Details

analyze419.0ms (18.9%)

Algorithm

1×

Search

True	Other	False	Iter
0%	100%	0%	0
0%	100%	0%	1
0%	100%	0%	2
25%	75%	0%	3
25%	62.5%	12.5%	4
25%	56.2%	18.8%	5
28.1%	50%	21.9%	6
29.7%	46.9%	23.5%	7
30.5%	45.3%	24.3%	8
30.8%	44.9%	24.3%	9
31.2%	44.5%	24.3%	10
31.3%	44.4%	24.3%	11
31.4%	44.3%	24.3%	12
31.4%	44.2%	24.3%	13
31.5%	44.2%	24.3%	14

Compiler

Compiled 9 to 6 computations (33.3% saved)

sample32.0ms (1.4%)

Algorithm

1×

intervals

Results

14.0ms	89×	body	1024	valid
4.0ms	49×	body	512	valid
3.0ms	94×	body	128	valid
1.0ms	20×	body	256	valid
1.0ms	4×	body	2048	valid

Compiler

Compiled 18 to 12 computations (33.3% saved)

simplify9.0ms (0.4%)

Algorithm

1×	egg-herbie

Rules

1×	`+-commutative_binary64`
1×	`sub-neg_binary64`
1×	`1-exp_binary64`
1×	`expm1-def_binary64`

Counts

1 → 2

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	6	8
1	12	8
2	13	8
3	11	8

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

1.0b

Counts

3 → 1

Alt Table

Status	Error	Program
▶	1.0b	(/.f64 (exp.f64 x) (expm1.f64 x))

Compiler

Compiled 25 to 15 computations (40% saved)

localize4.0ms (0.2%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.0b	(expm1.f64 x)
✓	1.0b	(/.f64 (exp.f64 x) (expm1.f64 x))

rewrite7.0ms (0.3%)

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 → 40

Calls

2 calls:

3.0ms	(/.f64 (exp.f64 x) (expm1.f64 x))
0.0ms	(expm1.f64 x)

series17.0ms (0.8%)

Counts

2 → 24

Calls

2 calls:

15.0ms	(/.f64 (exp.f64 x) (expm1.f64 x))
2.0ms	(expm1.f64 x)

simplify87.0ms (3.9%)

Algorithm

1×	egg-herbie

Rules

942×	`fma-neg_binary64`
666×	`times-frac_binary64`
570×	`fma-def_binary64`
504×	`cancel-sign-sub-inv_binary64`
262×	`associate-l_binary64`

Counts

64 → 95

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	82	688
1	165	643
2	385	641
3	904	635
4	2629	635
5	4940	635
6	5241	635

prune34.0ms (1.5%)

Pruning

3 alts after pruning (2 fresh and 1 done)

	Pruned	Kept	Total
New	93	2	95
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	93	3	96

Error

0.8b

Counts

96 → 3

Alt Table

Status	Error	Program
	29.5b	(cbrt.f64 (.f64 (.f64 (/.f64 (exp.f64 x) (expm1.f64 x)) (/.f64 (exp.f64 x) (expm1.f64 x))) (/.f64 (exp.f64 x) (expm1.f64 x))))
✓	1.0b	(/.f64 (exp.f64 x) (expm1.f64 x))
▶	19.6b	(+.f64 1/2 (/.f64 1 x))

Compiler

Compiled 669 to 251 computations (62.5% saved)

localize3.0ms (0.1%)

Local error

Found 1 expressions with local error:

New	Error	Program
✓	0.0b	(+.f64 1/2 (/.f64 1 x))

rewrite5.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

5×	`*-un-lft-identity_binary64`
3×	`add-log-exp_binary64`
3×	`fma-def_binary64`
2×	`distribute-lft-out_binary64`
2×	`add-sqr-sqrt_binary64`

Counts

1 → 18

Calls

1 calls:

5.0ms

(+.f64 1/2 (/.f64 1 x))

series2.0ms (0.1%)

Counts

1 → 3

Calls

1 calls:

2.0ms

(+.f64 1/2 (/.f64 1 x))

simplify93.0ms (4.2%)

Algorithm

1×	egg-herbie

Rules

809×	`fma-def_binary64`
425×	`unswap-sqr_binary64`
403×	`distribute-rgt-in_binary64`
330×	`associate-r_binary64`
260×	`fma-neg_binary64`

Counts

21 → 33

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	31	183
1	84	163
2	170	162
3	357	162
4	797	162
5	1860	162
6	3117	162
7	4800	162
8	4821	162
9	4911	162

prune15.0ms (0.7%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	31	2	33
Fresh	0	1	1
Picked	1	0	1
Done	0	1	1
Total	32	4	36

