Details

analyze2.3s (17.2%)

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)

sample8.3s (63.3%)

Symmetry

(sort a b)

Results

4.8s	4208×	body	2048	valid
1.8s	2523×	body	1024	valid
427.0ms	752×	body	512	valid
409.0ms	602×	body	1024	invalid
320.0ms	387×	body	2048	invalid
126.0ms	280×	body	512	invalid
89.0ms	264×	body	256	valid
84.0ms	495×	body	128	valid
47.0ms	297×	body	128	invalid
41.0ms	133×	body	256	invalid
24.0ms	14×	body	4096	valid

Compiler

Compiled 95 to 67 computations (29.5% saved)

simplify21.0ms (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

42.8b

Counts

3 → 1

Alt Table

Status	Error	Program
▶	42.8b	(/.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)

localize14.0ms (0.1%)

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))))
✓	41.0b	(/.f64 (.f64 eps (expm1.f64 (.f64 eps (+.f64 a b)))) (.f64 (expm1.f64 (.f64 eps a)) (expm1.f64 (*.f64 eps b))))

series322.0ms (2.4%)

Counts

4 → 144

Calls

4 calls:

252.0ms	(/.f64 (.f64 eps (expm1.f64 (.f64 eps (+.f64 a b)))) (.f64 (expm1.f64 (.f64 eps a)) (expm1.f64 (*.f64 eps b))))
29.0ms	(.f64 (expm1.f64 (.f64 eps a)) (expm1.f64 (*.f64 eps b)))
26.0ms	(.f64 eps (expm1.f64 (.f64 eps (+.f64 a b))))
14.0ms	(expm1.f64 (*.f64 eps (+.f64 a b)))

rewrite14.0ms (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:

5.0ms	(/.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)))
3.0ms	(.f64 eps (expm1.f64 (.f64 eps (+.f64 a b))))
0.0ms	(expm1.f64 (*.f64 eps (+.f64 a b)))

simplify127.0ms (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

prune194.0ms (1.5%)

Pruning

5 alts after pruning (5 fresh and 0 done)

	Pruned	Kept	Total
New	224	5	229
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	225	5	230

Error

0.0b

Counts

230 → 5

Alt Table

Status	Error	Program
	51.1b	(cbrt.f64 (.f64 (.f64 (/.f64 (.f64 eps (expm1.f64 (.f64 eps (+.f64 a b)))) (.f64 (expm1.f64 (.f64 eps a)) (expm1.f64 (.f64 eps b)))) (/.f64 (.f64 eps (expm1.f64 (.f64 eps (+.f64 a b)))) (.f64 (expm1.f64 (.f64 eps a)) (expm1.f64 (.f64 eps b))))) (/.f64 (.f64 eps (expm1.f64 (.f64 eps (+.f64 a b)))) (.f64 (expm1.f64 (.f64 eps a)) (expm1.f64 (*.f64 eps b))))))
▶	7.2b	(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))))
	27.2b	(/.f64 eps (/.f64 (expm1.f64 (.f64 a eps)) (/.f64 (expm1.f64 (.f64 (+.f64 a b) eps)) (expm1.f64 (*.f64 b eps)))))
	43.3b	(.f64 (.f64 eps (expm1.f64 (.f64 eps (+.f64 a b)))) (/.f64 1 (.f64 (expm1.f64 (.f64 eps a)) (expm1.f64 (.f64 eps b)))))
	42.7b	(/.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 11596 to 3905 computations (66.3% saved)

localize12.0ms (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))))
✓	0.1b	(fma.f64 1/12 (.f64 b (.f64 eps eps)) (/.f64 1 a))
✓	6.4b	(.f64 a (.f64 eps eps))
✓	6.8b	(.f64 b (.f64 eps eps))

series114.0ms (0.9%)

Counts

4 → 120

Calls

4 calls:

78.0ms	(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))))
19.0ms	(fma.f64 1/12 (.f64 b (.f64 eps eps)) (/.f64 1 a))
9.0ms	(.f64 a (.f64 eps eps))
8.0ms	(.f64 b (.f64 eps eps))

rewrite11.0ms (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:

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

simplify93.0ms (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

prune86.0ms (0.7%)

Pruning

5 alts after pruning (5 fresh and 0 done)

	Pruned	Kept	Total
New	119	3	122
Fresh	2	2	4
Picked	1	0	1
Done	0	0	0
Total	122	5	127

