Details

analyze2.5s (18.7%)

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)

sample8.1s (60.9%)

Symmetry

(sort a b)

Results

4.7s	4168×	body	2048	valid
1.8s	2509×	body	1024	valid
384.0ms	601×	body	1024	invalid
346.0ms	743×	body	512	valid
330.0ms	372×	body	2048	invalid
168.0ms	310×	body	512	invalid
130.0ms	567×	body	128	valid
85.0ms	255×	body	256	valid
45.0ms	275×	body	128	invalid
42.0ms	147×	body	256	invalid
25.0ms	14×	body	4096	valid

Compiler

Compiled 95 to 67 computations (29.5% 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

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

39.2b

Counts

3 → 1

Alt Table

Status	Error	Program
▶	39.2b	(/.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)

localize11.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(expm1.f64 (*.f64 eps a))
✓	0.1b	(.f64 (expm1.f64 (.f64 eps a)) (expm1.f64 (*.f64 eps b)))
✓	0.1b	(.f64 eps (expm1.f64 (.f64 eps (+.f64 a b))))
✓	37.5b	(/.f64 (.f64 eps (expm1.f64 (.f64 eps (+.f64 a b)))) (.f64 (expm1.f64 (.f64 eps a)) (expm1.f64 (*.f64 eps b))))

series321.0ms (2.4%)

Counts

4 → 132

Calls

4 calls:

262.0ms	(/.f64 (.f64 eps (expm1.f64 (.f64 eps (+.f64 a b)))) (.f64 (expm1.f64 (.f64 eps a)) (expm1.f64 (*.f64 eps b))))
28.0ms	(.f64 (expm1.f64 (.f64 eps a)) (expm1.f64 (*.f64 eps b)))
25.0ms	(.f64 eps (expm1.f64 (.f64 eps (+.f64 a b))))
6.0ms	(expm1.f64 (*.f64 eps a))

rewrite15.0ms (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 (.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))))
3.0ms	(.f64 (expm1.f64 (.f64 eps a)) (expm1.f64 (*.f64 eps b)))
0.0ms	(expm1.f64 (*.f64 eps a))

simplify120.0ms (0.9%)

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	613	8300
1	2021	7554
2	5057	7554

prune153.0ms (1.1%)

Pruning

5 alts after pruning (4 fresh and 1 done)

	Pruned	Kept	Total
New	209	4	213
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	209	5	214

Error

0.1b

Counts

214 → 5

Alt Table

Status	Error	Program
	59.1b	(/.f64 (.f64 eps (expm1.f64 (.f64 eps (+.f64 a b)))) (log.f64 (exp.f64 (.f64 (expm1.f64 (.f64 eps a)) (expm1.f64 (*.f64 eps b))))))
✓	39.2b	(/.f64 (.f64 eps (expm1.f64 (.f64 eps (+.f64 a b)))) (.f64 (expm1.f64 (.f64 eps a)) (expm1.f64 (*.f64 eps b))))
	58.6b	(-.f64 (+.f64 (/.f64 (.f64 (exp.f64 (.f64 b eps)) (pow.f64 eps 3)) (pow.f64 (.f64 eps (expm1.f64 (.f64 b eps))) 2)) (fma.f64 (/.f64 eps a) (/.f64 (exp.f64 (.f64 b eps)) (.f64 eps (expm1.f64 (.f64 b eps)))) (/.f64 (.f64 (.f64 eps eps) (exp.f64 (.f64 b eps))) (.f64 eps (expm1.f64 (.f64 b eps)))))) (fma.f64 1/2 (/.f64 (.f64 (pow.f64 eps 3) (pow.f64 (exp.f64 (.f64 b eps)) 2)) (pow.f64 (.f64 eps (expm1.f64 (.f64 b eps))) 2)) (fma.f64 1/2 (/.f64 (pow.f64 eps 3) (pow.f64 (.f64 eps (expm1.f64 (.f64 b eps))) 2)) (/.f64 eps (.f64 a (.f64 eps (expm1.f64 (*.f64 b eps))))))))
▶	8.1b	(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))))
	39.2b	(/.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 10748 to 3600 computations (66.5% saved)

localize11.0ms (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))
✓	5.1b	(.f64 b (.f64 eps eps))
✓	6.6b	(.f64 a (.f64 eps eps))

series58.0ms (0.4%)

