Details

analyze2.2s (17.7%)

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)

sample8.0s (65.3%)

Symmetry

(sort a b)

Results

4.8s	4288×	body	2048	valid
1.6s	2396×	body	1024	valid
417.0ms	647×	body	1024	invalid
355.0ms	754×	body	512	valid
342.0ms	420×	body	2048	invalid
118.0ms	298×	body	512	invalid
99.0ms	560×	body	128	valid
78.0ms	245×	body	256	valid
50.0ms	322×	body	128	invalid
45.0ms	138×	body	256	invalid
20.0ms	13×	body	4096	valid
3.0ms	1×	body	8192	exit

Compiler

Compiled 95 to 67 computations (29.5% saved)

simplify16.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

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

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	18	28
1	47	28
2	108	28
3	271	28
4	989	28

Stop Event

1×	node limit

Counts

1 → 2

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

30.4b

Counts

3 → 1

Alt Table

Status	Error	Program
▶	30.4b	(.f64 eps (/.f64 (/.f64 (expm1.f64 (.f64 eps (+.f64 a b))) (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 (+.f64 a b)))
✓	1.1b	(/.f64 (/.f64 (expm1.f64 (.f64 eps (+.f64 a b))) (expm1.f64 (.f64 eps a))) (expm1.f64 (*.f64 eps b)))
✓	12.7b	(/.f64 (expm1.f64 (.f64 eps (+.f64 a b))) (expm1.f64 (.f64 eps a)))
✓	27.5b	(.f64 eps (/.f64 (/.f64 (expm1.f64 (.f64 eps (+.f64 a b))) (expm1.f64 (.f64 eps a))) (expm1.f64 (.f64 eps b))))

series349.0ms (2.8%)

Counts

4 → 144

Calls

4 calls:

168.0ms	(.f64 eps (/.f64 (/.f64 (expm1.f64 (.f64 eps (+.f64 a b))) (expm1.f64 (.f64 eps a))) (expm1.f64 (.f64 eps b))))
131.0ms	(/.f64 (/.f64 (expm1.f64 (.f64 eps (+.f64 a b))) (expm1.f64 (.f64 eps a))) (expm1.f64 (*.f64 eps b)))
38.0ms	(/.f64 (expm1.f64 (.f64 eps (+.f64 a b))) (expm1.f64 (.f64 eps a)))
11.0ms	(expm1.f64 (*.f64 eps (+.f64 a b)))

rewrite80.0ms (0.6%)

Algorithm

1×	batch-egg-rewrite

Rules

898×	`prod-diff_binary64`
151×	`add-sqr-sqrt_binary64`
143×	`log1p-expm1-u_binary64`
143×	`expm1-log1p-u_binary64`
139×	`add-cbrt-cube_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	14	79
1	300	79
2	4272	79

Stop Event

1×	node limit

Counts

4 → 121

Calls

4 calls:

77.0ms	(expm1.f64 (*.f64 eps (+.f64 a b)))
77.0ms	(/.f64 (/.f64 (expm1.f64 (.f64 eps (+.f64 a b))) (expm1.f64 (.f64 eps a))) (expm1.f64 (*.f64 eps b)))
77.0ms	(/.f64 (expm1.f64 (.f64 eps (+.f64 a b))) (expm1.f64 (.f64 eps a)))
77.0ms	(.f64 eps (/.f64 (/.f64 (expm1.f64 (.f64 eps (+.f64 a b))) (expm1.f64 (.f64 eps a))) (expm1.f64 (.f64 eps b))))

simplify112.0ms (0.9%)

Algorithm

1×	egg-herbie

Rules

834×	`fma-def_binary64`
684×	`times-frac_binary64`
614×	`associate-/l*_binary64`
260×	`*-commutative_binary64`
242×	`+-commutative_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	718	9708
1	2546	9052

Stop Event

1×	node limit

Counts

265 → 224

prune195.0ms (1.6%)

Pruning

5 alts after pruning (5 fresh and 0 done)

	Pruned	Kept	Total
New	219	5	224
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	220	5	225

