Details

analyze2.4s (20.1%)

Algorithm

1×

Search

True	Other	False	Iter
0%	49.9%	50.1%	0
0%	49.9%	50.1%	1
0%	49.9%	50.1%	2
0%	49.9%	50.1%	3
0%	49.9%	50.1%	4
0%	49.9%	50.1%	5
0%	49.9%	50.1%	6
0%	49.9%	50.1%	7
0%	49.9%	50.1%	8
0.4%	49.5%	50.1%	9
0.4%	49.3%	50.3%	10
0.6%	48.9%	50.5%	11
1.1%	48.1%	50.9%	12
1.5%	47.3%	51.2%	13
1.7%	46.9%	51.5%	14

Compiler

Compiled 34 to 24 computations (29.4% saved)

sample263.0ms (2.2%)

Algorithm

1×

intervals

Symmetry

(sort a b)

Results

110.0ms	130×	body	2048	valid
34.0ms	74×	body	1024	valid
13.0ms	19×	body	1024	overflowed
7.0ms	24×	body	512	valid
7.0ms	303×	pre	128	true
5.0ms	21×	body	128	valid
3.0ms	6×	body	2048	overflowed
2.0ms	8×	body	512	overflowed
2.0ms	1×	body	4096	valid
1.0ms	8×	body	256	overflowed
1.0ms	6×	body	256	valid
0.0ms	6×	body	128	overflowed

Compiler

Compiled 64 to 46 computations (28.1% saved)

simplify22.0ms (0.2%)

Algorithm

1×	egg-herbie

Rules

986×	`times-frac_binary64`
580×	`associate-/l*_binary64`
372×	`fma-def_binary64`
126×	`distribute-rgt-in_binary64`
122×	`distribute-lft-in_binary64`

Counts

1 → 2

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	18	28
1	47	28
2	108	28
3	254	28
4	897	28
5	5292	28

prune4.0ms (0%)

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

42.2b

Counts

3 → 1

Alt Table

Status	Error	Program
▶	42.2b	(/.f64 (.f64 eps (expm1.f64 (.f64 eps (+.f64 a b)))) (.f64 (expm1.f64 (.f64 eps a)) (expm1.f64 (*.f64 eps b))))

Compiler

Compiled 87 to 54 computations (37.9% saved)

localize22.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(expm1.f64 (*.f64 eps (+.f64 a b)))
✓	0.1b	(.f64 (expm1.f64 (.f64 eps a)) (expm1.f64 (*.f64 eps b)))
✓	0.1b	(.f64 eps (expm1.f64 (.f64 eps (+.f64 a b))))
✓	40.1b	(/.f64 (.f64 eps (expm1.f64 (.f64 eps (+.f64 a b)))) (.f64 (expm1.f64 (.f64 eps a)) (expm1.f64 (*.f64 eps b))))

series369.0ms (3.1%)

Counts

4 → 144

Calls

4 calls:

295.0ms	(/.f64 (.f64 eps (expm1.f64 (.f64 eps (+.f64 a b)))) (.f64 (expm1.f64 (.f64 eps a)) (expm1.f64 (*.f64 eps b))))
31.0ms	(.f64 (expm1.f64 (.f64 eps a)) (expm1.f64 (*.f64 eps b)))
27.0ms	(.f64 eps (expm1.f64 (.f64 eps (+.f64 a b))))
15.0ms	(expm1.f64 (*.f64 eps (+.f64 a b)))

rewrite16.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

20×	`add-cbrt-cube_binary64`
20×	`add-exp-log_binary64`
12×	`add-sqr-sqrt_binary64`
8×	`*-un-lft-identity_binary64`
8×	`add-cube-cbrt_binary64`

Counts

4 → 74

Calls

4 calls:

4.0ms	(.f64 eps (expm1.f64 (.f64 eps (+.f64 a b))))
4.0ms	(/.f64 (.f64 eps (expm1.f64 (.f64 eps (+.f64 a b)))) (.f64 (expm1.f64 (.f64 eps a)) (expm1.f64 (*.f64 eps b))))
3.0ms	(.f64 (expm1.f64 (.f64 eps a)) (expm1.f64 (*.f64 eps b)))
0.0ms	(expm1.f64 (*.f64 eps (+.f64 a b)))

simplify136.0ms (1.1%)

Algorithm

1×	egg-herbie

Rules

828×	`fma-def_binary64`
622×	`times-frac_binary64`
470×	`associate-/l*_binary64`
249×	`*-commutative_binary64`
191×	`+-commutative_binary64`

Counts

218 → 229

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	646	8872
1	2166	8105
2	5325	8105

prune196.0ms (1.7%)

Pruning

3 alts after pruning (3 fresh and 0 done)

	Pruned	Kept	Total
New	226	3	229
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	227	3	230

Error

0.0b

Counts

230 → 3

Alt Table

Status	Error	Program
	42.1b	(/.f64 1 (/.f64 (.f64 (expm1.f64 (.f64 eps a)) (expm1.f64 (.f64 eps b))) (.f64 eps (expm1.f64 (*.f64 eps (+.f64 a b))))))
▶	7.6b	(fma.f64 1/12 (.f64 a (.f64 eps eps)) (+.f64 (/.f64 1 b) (fma.f64 1/12 (.f64 b (.f64 eps eps)) (/.f64 1 a))))
	29.4b	(/.f64 eps (/.f64 (expm1.f64 (.f64 a eps)) (/.f64 (expm1.f64 (.f64 (+.f64 a b) eps)) (expm1.f64 (*.f64 b eps)))))

Compiler

Compiled 11430 to 3843 computations (66.4% saved)

localize12.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(+.f64 (/.f64 1 b) (fma.f64 1/12 (.f64 b (.f64 eps eps)) (/.f64 1 a)))
✓	0.1b	(fma.f64 1/12 (.f64 b (.f64 eps eps)) (/.f64 1 a))
✓	5.9b	(.f64 a (.f64 eps eps))
✓	7.1b	(.f64 b (.f64 eps eps))

series112.0ms (0.9%)

Counts

4 → 120

Calls

4 calls:

66.0ms	(fma.f64 1/12 (.f64 b (.f64 eps eps)) (/.f64 1 a))
29.0ms	(+.f64 (/.f64 1 b) (fma.f64 1/12 (.f64 b (.f64 eps eps)) (/.f64 1 a)))
8.0ms	(.f64 b (.f64 eps eps))
8.0ms	(.f64 a (.f64 eps eps))

rewrite19.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

16×	`*-un-lft-identity_binary64`
15×	`add-sqr-sqrt_binary64`
14×	`add-cbrt-cube_binary64`
14×	`add-exp-log_binary64`
14×	`pow1_binary64`

Counts

4 → 81

Calls

4 calls:

6.0ms	(+.f64 (/.f64 1 b) (fma.f64 1/12 (.f64 b (.f64 eps eps)) (/.f64 1 a)))
5.0ms	(.f64 a (.f64 eps eps))
4.0ms	(.f64 b (.f64 eps eps))
0.0ms	(fma.f64 1/12 (.f64 b (.f64 eps eps)) (/.f64 1 a))

simplify144.0ms (1.2%)

Algorithm

1×	egg-herbie

Rules

562×	`associate-+l+_binary64`
523×	`associate-l_binary64`
384×	`associate-r_binary64`
262×	`cancel-sign-sub-inv_binary64`
220×	`unswap-sqr_binary64`

Counts

201 → 131

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	105	2505
1	236	2362
2	656	2362
3	2257	2360
4	4524	2360
5	5001	2360

prune131.0ms (1.1%)

Pruning

5 alts after pruning (4 fresh and 1 done)