Counts

4 → 120

Calls

4 calls:

21.0ms	(fma.f64 1/12 (.f64 b (.f64 eps eps)) (/.f64 1 a))
20.0ms	(+.f64 (/.f64 1 b) (fma.f64 1/12 (.f64 b (.f64 eps eps)) (/.f64 1 a)))
9.0ms	(.f64 b (.f64 eps eps))
8.0ms	(.f64 a (.f64 eps eps))

rewrite23.0ms (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:

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

simplify101.0ms (0.8%)

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

prune96.0ms (0.7%)

Pruning

6 alts after pruning (4 fresh and 2 done)

	Pruned	Kept	Total
New	130	1	131
Fresh	0	3	3
Picked	0	1	1
Done	0	1	1
Total	130	6	136

Error

0.1b

Counts

136 → 6

Alt Table

Status	Error	Program
	59.1b	(/.f64 (.f64 eps (expm1.f64 (.f64 eps (+.f64 a b)))) (log.f64 (exp.f64 (.f64 (expm1.f64 (.f64 eps a)) (expm1.f64 (*.f64 eps b))))))
▶	8.7b	(fma.f64 1/12 (.f64 a (.f64 eps eps)) (fma.f64 (/.f64 1 (.f64 (cbrt.f64 b) (cbrt.f64 b))) (/.f64 1 (cbrt.f64 b)) (fma.f64 1/12 (.f64 b (*.f64 eps eps)) (/.f64 1 a))))
✓	39.2b	(/.f64 (.f64 eps (expm1.f64 (.f64 eps (+.f64 a b)))) (.f64 (expm1.f64 (.f64 eps a)) (expm1.f64 (*.f64 eps b))))
	58.6b	(-.f64 (+.f64 (/.f64 (.f64 (exp.f64 (.f64 b eps)) (pow.f64 eps 3)) (pow.f64 (.f64 eps (expm1.f64 (.f64 b eps))) 2)) (fma.f64 (/.f64 eps a) (/.f64 (exp.f64 (.f64 b eps)) (.f64 eps (expm1.f64 (.f64 b eps)))) (/.f64 (.f64 (.f64 eps eps) (exp.f64 (.f64 b eps))) (.f64 eps (expm1.f64 (.f64 b eps)))))) (fma.f64 1/2 (/.f64 (.f64 (pow.f64 eps 3) (pow.f64 (exp.f64 (.f64 b eps)) 2)) (pow.f64 (.f64 eps (expm1.f64 (.f64 b eps))) 2)) (fma.f64 1/2 (/.f64 (pow.f64 eps 3) (pow.f64 (.f64 eps (expm1.f64 (.f64 b eps))) 2)) (/.f64 eps (.f64 a (.f64 eps (expm1.f64 (*.f64 b eps))))))))
✓	8.1b	(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))))
	39.2b	(/.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 3914 to 1851 computations (52.7% saved)

localize20.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.5b	(*.f64 (cbrt.f64 b) (cbrt.f64 b))
✓	0.6b	(cbrt.f64 b)
	5.1b	(.f64 b (.f64 eps eps))
	6.6b	(.f64 a (.f64 eps eps))

series74.0ms (0.6%)

Counts

2 → 24

Calls

2 calls:

37.0ms	(cbrt.f64 b)
37.0ms	(*.f64 (cbrt.f64 b) (cbrt.f64 b))

rewrite7.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

19×	`add-sqr-sqrt_binary64`
19×	`cbrt-prod_binary64`
11×	`*-un-lft-identity_binary64`
11×	`add-cube-cbrt_binary64`
9×	`pow1_binary64`

Counts

2 → 55

Calls

2 calls:

4.0ms	(*.f64 (cbrt.f64 b) (cbrt.f64 b))
1.0ms	(cbrt.f64 b)

simplify64.0ms (0.5%)