Error

0.2b

Counts

225 → 5

Alt Table

Status	Error	Program
	29.0b	(/.f64 eps (.f64 (expm1.f64 (.f64 eps b)) (/.f64 (expm1.f64 (.f64 eps a)) (expm1.f64 (.f64 eps (+.f64 a b))))))
▶	7.0b	(+.f64 (fma.f64 1/12 (.f64 a (.f64 eps eps)) (/.f64 1 b)) (fma.f64 1/12 (.f64 b (.f64 eps eps)) (/.f64 1 a)))
	57.6b	(.f64 eps (pow.f64 (pow.f64 (/.f64 (expm1.f64 (.f64 eps (+.f64 a b))) (.f64 (expm1.f64 (.f64 eps a)) (expm1.f64 (*.f64 eps b)))) 3) 1/3))
	15.4b	(/.f64 (+.f64 a b) (*.f64 a b))
	37.1b	(.f64 eps (+.f64 (fma.f64 1/12 (.f64 b eps) (/.f64 1 (.f64 a eps))) (fma.f64 1/12 (.f64 a eps) (/.f64 1 (*.f64 b eps)))))

Compiler

Compiled 13825 to 5080 computations (63.3% saved)

localize11.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(fma.f64 1/12 (.f64 b (.f64 eps eps)) (/.f64 1 a))
✓	0.0b	(fma.f64 1/12 (.f64 a (.f64 eps eps)) (/.f64 1 b))
✓	5.7b	(.f64 b (.f64 eps eps))
✓	9.0b	(.f64 a (.f64 eps eps))

series55.0ms (0.5%)

Counts

4 → 120

Calls

4 calls:

21.0ms	(fma.f64 1/12 (.f64 b (.f64 eps eps)) (/.f64 1 a))
16.0ms	(fma.f64 1/12 (.f64 a (.f64 eps eps)) (/.f64 1 b))
12.0ms	(.f64 b (.f64 eps eps))
7.0ms	(.f64 a (.f64 eps eps))

rewrite53.0ms (0.4%)

Algorithm

1×	batch-egg-rewrite

Rules

625×	`log-prod_binary64`
227×	`expm1-udef_binary64`
227×	`log1p-udef_binary64`
209×	`log-pow_binary64`
188×	`prod-diff_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	13	42
1	267	42
2	3209	42

Stop Event

1×	node limit

Counts

4 → 94

Calls

4 calls:

52.0ms	(fma.f64 1/12 (.f64 b (.f64 eps eps)) (/.f64 1 a))
52.0ms	(fma.f64 1/12 (.f64 a (.f64 eps eps)) (/.f64 1 b))
52.0ms	(.f64 b (.f64 eps eps))
52.0ms	(.f64 a (.f64 eps eps))

simplify124.0ms (1%)

Algorithm

1×	egg-herbie

Rules

603×	`sqr-pow_binary64`
417×	`associate-l_binary64`
359×	`*-commutative_binary64`
326×	`fabs-mul_binary64`
312×	`cube-prod_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	16	1290
1	32	1236
2	65	1236
3	147	1236
4	384	1236
5	1224	1236
6	1649	1236
7	2071	1236
8	2171	1236
9	2317	1236
10	2491	1236
11	2738	1236
12	3059	1236
13	3433	1236
14	3887	1236
15	4468	1236

Stop Event

1×	node limit

Counts

214 → 108

prune93.0ms (0.8%)

Pruning

5 alts after pruning (5 fresh and 0 done)

	Pruned	Kept	Total
New	107	1	108
Fresh	0	4	4
Picked	1	0	1
Done	0	0	0
Total	108	5	113

