Details

analyze2.6s (14%)

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)

sample378.0ms (2%)

Algorithm

1×

intervals

Symmetry

(sort a b)

Results

158.0ms	129×	body	2048	valid
49.0ms	79×	body	1024	valid
16.0ms	18×	body	2048	overflowed
10.0ms	316×	pre	128	true
10.0ms	24×	body	512	valid
8.0ms	16×	body	1024	overflowed
3.0ms	8×	body	512	overflowed
2.0ms	8×	body	256	valid
2.0ms	15×	body	128	valid
1.0ms	1×	body	4096	valid
1.0ms	6×	body	256	overflowed
1.0ms	12×	body	128	overflowed

Compiler

Compiled 64 to 46 computations (28.1% saved)

simplify30.0ms (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

prune5.0ms (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

41.3b

Counts

3 → 1

Alt Table

Status	Error	Program
▶	41.3b	(/.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)

localize43.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(expm1.f64 (*.f64 eps b))
✓	0.1b	(.f64 eps (expm1.f64 (.f64 eps (+.f64 a b))))
✓	0.8b	(.f64 (expm1.f64 (.f64 eps a)) (expm1.f64 (*.f64 eps b)))
✓	39.6b	(/.f64 (.f64 eps (expm1.f64 (.f64 eps (+.f64 a b)))) (.f64 (expm1.f64 (.f64 eps a)) (expm1.f64 (*.f64 eps b))))

series533.0ms (2.8%)

Counts

4 → 132

Calls

4 calls:

443.0ms	(/.f64 (.f64 eps (expm1.f64 (.f64 eps (+.f64 a b)))) (.f64 (expm1.f64 (.f64 eps a)) (expm1.f64 (*.f64 eps b))))
43.0ms	(.f64 (expm1.f64 (.f64 eps a)) (expm1.f64 (*.f64 eps b)))
38.0ms	(.f64 eps (expm1.f64 (.f64 eps (+.f64 a b))))
9.0ms	(expm1.f64 (*.f64 eps b))

rewrite23.0ms (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:

9.0ms	(/.f64 (.f64 eps (expm1.f64 (.f64 eps (+.f64 a b)))) (.f64 (expm1.f64 (.f64 eps a)) (expm1.f64 (*.f64 eps b))))
4.0ms	(.f64 eps (expm1.f64 (.f64 eps (+.f64 a b))))
4.0ms	(.f64 (expm1.f64 (.f64 eps a)) (expm1.f64 (*.f64 eps b)))
1.0ms	(expm1.f64 (*.f64 eps b))

simplify196.0ms (1%)

Algorithm

1×	egg-herbie

Rules

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

Counts

206 → 213

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	612	8300
1	2021	7554
2	5059	7554

prune219.0ms (1.2%)

Pruning

3 alts after pruning (3 fresh and 0 done)

	Pruned	Kept	Total
New	210	3	213
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	211	3	214

Error

0.0b

Counts

214 → 3

Alt Table

Status	Error	Program
	29.1b	(/.f64 (.f64 (/.f64 eps (expm1.f64 (.f64 a eps))) (expm1.f64 (.f64 (+.f64 a b) eps))) (expm1.f64 (.f64 eps b)))
▶	5.5b	(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))))
	41.3b	(/.f64 1 (/.f64 (.f64 (expm1.f64 (.f64 eps a)) (expm1.f64 (.f64 eps b))) (.f64 eps (expm1.f64 (*.f64 eps (+.f64 a b))))))

Compiler

Compiled 10529 to 3504 computations (66.7% saved)

localize20.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(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))))
✓	0.0b	(fma.f64 1/12 (.f64 b (.f64 eps eps)) (/.f64 1 a))
✓	7.7b	(.f64 a (.f64 eps eps))
✓	9.0b	(.f64 b (.f64 eps eps))

series91.0ms (0.5%)

Counts

4 → 120

Calls

4 calls:

39.0ms	(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))))
29.0ms	(fma.f64 1/12 (.f64 b (.f64 eps eps)) (/.f64 1 a))
11.0ms	(.f64 b (.f64 eps eps))
11.0ms	(.f64 a (.f64 eps eps))

rewrite22.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

14×	`add-cbrt-cube_binary64`
14×	`add-exp-log_binary64`
14×	`pow1_binary64`
8×	`add-sqr-sqrt_binary64`
6×	`associate-l_binary64`

Counts

4 → 62

Calls

4 calls:

11.0ms	(.f64 a (.f64 eps eps))
6.0ms	(.f64 b (.f64 eps eps))
1.0ms	(fma.f64 1/12 (.f64 b (.f64 eps eps)) (/.f64 1 a))
1.0ms	(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))))

simplify140.0ms (0.7%)