	Pruned	Kept	Total
New	129	2	131
Fresh	0	2	2
Picked	0	1	1
Done	0	0	0
Total	129	5	134

Error

0.0b

Counts

134 → 5

Alt Table

Status	Error	Program
	42.1b	(/.f64 1 (/.f64 (.f64 (expm1.f64 (.f64 eps a)) (expm1.f64 (.f64 eps b))) (.f64 eps (expm1.f64 (*.f64 eps (+.f64 a b))))))
✓	7.6b	(fma.f64 1/12 (.f64 a (.f64 eps eps)) (+.f64 (/.f64 1 b) (fma.f64 1/12 (.f64 b (.f64 eps eps)) (/.f64 1 a))))
	29.4b	(/.f64 eps (/.f64 (expm1.f64 (.f64 a eps)) (/.f64 (expm1.f64 (.f64 (+.f64 a b) eps)) (expm1.f64 (*.f64 b eps)))))
	46.5b	(fma.f64 1/12 (.f64 a (.f64 eps eps)) (/.f64 (+.f64 (pow.f64 (/.f64 1 b) 3) (pow.f64 (fma.f64 1/12 (.f64 b (.f64 eps eps)) (/.f64 1 a)) 3)) (+.f64 (.f64 (/.f64 1 b) (/.f64 1 b)) (-.f64 (.f64 (fma.f64 1/12 (.f64 b (.f64 eps eps)) (/.f64 1 a)) (fma.f64 1/12 (.f64 b (.f64 eps eps)) (/.f64 1 a))) (.f64 (/.f64 1 b) (fma.f64 1/12 (.f64 b (*.f64 eps eps)) (/.f64 1 a)))))))
▶	8.1b	(fma.f64 1/12 (.f64 a (.f64 eps eps)) (fma.f64 (.f64 (cbrt.f64 (/.f64 1 b)) (cbrt.f64 (/.f64 1 b))) (cbrt.f64 (/.f64 1 b)) (fma.f64 1/12 (.f64 b (*.f64 eps eps)) (/.f64 1 a))))

Compiler

Compiled 3845 to 1848 computations (51.9% saved)

localize15.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.5b	(*.f64 (cbrt.f64 (/.f64 1 b)) (cbrt.f64 (/.f64 1 b)))
✓	0.6b	(cbrt.f64 (/.f64 1 b))
	5.9b	(.f64 a (.f64 eps eps))
	7.1b	(.f64 b (.f64 eps eps))

series76.0ms (0.6%)

Counts

2 → 24

Calls

2 calls:

38.0ms	(cbrt.f64 (/.f64 1 b))
37.0ms	(*.f64 (cbrt.f64 (/.f64 1 b)) (cbrt.f64 (/.f64 1 b)))

rewrite26.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

93×	`cbrt-prod_binary64`
81×	`add-sqr-sqrt_binary64`
61×	`times-frac_binary64`
51×	`*-un-lft-identity_binary64`
41×	`add-cube-cbrt_binary64`

Counts

2 → 113

Calls

2 calls:

11.0ms	(*.f64 (cbrt.f64 (/.f64 1 b)) (cbrt.f64 (/.f64 1 b)))
2.0ms	(cbrt.f64 (/.f64 1 b))

simplify110.0ms (0.9%)

Algorithm

1×	egg-herbie

Rules

468×	`distribute-rgt-in_binary64`
444×	`log-div_binary64`
414×	`unswap-sqr_binary64`
331×	`fma-def_binary64`
287×	`log-prod_binary64`

Counts

137 → 146

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	83	2116
1	128	2012
2	353	1946
3	820	1926
4	2636	1770
5	4510	1770
6	5023	1770

prune295.0ms (2.5%)

Pruning

6 alts after pruning (4 fresh and 2 done)

	Pruned	Kept	Total
New	268	2	270
Fresh	1	2	3
Picked	0	1	1
Done	0	1	1
Total	269	6	275