Error

0.2b

Counts

113 → 5

Alt Table

Status	Error	Program
▶	7.4b	(+.f64 (fma.f64 1/12 (.f64 eps (.f64 eps a)) (/.f64 1 b)) (fma.f64 1/12 (.f64 b (.f64 eps eps)) (/.f64 1 a)))
	29.0b	(/.f64 eps (.f64 (expm1.f64 (.f64 eps b)) (/.f64 (expm1.f64 (.f64 eps a)) (expm1.f64 (.f64 eps (+.f64 a b))))))
	57.6b	(.f64 eps (pow.f64 (pow.f64 (/.f64 (expm1.f64 (.f64 eps (+.f64 a b))) (.f64 (expm1.f64 (.f64 eps a)) (expm1.f64 (*.f64 eps b)))) 3) 1/3))
	15.4b	(/.f64 (+.f64 a b) (*.f64 a b))
	37.1b	(.f64 eps (+.f64 (fma.f64 1/12 (.f64 b eps) (/.f64 1 (.f64 a eps))) (fma.f64 1/12 (.f64 a eps) (/.f64 1 (*.f64 b eps)))))

Compiler

Compiled 3043 to 1588 computations (47.8% saved)

localize12.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.0b	(fma.f64 1/12 (.f64 b (.f64 eps eps)) (/.f64 1 a))
✓	0.0b	(fma.f64 1/12 (.f64 eps (.f64 eps a)) (/.f64 1 b))
✓	0.1b	(.f64 eps (.f64 eps a))
	5.7b	(.f64 b (.f64 eps eps))

series24.0ms (0.2%)

Counts

2 → 60

Calls

2 calls:

17.0ms	(fma.f64 1/12 (.f64 eps (.f64 eps a)) (/.f64 1 b))
7.0ms	(.f64 eps (.f64 eps a))

rewrite38.0ms (0.3%)

Algorithm

1×	batch-egg-rewrite

Rules

822×	`log1p-expm1-u_binary64`
822×	`expm1-log1p-u_binary64`
97×	`add-sqr-sqrt_binary64`
94×	`prod-diff_binary64`
89×	`add-cbrt-cube_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	10	21
1	199	21
2	2294	21

Stop Event

1×	node limit

Counts

2 → 38

Calls

2 calls:

38.0ms	(fma.f64 1/12 (.f64 eps (.f64 eps a)) (/.f64 1 b))
38.0ms	(.f64 eps (.f64 eps a))

simplify89.0ms (0.7%)

Algorithm

1×	egg-herbie

Rules

775×	`sqr-pow_binary64`
398×	`fabs-mul_binary64`
386×	`cube-prod_binary64`
381×	`pow-sqr_binary64`
253×	`*-commutative_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	12	618
1	24	618
2	44	618
3	94	618
4	237	618
5	721	618
6	1021	618
7	1439	618
8	1539	618
9	1674	618
10	1846	618
11	2087	618
12	2402	618
13	2774	618
14	3228	618
15	3803	618
16	4511	618

Stop Event

1×	node limit

Counts

98 → 45

prune78.0ms (0.6%)

Pruning

5 alts after pruning (4 fresh and 1 done)

	Pruned	Kept	Total
New	99	0	99
Fresh	0	4	4
Picked	0	1	1
Done	0	0	0
Total	99	5	104

Error

0.2b

Counts

104 → 5

Alt Table

Status	Error	Program
✓	7.4b	(+.f64 (fma.f64 1/12 (.f64 eps (.f64 eps a)) (/.f64 1 b)) (fma.f64 1/12 (.f64 b (.f64 eps eps)) (/.f64 1 a)))
	29.0b	(/.f64 eps (.f64 (expm1.f64 (.f64 eps b)) (/.f64 (expm1.f64 (.f64 eps a)) (expm1.f64 (.f64 eps (+.f64 a b))))))
	57.6b	(.f64 eps (pow.f64 (pow.f64 (/.f64 (expm1.f64 (.f64 eps (+.f64 a b))) (.f64 (expm1.f64 (.f64 eps a)) (expm1.f64 (*.f64 eps b)))) 3) 1/3))
▶	15.4b	(/.f64 (+.f64 a b) (*.f64 a b))
	37.1b	(.f64 eps (+.f64 (fma.f64 1/12 (.f64 b eps) (/.f64 1 (.f64 a eps))) (fma.f64 1/12 (.f64 a eps) (/.f64 1 (*.f64 b eps)))))