Algorithm

1×	egg-herbie

Rules

766×	`unswap-sqr_binary64`
610×	`fma-def_binary64`
470×	`associate-l_binary64`
333×	`associate-r_binary64`
295×	`associate-+r+_binary64`

Counts

182 → 122

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	103	2698
1	202	2339
2	549	2269
3	1651	2269
4	3788	2269
5	5058	2269

prune154.0ms (0.8%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	121	1	122
Fresh	0	2	2
Picked	0	1	1
Done	0	0	0
Total	121	4	125

Error

Counts

125 → 4

Alt Table

Status	Error	Program
	31.9b	(.f64 (sqrt.f64 (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))))) (sqrt.f64 (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))))))
▶	29.1b	(/.f64 (.f64 (/.f64 eps (expm1.f64 (.f64 a eps))) (expm1.f64 (.f64 (+.f64 a b) eps))) (expm1.f64 (.f64 eps b)))
✓	5.5b	(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))))
	41.3b	(/.f64 1 (/.f64 (.f64 (expm1.f64 (.f64 eps a)) (expm1.f64 (.f64 eps b))) (.f64 eps (expm1.f64 (*.f64 eps (+.f64 a b))))))

Compiler

Compiled 3198 to 1559 computations (51.3% saved)

localize18.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.0b	(expm1.f64 (*.f64 eps b))
✓	6.0b	(.f64 (/.f64 eps (expm1.f64 (.f64 a eps))) (expm1.f64 (*.f64 (+.f64 a b) eps)))
✓	15.2b	(/.f64 eps (expm1.f64 (*.f64 a eps)))
✓	16.9b	(/.f64 (.f64 (/.f64 eps (expm1.f64 (.f64 a eps))) (expm1.f64 (.f64 (+.f64 a b) eps))) (expm1.f64 (.f64 eps b)))

series635.0ms (3.4%)

Counts

3 → 96

Calls

3 calls:

471.0ms

(/.f64 (*.f64 (/.f64 eps (expm1.f64 (*.f64 a eps))) (expm1.f64 (*.f64 (+.f64 a b) eps))) (expm1.f64 (*.f64 eps b)))

121.0ms

(*.f64 (/.f64 eps (expm1.f64 (*.f64 a eps))) (expm1.f64 (*.f64 (+.f64 a b) eps)))

43.0ms

(/.f64 eps (expm1.f64 (*.f64 a eps)))

rewrite32.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

26×	`add-sqr-sqrt_binary64`
22×	`times-frac_binary64`
21×	`*-un-lft-identity_binary64`
21×	`add-cube-cbrt_binary64`
19×	`add-cbrt-cube_binary64`

Counts

3 → 89

Calls

3 calls:

9.0ms

(/.f64 (*.f64 (/.f64 eps (expm1.f64 (*.f64 a eps))) (expm1.f64 (*.f64 (+.f64 a b) eps))) (expm1.f64 (*.f64 eps b)))

8.0ms

(*.f64 (/.f64 eps (expm1.f64 (*.f64 a eps))) (expm1.f64 (*.f64 (+.f64 a b) eps)))

4.0ms

(/.f64 eps (expm1.f64 (*.f64 a eps)))

simplify230.0ms (1.2%)

Algorithm

1×	egg-herbie

Rules

486×	`associate-/l*_binary64`
472×	`times-frac_binary64`
418×	`fma-def_binary64`
283×	`associate-/r*_binary64`
200×	`associate-*l/_binary64`

Counts

185 → 190

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	557	7870
1	1770	7162
2	4979	7162

prune283.0ms (1.5%)

Pruning

4 alts after pruning (2 fresh and 2 done)

	Pruned	Kept	Total
New	217	0	217
Fresh	0	2	2
Picked	0	1	1
Done	0	1	1
Total	217	4	221

Error

Counts

221 → 4

Alt Table

Status	Error	Program
▶	31.9b	(.f64 (sqrt.f64 (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))))) (sqrt.f64 (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))))))
✓	29.1b	(/.f64 (.f64 (/.f64 eps (expm1.f64 (.f64 a eps))) (expm1.f64 (.f64 (+.f64 a b) eps))) (expm1.f64 (.f64 eps b)))
✓	5.5b	(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))))
	41.3b	(/.f64 1 (/.f64 (.f64 (expm1.f64 (.f64 eps a)) (expm1.f64 (.f64 eps b))) (.f64 eps (expm1.f64 (*.f64 eps (+.f64 a b))))))