Algorithm

1×	egg-herbie

Rules

577×	`distribute-rgt-in_binary64`
561×	`log-prod_binary64`
538×	`distribute-lft-in_binary64`
525×	`unswap-sqr_binary64`
384×	`fma-def_binary64`

Counts

79 → 74

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	58	610
1	98	554
2	296	516
3	769	502
4	1799	410
5	4642	410
6	4805	410

prune146.0ms (1.1%)

Pruning

6 alts after pruning (3 fresh and 3 done)

	Pruned	Kept	Total
New	174	0	174
Fresh	0	3	3
Picked	0	1	1
Done	0	2	2
Total	174	6	180

Error

0.1b

Counts

180 → 6

Alt Table

Status	Error	Program
	59.1b	(/.f64 (.f64 eps (expm1.f64 (.f64 eps (+.f64 a b)))) (log.f64 (exp.f64 (.f64 (expm1.f64 (.f64 eps a)) (expm1.f64 (*.f64 eps b))))))
✓	8.7b	(fma.f64 1/12 (.f64 a (.f64 eps eps)) (fma.f64 (/.f64 1 (.f64 (cbrt.f64 b) (cbrt.f64 b))) (/.f64 1 (cbrt.f64 b)) (fma.f64 1/12 (.f64 b (*.f64 eps eps)) (/.f64 1 a))))
✓	39.2b	(/.f64 (.f64 eps (expm1.f64 (.f64 eps (+.f64 a b)))) (.f64 (expm1.f64 (.f64 eps a)) (expm1.f64 (*.f64 eps b))))
	58.6b	(-.f64 (+.f64 (/.f64 (.f64 (exp.f64 (.f64 b eps)) (pow.f64 eps 3)) (pow.f64 (.f64 eps (expm1.f64 (.f64 b eps))) 2)) (fma.f64 (/.f64 eps a) (/.f64 (exp.f64 (.f64 b eps)) (.f64 eps (expm1.f64 (.f64 b eps)))) (/.f64 (.f64 (.f64 eps eps) (exp.f64 (.f64 b eps))) (.f64 eps (expm1.f64 (.f64 b eps)))))) (fma.f64 1/2 (/.f64 (.f64 (pow.f64 eps 3) (pow.f64 (exp.f64 (.f64 b eps)) 2)) (pow.f64 (.f64 eps (expm1.f64 (.f64 b eps))) 2)) (fma.f64 1/2 (/.f64 (pow.f64 eps 3) (pow.f64 (.f64 eps (expm1.f64 (.f64 b eps))) 2)) (/.f64 eps (.f64 a (.f64 eps (expm1.f64 (*.f64 b eps))))))))
✓	8.1b	(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))))
▶	39.2b	(/.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 6155 to 2556 computations (58.5% saved)

localize13.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(/.f64 1 (/.f64 (.f64 (expm1.f64 (.f64 eps a)) (expm1.f64 (.f64 eps b))) (.f64 eps (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))))
✓	37.8b	(/.f64 (.f64 (expm1.f64 (.f64 eps a)) (expm1.f64 (.f64 eps b))) (.f64 eps (expm1.f64 (*.f64 eps (+.f64 a b)))))

series492.0ms (3.7%)

Counts

2 → 72

Calls

2 calls:

270.0ms

(/.f64 1 (/.f64 (*.f64 (expm1.f64 (*.f64 eps a)) (expm1.f64 (*.f64 eps b))) (*.f64 eps (expm1.f64 (*.f64 eps (+.f64 a b))))))

222.0ms

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

rewrite18.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

58×	`add-exp-log_binary64`
32×	`add-cbrt-cube_binary64`
26×	`div-exp_binary64`
20×	`times-frac_binary64`
16×	`prod-exp_binary64`

Counts

2 → 81

Calls

2 calls:

5.0ms

(/.f64 1 (/.f64 (*.f64 (expm1.f64 (*.f64 eps a)) (expm1.f64 (*.f64 eps b))) (*.f64 eps (expm1.f64 (*.f64 eps (+.f64 a b))))))

4.0ms

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

simplify161.0ms (1.2%)

Algorithm

1×	egg-herbie

Rules

657×	`associate-/r*_binary64`
600×	`fma-def_binary64`
305×	`*-commutative_binary64`
213×	`+-commutative_binary64`
187×	`associate-/r/_binary64`