Error

0.0b

Counts

275 → 6

Alt Table

Status	Error	Program
	42.1b	(/.f64 1 (/.f64 (.f64 (expm1.f64 (.f64 eps a)) (expm1.f64 (.f64 eps b))) (.f64 eps (expm1.f64 (*.f64 eps (+.f64 a b))))))
✓	7.6b	(fma.f64 1/12 (.f64 a (.f64 eps eps)) (+.f64 (/.f64 1 b) (fma.f64 1/12 (.f64 b (.f64 eps eps)) (/.f64 1 a))))
▶	8.1b	(fma.f64 1/12 (.f64 a (.f64 eps eps)) (fma.f64 (/.f64 (cbrt.f64 (/.f64 1 b)) (cbrt.f64 b)) (cbrt.f64 (/.f64 1 b)) (fma.f64 1/12 (.f64 b (.f64 eps eps)) (/.f64 1 a))))
	8.1b	(fma.f64 1/12 (.f64 a (.f64 eps eps)) (fma.f64 (/.f64 1 (.f64 (cbrt.f64 b) (cbrt.f64 b))) (cbrt.f64 (/.f64 1 b)) (fma.f64 1/12 (.f64 b (*.f64 eps eps)) (/.f64 1 a))))
	29.4b	(/.f64 eps (/.f64 (expm1.f64 (.f64 a eps)) (/.f64 (expm1.f64 (.f64 (+.f64 a b) eps)) (expm1.f64 (*.f64 b eps)))))
✓	8.1b	(fma.f64 1/12 (.f64 a (.f64 eps eps)) (fma.f64 (.f64 (cbrt.f64 (/.f64 1 b)) (cbrt.f64 (/.f64 1 b))) (cbrt.f64 (/.f64 1 b)) (fma.f64 1/12 (.f64 b (*.f64 eps eps)) (/.f64 1 a))))

Compiler

Compiled 10372 to 6000 computations (42.2% saved)

localize16.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.5b	(cbrt.f64 b)
	0.6b	(cbrt.f64 (/.f64 1 b))
	5.9b	(.f64 a (.f64 eps eps))
	7.1b	(.f64 b (.f64 eps eps))

series31.0ms (0.3%)

Counts

1 → 12

Calls

1 calls:

30.0ms

(cbrt.f64 b)

rewrite1.0ms (0%)

Algorithm

1×	rewrite-expression-head

Rules

3×	`cbrt-prod_binary64`
2×	`*-un-lft-identity_binary64`
2×	`add-sqr-sqrt_binary64`
2×	`add-cube-cbrt_binary64`
1×	`add-cbrt-cube_binary64`

Counts

1 → 13

Calls

1 calls:

1.0ms

(cbrt.f64 b)

simplify58.0ms (0.5%)

Algorithm

1×	egg-herbie

Rules

610×	`associate-/l/_binary64`
374×	`log-prod_binary64`
316×	`distribute-rgt-neg-in_binary64`
314×	`distribute-lft-neg-in_binary64`
287×	`*-commutative_binary64`

Counts

25 → 18

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	24	141
1	38	137
2	86	137
3	208	137
4	626	133
5	1904	133
6	2565	133
7	3552	133
8	4861	133

prune154.0ms (1.3%)

Pruning

6 alts after pruning (3 fresh and 3 done)

	Pruned	Kept	Total
New	142	0	142
Fresh	0	3	3
Picked	0	1	1
Done	0	2	2
Total	142	6	148

