Local error

Found 1 expressions with local error:

New	Error	Program
✓	0.0b	(tanh.f64 x)

series71.0ms (0.6%)

Counts

1 → 12

Calls

1 calls:

71.0ms

(tanh.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 → 12

Calls

1 calls:

1.0ms

(tanh.f64 x)

simplify144.0ms (1.1%)

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

prune30.0ms (0.2%)

Pruning

3 alts after pruning (2 fresh and 1 done)

	Pruned	Kept	Total
New	23	1	24
Fresh	1	1	2
Picked	0	1	1
Done	0	0	0
Total	24	3	27

Error

Counts

27 → 3

Alt Table

Status	Error	Program
▶	0.5b	(/.f64 (expm1.f64 (+.f64 x x)) (+.f64 1 (pow.f64 (exp.f64 x) 2)))
✓	0.0b	(tanh.f64 x)
	1.3b	(/.f64 (sinh.f64 x) (cosh.f64 x))

Compiler

Compiled 248 to 158 computations (36.3% saved)

localize19.0ms (0.2%)

Local error

Found 4 expressions with local error:

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

series108.0ms (0.8%)

Counts

4 → 32

Calls

4 calls:

88.0ms	(/.f64 (expm1.f64 (+.f64 x x)) (+.f64 1 (pow.f64 (exp.f64 x) 2)))
11.0ms	(+.f64 1 (pow.f64 (exp.f64 x) 2))
5.0ms	(pow.f64 (exp.f64 x) 2)
3.0ms	(expm1.f64 (+.f64 x x))

rewrite71.0ms (0.6%)

Algorithm

1×	rewrite-expression-head

Rules

27×	`*-un-lft-identity_binary64`
17×	`add-sqr-sqrt_binary64`
17×	`add-cube-cbrt_binary64`
12×	`times-frac_binary64`
6×	`add-cbrt-cube_binary64`

Counts

4 → 87

Calls

4 calls:

30.0ms	(+.f64 1 (pow.f64 (exp.f64 x) 2))
13.0ms	(/.f64 (expm1.f64 (+.f64 x x)) (+.f64 1 (pow.f64 (exp.f64 x) 2)))
4.0ms	(pow.f64 (exp.f64 x) 2)
1.0ms	(expm1.f64 (+.f64 x x))

simplify506.0ms (4%)

Algorithm

1×	egg-herbie

Rules

621×	`unswap-sqr_binary64`
500×	`fma-neg_binary64`
372×	`fma-def_binary64`
286×	`exp-prod_binary64`
275×	`log-prod_binary64`

Counts

119 → 163

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	150	1850
1	318	1634
2	811	1617
3	2931	1615
4	4478	1615
5	4817	1615
6	4993	1615
7	4895	1615

prune405.0ms (3.2%)

Pruning

3 alts after pruning (1 fresh and 2 done)

	Pruned	Kept	Total
New	163	0	163
Fresh	0	1	1
Picked	0	1	1
Done	0	1	1
Total	163	3	166

Error

Counts

166 → 3

Alt Table

Status	Error	Program
✓	0.5b	(/.f64 (expm1.f64 (+.f64 x x)) (+.f64 1 (pow.f64 (exp.f64 x) 2)))
✓	0.0b	(tanh.f64 x)
▶	1.3b	(/.f64 (sinh.f64 x) (cosh.f64 x))

Compiler

Compiled 2883 to 1453 computations (49.6% saved)

localize10.0ms (0.1%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.0b	(sinh.f64 x)
✓	1.2b	(/.f64 (sinh.f64 x) (cosh.f64 x))

series135.0ms (1.1%)

Counts

2 → 24

Calls

2 calls:

100.0ms	(/.f64 (sinh.f64 x) (cosh.f64 x))
35.0ms	(sinh.f64 x)

rewrite17.0ms (0.1%)

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 → 41

Calls

2 calls:

5.0ms	(/.f64 (sinh.f64 x) (cosh.f64 x))
1.0ms	(sinh.f64 x)

simplify303.0ms (2.4%)

Algorithm

1×	egg-herbie

Rules

676×	`associate-/l/_binary64`
520×	`fma-def_binary64`
515×	`times-frac_binary64`
352×	`associate-/r/_binary64`
242×	`cancel-sign-sub-inv_binary64`

Counts

65 → 63

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	97	936
1	198	895
2	518	883
3	1423	751
4	4125	751
5	4893	751
6	4996	751
7	4884	751

prune81.0ms (0.6%)

Pruning

3 alts after pruning (0 fresh and 3 done)

	Pruned	Kept	Total
New	63	0	63
Fresh	0	0	0
Picked	0	1	1
Done	0	2	2
Total	63	3	66

Error

Counts

66 → 3

Alt Table

Status	Error	Program
✓	0.5b	(/.f64 (expm1.f64 (+.f64 x x)) (+.f64 1 (pow.f64 (exp.f64 x) 2)))
✓	0.0b	(tanh.f64 x)
✓	1.3b	(/.f64 (sinh.f64 x) (cosh.f64 x))

Compiler

Compiled 739 to 290 computations (60.8% saved)

regimes137.0ms (1.1%)

Accuracy

Total 0.0b remaining (80.2%)

Threshold costs 0.0b (80.2%)

Counts

25 → 1

Compiler

Compiled 792 to 488 computations (38.4% saved)

simplify3.0ms (0%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	3	3
1	3	3

end122.0ms (1%)

Compiler: Compiled 27 to 19 computations (29.6% saved)

Details

analyze61.0ms (0.5%)

sample9.7s (76.3%)

simplify160.0ms (1.3%)

prune10.0ms (0.1%)

localize29.0ms (0.2%)

series47.0ms (0.4%)

rewrite69.0ms (0.5%)

simplify318.0ms (2.5%)

prune164.0ms (1.3%)

localize3.0ms (0%)

series71.0ms (0.6%)

rewrite2.0ms (0%)

simplify144.0ms (1.1%)

prune30.0ms (0.2%)

localize19.0ms (0.2%)

series108.0ms (0.8%)

rewrite71.0ms (0.6%)

simplify506.0ms (4%)

prune405.0ms (3.2%)

localize10.0ms (0.1%)

series135.0ms (1.1%)

rewrite17.0ms (0.1%)

simplify303.0ms (2.4%)

prune81.0ms (0.6%)

regimes137.0ms (1.1%)

simplify3.0ms (0%)

end122.0ms (1%)

Profiling