Counts

153 → 176

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	842	11743
1	2782	10959
2	5482	10959

prune261.0ms (2%)

Pruning

6 alts after pruning (2 fresh and 4 done)

	Pruned	Kept	Total
New	296	0	296
Fresh	0	2	2
Picked	0	1	1
Done	0	3	3
Total	296	6	302

Error

0.1b

Counts

302 → 6

Alt Table

Status	Error	Program
	59.1b	(/.f64 (.f64 eps (expm1.f64 (.f64 eps (+.f64 a b)))) (log.f64 (exp.f64 (.f64 (expm1.f64 (.f64 eps a)) (expm1.f64 (*.f64 eps b))))))
✓	8.7b	(fma.f64 1/12 (.f64 a (.f64 eps eps)) (fma.f64 (/.f64 1 (.f64 (cbrt.f64 b) (cbrt.f64 b))) (/.f64 1 (cbrt.f64 b)) (fma.f64 1/12 (.f64 b (*.f64 eps eps)) (/.f64 1 a))))
✓	39.2b	(/.f64 (.f64 eps (expm1.f64 (.f64 eps (+.f64 a b)))) (.f64 (expm1.f64 (.f64 eps a)) (expm1.f64 (*.f64 eps b))))
	58.6b	(-.f64 (+.f64 (/.f64 (.f64 (exp.f64 (.f64 b eps)) (pow.f64 eps 3)) (pow.f64 (.f64 eps (expm1.f64 (.f64 b eps))) 2)) (fma.f64 (/.f64 eps a) (/.f64 (exp.f64 (.f64 b eps)) (.f64 eps (expm1.f64 (.f64 b eps)))) (/.f64 (.f64 (.f64 eps eps) (exp.f64 (.f64 b eps))) (.f64 eps (expm1.f64 (.f64 b eps)))))) (fma.f64 1/2 (/.f64 (.f64 (pow.f64 eps 3) (pow.f64 (exp.f64 (.f64 b eps)) 2)) (pow.f64 (.f64 eps (expm1.f64 (.f64 b eps))) 2)) (fma.f64 1/2 (/.f64 (pow.f64 eps 3) (pow.f64 (.f64 eps (expm1.f64 (.f64 b eps))) 2)) (/.f64 eps (.f64 a (.f64 eps (expm1.f64 (*.f64 b eps))))))))
✓	8.1b	(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))))
✓	39.2b	(/.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 18115 to 6788 computations (62.5% saved)

regimes374.0ms (2.8%)

Accuracy

Total 1.3b remaining (97.5%)

Threshold costs 0b (0%)

Counts

60 → 3

Compiler

Compiled 5998 to 3608 computations (39.8% saved)

bsearch2.0ms (0%)

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

simplify4.0ms (0%)

Algorithm

1×	egg-herbie

Rules

9×	`*-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	40	137
1	60	137
2	63	137
3	61	137

end150.0ms (1.1%)

Remove: (sort a b)
Compiler: Compiled 588 to 325 computations (44.7% saved)

Details

analyze2.5s (18.7%)

sample8.1s (60.9%)

simplify22.0ms (0.2%)

prune5.0ms (0%)

localize11.0ms (0.1%)

series321.0ms (2.4%)

rewrite15.0ms (0.1%)

simplify120.0ms (0.9%)

prune153.0ms (1.1%)

localize11.0ms (0.1%)

series58.0ms (0.4%)

rewrite23.0ms (0.2%)

simplify101.0ms (0.8%)

prune96.0ms (0.7%)

localize20.0ms (0.2%)

series74.0ms (0.6%)

rewrite7.0ms (0.1%)

simplify64.0ms (0.5%)

prune146.0ms (1.1%)

localize13.0ms (0.1%)

series492.0ms (3.7%)

rewrite18.0ms (0.1%)

simplify161.0ms (1.2%)

prune261.0ms (2%)

regimes374.0ms (2.8%)

bsearch2.0ms (0%)

simplify4.0ms (0%)

end150.0ms (1.1%)

Profiling