Compiler

Compiled 2732 to 1399 computations (48.8% saved)

localize4.0ms (0%)

Local error

Found 1 expressions with local error:

New	Error	Program
✓	15.5b	(/.f64 (+.f64 a b) (*.f64 a b))

series7.0ms (0.1%)

Counts

1 → 24

Calls

1 calls:

7.0ms

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

rewrite42.0ms (0.3%)

Algorithm

1×	batch-egg-rewrite

Rules

816×	`log1p-expm1-u_binary64`
816×	`expm1-log1p-u_binary64`
601×	`prod-diff_binary64`
71×	`add-sqr-sqrt_binary64`
67×	`add-cbrt-cube_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	6	10
1	136	10
2	2126	10

Stop Event

1×	node limit

Counts

1 → 40

Calls

1 calls:

41.0ms

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

simplify8.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

1×	`+-commutative_binary64`
1×	`1-exp_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	7	204
1	10	204

Stop Event

1×

saturated

Counts

64 → 44

prune33.0ms (0.3%)

Pruning

6 alts after pruning (4 fresh and 2 done)

	Pruned	Kept	Total
New	42	2	44
Fresh	1	2	3
Picked	0	1	1
Done	0	1	1
Total	43	6	49

Error

0.2b

Counts

49 → 6

Alt Table

Status	Error	Program
	29.0b	(/.f64 eps (.f64 (expm1.f64 (.f64 eps b)) (/.f64 (expm1.f64 (.f64 eps a)) (expm1.f64 (.f64 eps (+.f64 a b))))))
	10.9b	(*.f64 (/.f64 (pow.f64 (cbrt.f64 (+.f64 a b)) 2) b) (/.f64 (cbrt.f64 (+.f64 a b)) a))
✓	7.4b	(+.f64 (fma.f64 1/12 (.f64 eps (.f64 eps a)) (/.f64 1 b)) (fma.f64 1/12 (.f64 b (.f64 eps eps)) (/.f64 1 a)))
	6.5b	(*.f64 (/.f64 (+.f64 a b) a) (/.f64 1 b))
	57.6b	(.f64 eps (pow.f64 (pow.f64 (/.f64 (expm1.f64 (.f64 eps (+.f64 a b))) (.f64 (expm1.f64 (.f64 eps a)) (expm1.f64 (*.f64 eps b)))) 3) 1/3))
✓	15.4b	(/.f64 (+.f64 a b) (*.f64 a b))

Compiler

Compiled 637 to 236 computations (63% saved)

regimes412.0ms (3.3%)

Accuracy

Total 2.6b remaining (99.1%)

Threshold costs 0b (0%)

Counts

99 → 2

Compiler

Compiled 8230 to 5088 computations (38.2% saved)

bsearch4.0ms (0%)

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

simplify3.0ms (0%)

Algorithm

1×	egg-herbie

Rules

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

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	35	83
1	51	83
2	54	83

Stop Event

1×

saturated

end236.0ms (1.9%)

Compiler: Compiled 338 to 210 computations (37.9% saved)

Details

analyze2.2s (17.7%)

sample8.0s (65.3%)

simplify16.0ms (0.1%)

prune4.0ms (0%)

localize11.0ms (0.1%)

series349.0ms (2.8%)

rewrite80.0ms (0.6%)

simplify112.0ms (0.9%)

prune195.0ms (1.6%)

localize11.0ms (0.1%)

series55.0ms (0.5%)

rewrite53.0ms (0.4%)

simplify124.0ms (1%)

prune93.0ms (0.8%)

localize12.0ms (0.1%)

series24.0ms (0.2%)

rewrite38.0ms (0.3%)

simplify89.0ms (0.7%)

prune78.0ms (0.6%)

localize4.0ms (0%)

series7.0ms (0.1%)

rewrite42.0ms (0.3%)

simplify8.0ms (0.1%)

prune33.0ms (0.3%)

regimes412.0ms (3.3%)

bsearch4.0ms (0%)

simplify3.0ms (0%)

end236.0ms (1.9%)

Profiling