Compiler

Compiled 9881 to 2987 computations (69.8% saved)

localize25.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(sqrt.f64 (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)))))
✓	0.3b	(.f64 (sqrt.f64 (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))))) (sqrt.f64 (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))))))
	7.7b	(.f64 a (.f64 eps eps))
	9.0b	(.f64 b (.f64 eps eps))

series265.0ms (1.4%)

Counts

2 → 48

Calls

2 calls:

210.0ms

(sqrt.f64 (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)))))

54.0ms

(*.f64 (sqrt.f64 (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))))) (sqrt.f64 (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))))))

rewrite30.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

28×	`add-sqr-sqrt_binary64`
21×	`sqrt-prod_binary64`
18×	`pow1_binary64`
11×	`*-un-lft-identity_binary64`
11×	`add-cube-cbrt_binary64`

Counts

2 → 68

Calls

2 calls:

9.0ms

(*.f64 (sqrt.f64 (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))))) (sqrt.f64 (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))))))

2.0ms

(sqrt.f64 (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)))))

simplify199.0ms (1%)

Algorithm

1×	egg-herbie

Rules

541×	`times-frac_binary64`
483×	`cancel-sign-sub-inv_binary64`
327×	`distribute-rgt-in_binary64`
201×	`associate-l_binary64`
196×	`associate-r_binary64`

Counts

116 → 130

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	216	5435
1	585	4171
2	2248	3868
3	4986	3868

prune647.0ms (3.4%)

Pruning

4 alts after pruning (1 fresh and 3 done)

	Pruned	Kept	Total
New	305	0	305
Fresh	0	1	1
Picked	0	1	1
Done	0	2	2
Total	305	4	309

Error

Counts

309 → 4

Alt Table

Status	Error	Program
✓	31.9b	(.f64 (sqrt.f64 (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))))) (sqrt.f64 (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))))))
✓	29.1b	(/.f64 (.f64 (/.f64 eps (expm1.f64 (.f64 a eps))) (expm1.f64 (.f64 (+.f64 a b) eps))) (expm1.f64 (.f64 eps b)))
✓	5.5b	(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))))
	41.3b	(/.f64 1 (/.f64 (.f64 (expm1.f64 (.f64 eps a)) (expm1.f64 (.f64 eps b))) (.f64 eps (expm1.f64 (*.f64 eps (+.f64 a b))))))

Compiler

Compiled 17555 to 9383 computations (46.6% saved)

regimes1.0s (5.4%)

Accuracy

Total 0.3b remaining (91.1%)

Threshold costs 0.3b (91.1%)

Counts

131 → 3

Compiler

Compiled 11686 to 7624 computations (34.8% saved)

bsearch10.0ms (0.1%)

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

simplify7.0ms (0%)

Algorithm

1×	egg-herbie

Rules

9×	`*-commutative_binary64`
6×	`+-commutative_binary64`
3×	`sub-neg_binary64`
1×	`1-exp_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	42	155
1	61	155
2	64	155
3	62	155

end15.0ms (0.1%)

Compiler: Compiled 315 to 177 computations (43.8% saved)

sample11.0s (58.2%)

Algorithm

1×

intervals

Results

6.1s	4106×	body	2048	valid
2.0s	2425×	body	1024	valid
407.0ms	626×	body	1024	overflowed
406.0ms	9796×	pre	128	true
380.0ms	381×	body	2048	overflowed
343.0ms	693×	body	512	valid
134.0ms	311×	body	512	overflowed
77.0ms	250×	body	256	valid
75.0ms	515×	body	128	valid
51.0ms	316×	body	128	overflowed
46.0ms	159×	body	256	overflowed
25.0ms	11×	body	4096	valid
4.0ms	3×	body	2048	invalid

Compiler

Compiled 258 to 156 computations (39.5% saved)

Details

analyze2.6s (14%)

sample378.0ms (2%)

simplify30.0ms (0.2%)

prune5.0ms (0%)

localize43.0ms (0.2%)

series533.0ms (2.8%)

rewrite23.0ms (0.1%)

simplify196.0ms (1%)

prune219.0ms (1.2%)

localize20.0ms (0.1%)

series91.0ms (0.5%)

rewrite22.0ms (0.1%)

simplify140.0ms (0.7%)

prune154.0ms (0.8%)

localize18.0ms (0.1%)

series635.0ms (3.4%)

rewrite32.0ms (0.2%)

simplify230.0ms (1.2%)

prune283.0ms (1.5%)

localize25.0ms (0.1%)

series265.0ms (1.4%)

rewrite30.0ms (0.2%)

simplify199.0ms (1%)

prune647.0ms (3.4%)

regimes1.0s (5.4%)

bsearch10.0ms (0.1%)

simplify7.0ms (0%)

end15.0ms (0.1%)

sample11.0s (58.2%)

Profiling