Error

0.8b

Counts

36 → 4

Alt Table

Status	Error	Program
✓	1.0b	(/.f64 (exp.f64 x) (expm1.f64 x))
	63.0b	(log.f64 (*.f64 (exp.f64 1/2) (exp.f64 (/.f64 1 x))))
	29.5b	(cbrt.f64 (.f64 (.f64 (/.f64 (exp.f64 x) (expm1.f64 x)) (/.f64 (exp.f64 x) (expm1.f64 x))) (/.f64 (exp.f64 x) (expm1.f64 x))))
▶	19.6b	(fma.f64 (*.f64 (cbrt.f64 1/2) (cbrt.f64 1/2)) (cbrt.f64 1/2) (/.f64 1 x))

Compiler

Compiled 372 to 298 computations (19.9% saved)

localize6.0ms (0.3%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.0b	(fma.f64 (*.f64 (cbrt.f64 1/2) (cbrt.f64 1/2)) (cbrt.f64 1/2) (/.f64 1 x))
✓	1.0b	(*.f64 (cbrt.f64 1/2) (cbrt.f64 1/2))

rewrite7.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

18×	`add-sqr-sqrt_binary64`
16×	`cbrt-prod_binary64`
10×	`*-un-lft-identity_binary64`
10×	`add-cube-cbrt_binary64`
9×	`pow1_binary64`

Counts

2 → 52

Calls

2 calls:

5.0ms	(*.f64 (cbrt.f64 1/2) (cbrt.f64 1/2))
0.0ms	(fma.f64 (*.f64 (cbrt.f64 1/2) (cbrt.f64 1/2)) (cbrt.f64 1/2) (/.f64 1 x))

series18.0ms (0.8%)

Counts

2 → 12

Calls

2 calls:

18.0ms	(fma.f64 (*.f64 (cbrt.f64 1/2) (cbrt.f64 1/2)) (cbrt.f64 1/2) (/.f64 1 x))
0.0ms	(*.f64 (cbrt.f64 1/2) (cbrt.f64 1/2))

simplify80.0ms (3.6%)

Algorithm

1×	egg-herbie

Rules

628×	`fma-def_binary64`
384×	`associate-+l+_binary64`
316×	`associate-*r/_binary64`
304×	`associate-*l/_binary64`
303×	`*-commutative_binary64`

Counts

64 → 111

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	61	624
1	88	589
2	198	585
3	402	571
4	1080	495
5	1933	495
6	4106	495
7	4877	495

prune59.0ms (2.7%)

Pruning

3 alts after pruning (2 fresh and 1 done)

	Pruned	Kept	Total
New	109	2	111
Fresh	2	0	2
Picked	1	0	1
Done	0	1	1
Total	112	3	115

Error

0.8b

Counts

115 → 3

Alt Table

Status	Error	Program
▶	19.6b	(fma.f64 (*.f64 (sqrt.f64 (cbrt.f64 1/2)) (pow.f64 (sqrt.f64 (cbrt.f64 1/2)) 3)) (cbrt.f64 1/2) (/.f64 1 x))
✓	1.0b	(/.f64 (exp.f64 x) (expm1.f64 x))
	20.4b	(.f64 (.f64 (cbrt.f64 (fma.f64 (.f64 (cbrt.f64 1/2) (cbrt.f64 1/2)) (cbrt.f64 1/2) (/.f64 1 x))) (cbrt.f64 (fma.f64 (.f64 (cbrt.f64 1/2) (cbrt.f64 1/2)) (cbrt.f64 1/2) (/.f64 1 x)))) (cbrt.f64 (fma.f64 (*.f64 (cbrt.f64 1/2) (cbrt.f64 1/2)) (cbrt.f64 1/2) (/.f64 1 x))))

Compiler

Compiled 1158 to 1071 computations (7.5% saved)

localize8.0ms (0.3%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(fma.f64 (*.f64 (sqrt.f64 (cbrt.f64 1/2)) (pow.f64 (sqrt.f64 (cbrt.f64 1/2)) 3)) (cbrt.f64 1/2) (/.f64 1 x))
✓	1.0b	(pow.f64 (sqrt.f64 (cbrt.f64 1/2)) 3)
	1.0b	(sqrt.f64 (cbrt.f64 1/2))
✓	1.0b	(sqrt.f64 (cbrt.f64 1/2))

rewrite7.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

18×	`sqrt-prod_binary64`
14×	`add-sqr-sqrt_binary64`
12×	`*-un-lft-identity_binary64`
12×	`add-cube-cbrt_binary64`
10×	`cbrt-prod_binary64`

Counts

3 → 71

Calls

3 calls:

3.0ms	(pow.f64 (sqrt.f64 (cbrt.f64 1/2)) 3)
1.0ms	(sqrt.f64 (cbrt.f64 1/2))
0.0ms	(fma.f64 (*.f64 (sqrt.f64 (cbrt.f64 1/2)) (pow.f64 (sqrt.f64 (cbrt.f64 1/2)) 3)) (cbrt.f64 1/2) (/.f64 1 x))

series18.0ms (0.8%)

Counts

3 → 12

Calls

3 calls:

18.0ms	(fma.f64 (*.f64 (sqrt.f64 (cbrt.f64 1/2)) (pow.f64 (sqrt.f64 (cbrt.f64 1/2)) 3)) (cbrt.f64 1/2) (/.f64 1 x))
0.0ms	(sqrt.f64 (cbrt.f64 1/2))
0.0ms	(pow.f64 (sqrt.f64 (cbrt.f64 1/2)) 3)

simplify109.0ms (4.9%)

Algorithm

1×	egg-herbie

Rules

649×	`fma-def_binary64`
448×	`*-commutative_binary64`
448×	`associate-l_binary64`
429×	`log-prod_binary64`
371×	`distribute-rgt-in_binary64`

Counts

83 → 141

Iterations

Useful iterations: 5 (0.0ms)

Iter	Nodes	Cost
0	79	932
1	145	673
2	398	649
3	1234	643
4	2233	643
5	4458	640
6	4950	640
7	4894	640

prune92.0ms (4.1%)

Pruning

3 alts after pruning (2 fresh and 1 done)

	Pruned	Kept	Total
New	168	1	169
Fresh	0	1	1
Picked	1	0	1
Done	0	1	1
Total	169	3	172

Error

0.8b

Counts

172 → 3

Alt Table

Status	Error	Program
✓	1.0b	(/.f64 (exp.f64 x) (expm1.f64 x))
	20.4b	(.f64 (.f64 (cbrt.f64 (fma.f64 (.f64 (cbrt.f64 1/2) (cbrt.f64 1/2)) (cbrt.f64 1/2) (/.f64 1 x))) (cbrt.f64 (fma.f64 (.f64 (cbrt.f64 1/2) (cbrt.f64 1/2)) (cbrt.f64 1/2) (/.f64 1 x)))) (cbrt.f64 (fma.f64 (*.f64 (cbrt.f64 1/2) (cbrt.f64 1/2)) (cbrt.f64 1/2) (/.f64 1 x))))
	19.6b	(fma.f64 (.f64 (sqrt.f64 (cbrt.f64 1/2)) (.f64 (pow.f64 (*.f64 (cbrt.f64 (sqrt.f64 (cbrt.f64 1/2))) (cbrt.f64 (sqrt.f64 (cbrt.f64 1/2)))) 3) (pow.f64 (cbrt.f64 (sqrt.f64 (cbrt.f64 1/2))) 3))) (cbrt.f64 1/2) (/.f64 1 x))

Compiler

Compiled 1957 to 1842 computations (5.9% saved)

regimes96.0ms (4.3%)

Accuracy

Total 0.1b remaining (19.6%)

Threshold costs 0.1b (19.6%)

Compiler

Compiled 1703 to 1516 computations (11% saved)

simplify3.0ms (0.1%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	5	8
1	5	8

end0.0ms (0%)

Compiler: Compiled 6 to 4 computations (33.3% saved)

sample985.0ms (44.4%)

Algorithm

1×

intervals

Results

412.0ms	2650×	body	1024	valid
115.0ms	1306×	body	512	valid
88.0ms	3133×	body	128	valid
43.0ms	250×	body	2048	valid
42.0ms	661×	body	256	valid
0.0ms	1×	body	2048	invalid

Compiler

Compiled 90 to 79 computations (12.2% saved)

Details

analyze419.0ms (18.9%)

sample32.0ms (1.4%)

simplify9.0ms (0.4%)

prune3.0ms (0.1%)

localize4.0ms (0.2%)

rewrite7.0ms (0.3%)

series17.0ms (0.8%)

simplify87.0ms (3.9%)

prune34.0ms (1.5%)

localize3.0ms (0.1%)

rewrite5.0ms (0.2%)

series2.0ms (0.1%)

simplify93.0ms (4.2%)

prune15.0ms (0.7%)

localize6.0ms (0.3%)

rewrite7.0ms (0.3%)

series18.0ms (0.8%)

simplify80.0ms (3.6%)

prune59.0ms (2.7%)

localize8.0ms (0.3%)

rewrite7.0ms (0.3%)

series18.0ms (0.8%)

simplify109.0ms (4.9%)

prune92.0ms (4.1%)

regimes96.0ms (4.3%)

simplify3.0ms (0.1%)

end0.0ms (0%)

sample985.0ms (44.4%)

Profiling