Error

0.0b

Counts

127 → 5

Alt Table

Status	Error	Program
	27.2b	(/.f64 eps (/.f64 (expm1.f64 (.f64 a eps)) (/.f64 (expm1.f64 (.f64 (+.f64 a b) eps)) (expm1.f64 (*.f64 b eps)))))
	43.3b	(.f64 (.f64 eps (expm1.f64 (.f64 eps (+.f64 a b)))) (/.f64 1 (.f64 (expm1.f64 (.f64 eps a)) (expm1.f64 (.f64 eps b)))))
▶	2.4b	(+.f64 (/.f64 1 b) (/.f64 1 a))
	8.3b	(.f64 (.f64 (cbrt.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))))) (cbrt.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)))))) (cbrt.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))))))
	47.2b	(cbrt.f64 (pow.f64 (fma.f64 eps (.f64 (+.f64 b a) (.f64 eps 1/12)) (+.f64 (/.f64 1 a) (/.f64 1 b))) 3))

Compiler

Compiled 3284 to 1614 computations (50.9% saved)

localize5.0ms (0%)

Local error

Found 1 expressions with local error:

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

series6.0ms (0%)

Counts

1 → 6

Calls

1 calls:

5.0ms

(+.f64 (/.f64 1 b) (/.f64 1 a))

rewrite13.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

20×	`*-un-lft-identity_binary64`
15×	`times-frac_binary64`
13×	`fma-def_binary64`
10×	`add-sqr-sqrt_binary64`
10×	`add-cube-cbrt_binary64`

Counts

1 → 34

Calls

1 calls:

10.0ms

(+.f64 (/.f64 1 b) (/.f64 1 a))

simplify118.0ms (0.9%)

Algorithm

1×	egg-herbie

Rules

450×	`fma-neg_binary64`
421×	`div-sub_binary64`
357×	`fma-def_binary64`
329×	`sub-neg_binary64`
281×	`distribute-rgt-in_binary64`

Counts

40 → 37

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	36	332
1	106	302
2	241	301
3	565	301
4	1313	301
5	2794	301
6	4202	301
7	4546	301
8	4845	301
9	4973	301
10	4870	301

prune32.0ms (0.2%)

Pruning

5 alts after pruning (4 fresh and 1 done)

	Pruned	Kept	Total
New	35	2	37
Fresh	2	2	4
Picked	0	1	1
Done	0	0	0
Total	37	5	42

Error

0.0b

Counts

42 → 5

Alt Table

Status	Error	Program
	27.2b	(/.f64 eps (/.f64 (expm1.f64 (.f64 a eps)) (/.f64 (expm1.f64 (.f64 (+.f64 a b) eps)) (expm1.f64 (*.f64 b eps)))))
	43.3b	(.f64 (.f64 eps (expm1.f64 (.f64 eps (+.f64 a b)))) (/.f64 1 (.f64 (expm1.f64 (.f64 eps a)) (expm1.f64 (.f64 eps b)))))
✓	2.4b	(+.f64 (/.f64 1 b) (/.f64 1 a))
	18.4b	(fma.f64 (sqrt.f64 (/.f64 1 b)) (sqrt.f64 (/.f64 1 b)) (/.f64 1 a))
▶	3.6b	(.f64 (.f64 (cbrt.f64 (+.f64 (/.f64 1 b) (/.f64 1 a))) (cbrt.f64 (+.f64 (/.f64 1 b) (/.f64 1 a)))) (cbrt.f64 (+.f64 (/.f64 1 b) (/.f64 1 a))))

Compiler

Compiled 703 to 518 computations (26.3% saved)

localize8.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.0b	(+.f64 (/.f64 1 b) (/.f64 1 a))
✓	0.3b	(.f64 (.f64 (cbrt.f64 (+.f64 (/.f64 1 b) (/.f64 1 a))) (cbrt.f64 (+.f64 (/.f64 1 b) (/.f64 1 a)))) (cbrt.f64 (+.f64 (/.f64 1 b) (/.f64 1 a))))
✓	0.5b	(*.f64 (cbrt.f64 (+.f64 (/.f64 1 b) (/.f64 1 a))) (cbrt.f64 (+.f64 (/.f64 1 b) (/.f64 1 a))))
✓	0.5b	(cbrt.f64 (+.f64 (/.f64 1 b) (/.f64 1 a)))

series56.0ms (0.4%)

Counts

3 → 72

Calls

3 calls:

26.0ms

(*.f64 (cbrt.f64 (+.f64 (/.f64 1 b) (/.f64 1 a))) (cbrt.f64 (+.f64 (/.f64 1 b) (/.f64 1 a))))

24.0ms

(cbrt.f64 (+.f64 (/.f64 1 b) (/.f64 1 a)))

6.0ms

(*.f64 (*.f64 (cbrt.f64 (+.f64 (/.f64 1 b) (/.f64 1 a))) (cbrt.f64 (+.f64 (/.f64 1 b) (/.f64 1 a)))) (cbrt.f64 (+.f64 (/.f64 1 b) (/.f64 1 a))))

rewrite117.0ms (0.9%)