Error

0.0b

Counts

148 → 6

Alt Table

Status	Error	Program
	42.1b	(/.f64 1 (/.f64 (.f64 (expm1.f64 (.f64 eps a)) (expm1.f64 (.f64 eps b))) (.f64 eps (expm1.f64 (*.f64 eps (+.f64 a b))))))
✓	7.6b	(fma.f64 1/12 (.f64 a (.f64 eps eps)) (+.f64 (/.f64 1 b) (fma.f64 1/12 (.f64 b (.f64 eps eps)) (/.f64 1 a))))
✓	8.1b	(fma.f64 1/12 (.f64 a (.f64 eps eps)) (fma.f64 (/.f64 (cbrt.f64 (/.f64 1 b)) (cbrt.f64 b)) (cbrt.f64 (/.f64 1 b)) (fma.f64 1/12 (.f64 b (.f64 eps eps)) (/.f64 1 a))))
	8.1b	(fma.f64 1/12 (.f64 a (.f64 eps eps)) (fma.f64 (/.f64 1 (.f64 (cbrt.f64 b) (cbrt.f64 b))) (cbrt.f64 (/.f64 1 b)) (fma.f64 1/12 (.f64 b (*.f64 eps eps)) (/.f64 1 a))))
	29.4b	(/.f64 eps (/.f64 (expm1.f64 (.f64 a eps)) (/.f64 (expm1.f64 (.f64 (+.f64 a b) eps)) (expm1.f64 (*.f64 b eps)))))
✓	8.1b	(fma.f64 1/12 (.f64 a (.f64 eps eps)) (fma.f64 (.f64 (cbrt.f64 (/.f64 1 b)) (cbrt.f64 (/.f64 1 b))) (cbrt.f64 (/.f64 1 b)) (fma.f64 1/12 (.f64 b (*.f64 eps eps)) (/.f64 1 a))))

Compiler

Compiled 5010 to 2579 computations (48.5% saved)

regimes346.0ms (2.9%)

Accuracy

Total 1.2b remaining (98.3%)

Threshold costs 0b (0%)

Counts

49 → 3

Compiler

Compiled 5134 to 3304 computations (35.6% saved)

bsearch2.0ms (0%)

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

simplify4.0ms (0%)

Algorithm

1×	egg-herbie

Rules

8×	`*-commutative_binary64`
5×	`+-commutative_binary64`
3×	`sub-neg_binary64`
1×	`1-exp_binary64`
1×	`if-if-or-not_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	41	134
1	58	134
2	61	134
3	59	134

end9.0ms (0.1%)

Compiler: Compiled 270 to 150 computations (44.4% saved)

sample6.9s (58%)

Algorithm

1×

intervals

Results

3.6s	4070×	body	2048	valid
1.1s	2408×	body	1024	valid
275.0ms	776×	body	512	valid
257.0ms	334×	body	2048	overflowed
218.0ms	9588×	pre	128	true
206.0ms	558×	body	1024	overflowed
77.0ms	280×	body	512	overflowed
47.0ms	242×	body	256	valid
43.0ms	494×	body	128	valid
25.0ms	281×	body	128	overflowed
22.0ms	134×	body	256	overflowed
14.0ms	10×	body	4096	valid
1.0ms	1×	body	2048	invalid

Compiler

Compiled 293 to 184 computations (37.2% saved)

Details

analyze2.4s (20.1%)

sample263.0ms (2.2%)

simplify22.0ms (0.2%)

prune4.0ms (0%)

localize22.0ms (0.2%)

series369.0ms (3.1%)

rewrite16.0ms (0.1%)

simplify136.0ms (1.1%)

prune196.0ms (1.7%)

localize12.0ms (0.1%)

series112.0ms (0.9%)

rewrite19.0ms (0.2%)

simplify144.0ms (1.2%)

prune131.0ms (1.1%)

localize15.0ms (0.1%)

series76.0ms (0.6%)

rewrite26.0ms (0.2%)

simplify110.0ms (0.9%)

prune295.0ms (2.5%)

localize16.0ms (0.1%)

series31.0ms (0.3%)

rewrite1.0ms (0%)

simplify58.0ms (0.5%)

prune154.0ms (1.3%)

regimes346.0ms (2.9%)

bsearch2.0ms (0%)

simplify4.0ms (0%)

end9.0ms (0.1%)

sample6.9s (58%)

Profiling