Algorithm

1×	rewrite-expression-head

Rules

171×	`cbrt-div_binary64`
126×	`*-un-lft-identity_binary64`
105×	`cbrt-prod_binary64`
90×	`frac-times_binary64`
74×	`distribute-lft-out_binary64`

Counts

3 → 229

Calls

3 calls:

37.0ms

(*.f64 (*.f64 (cbrt.f64 (+.f64 (/.f64 1 b) (/.f64 1 a))) (cbrt.f64 (+.f64 (/.f64 1 b) (/.f64 1 a)))) (cbrt.f64 (+.f64 (/.f64 1 b) (/.f64 1 a))))

28.0ms

(*.f64 (cbrt.f64 (+.f64 (/.f64 1 b) (/.f64 1 a))) (cbrt.f64 (+.f64 (/.f64 1 b) (/.f64 1 a))))

10.0ms

(cbrt.f64 (+.f64 (/.f64 1 b) (/.f64 1 a)))

simplify271.0ms (2.1%)

Algorithm

1×	egg-herbie

Rules

686×	`times-frac_binary64`
496×	`fma-def_binary64`
269×	`associate-l_binary64`
265×	`associate-/r*_binary64`
237×	`associate-*l/_binary64`

Counts

301 → 291

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	290	10938
1	624	9955
2	1743	9116
3	4534	9037
4	4830	8854
5	4886	8854

prune464.0ms (3.5%)

Pruning

6 alts after pruning (4 fresh and 2 done)

	Pruned	Kept	Total
New	483	1	484
Fresh	0	3	3
Picked	0	1	1
Done	0	1	1
Total	483	6	489

Error

0.0b

Counts

489 → 6

Alt Table

Status	Error	Program
	31.9b	(.f64 (.f64 (pow.f64 (cbrt.f64 (+.f64 (/.f64 1 b) (/.f64 1 a))) 2) (cbrt.f64 (sqrt.f64 (+.f64 (/.f64 1 b) (/.f64 1 a))))) (cbrt.f64 (sqrt.f64 (+.f64 (/.f64 1 b) (/.f64 1 a)))))
✓	3.6b	(.f64 (.f64 (cbrt.f64 (+.f64 (/.f64 1 b) (/.f64 1 a))) (cbrt.f64 (+.f64 (/.f64 1 b) (/.f64 1 a)))) (cbrt.f64 (+.f64 (/.f64 1 b) (/.f64 1 a))))
	27.2b	(/.f64 eps (/.f64 (expm1.f64 (.f64 a eps)) (/.f64 (expm1.f64 (.f64 (+.f64 a b) eps)) (expm1.f64 (*.f64 b eps)))))
	43.3b	(.f64 (.f64 eps (expm1.f64 (.f64 eps (+.f64 a b)))) (/.f64 1 (.f64 (expm1.f64 (.f64 eps a)) (expm1.f64 (.f64 eps b)))))
✓	2.4b	(+.f64 (/.f64 1 b) (/.f64 1 a))
	18.4b	(fma.f64 (sqrt.f64 (/.f64 1 b)) (sqrt.f64 (/.f64 1 b)) (/.f64 1 a))

Compiler

Compiled 19071 to 14372 computations (24.6% saved)

regimes320.0ms (2.4%)

Accuracy

Total 0.4b remaining (95.4%)

Threshold costs 0.4b (95.4%)

Counts

82 → 3

Compiler

Compiled 7630 to 5180 computations (32.1% saved)

bsearch3.0ms (0%)

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

simplify4.0ms (0%)

Algorithm

1×	egg-herbie

Rules

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

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	37	132
1	49	132
2	52	132
3	50	132

end133.0ms (1%)

Remove: (sort a b)
Compiler: Compiled 487 to 298 computations (38.8% saved)

Details

analyze2.3s (17.2%)

sample8.3s (63.3%)

simplify21.0ms (0.2%)

prune4.0ms (0%)

localize14.0ms (0.1%)

series322.0ms (2.4%)

rewrite14.0ms (0.1%)

simplify127.0ms (1%)

prune194.0ms (1.5%)

localize12.0ms (0.1%)

series114.0ms (0.9%)

rewrite11.0ms (0.1%)

simplify93.0ms (0.7%)

prune86.0ms (0.7%)

localize5.0ms (0%)

series6.0ms (0%)

rewrite13.0ms (0.1%)

simplify118.0ms (0.9%)

prune32.0ms (0.2%)

localize8.0ms (0.1%)

series56.0ms (0.4%)

rewrite117.0ms (0.9%)

simplify271.0ms (2.1%)

prune464.0ms (3.5%)

regimes320.0ms (2.4%)

bsearch3.0ms (0%)

simplify4.0ms (0%)

end133.0ms (1%)

Profiling