Details

analyze46.0ms (1.1%)

Algorithm

1×

Search

True	Other	False	Iter
0%	99.9%	0.1%	0
0%	99.9%	0.1%	1
0%	99.9%	0.1%	2
25%	74.9%	0.1%	3
62.4%	37.5%	0.1%	4
68.7%	31.2%	0.1%	5
68.7%	18.7%	12.6%	6
68.7%	17.2%	14.1%	7
68.7%	10.1%	21.2%	8
68.7%	9%	22.3%	9
68.7%	5.3%	26%	10
68.7%	4.6%	26.7%	11
68.7%	2.7%	28.6%	12
68.7%	2.3%	29%	13
68.7%	1.4%	30%	14

Compiler

Compiled 11 to 7 computations (36.4% saved)

sample818.0ms (19%)

Results

780.0ms	8256×	body	128	valid
4.0ms	25×	body	128	invalid

Compiler

Compiled 32 to 20 computations (37.5% saved)

simplify6.0ms (0.2%)

Algorithm

1×	egg-herbie

Rules

1×	`+-commutative_binary64`

Counts

1 → 1

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	7	13
1	8	13
2	8	13

prune2.0ms (0%)

Pruning

2 alts after pruning (2 fresh and 0 done)

	Kept	Total
New	1	1
Fresh	1	1
Picked	0	0
Done	0	0
Total	2	2

Error

0.8b

Counts

2 → 1

Alt Table

Status	Error	Program
▶	0.8b	(/.f64 (exp.f64 a) (+.f64 (exp.f64 a) (exp.f64 b)))

Compiler

Compiled 30 to 18 computations (40% saved)

localize5.0ms (0.1%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.0b	(+.f64 (exp.f64 a) (exp.f64 b))
✓	0.8b	(/.f64 (exp.f64 a) (+.f64 (exp.f64 a) (exp.f64 b)))

series34.0ms (0.8%)

Counts

2 → 48

Calls

2 calls:

30.0ms	(/.f64 (exp.f64 a) (+.f64 (exp.f64 a) (exp.f64 b)))
4.0ms	(+.f64 (exp.f64 a) (exp.f64 b))

rewrite165.0ms (3.8%)

Algorithm

2×	egg-rewrite

Rules

45×	`egg`
40×	`egg`

Counts

2 → 85

Calls

2 calls:

107.0ms	(+.f64 (exp.f64 a) (exp.f64 b))
56.0ms	(/.f64 (exp.f64 a) (+.f64 (exp.f64 a) (exp.f64 b)))

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	7	13
1	147	13
2	1998	13
3	5794	13
0	6	8
1	121	8
2	1530	8
3	4841	8
4	4780	8
5	4971	8

simplify52.0ms (1.2%)

Algorithm

1×	egg-herbie

Rules

475×	`times-frac_binary64`
464×	`associate-+l+_binary64`
426×	`fma-def_binary64`
303×	`associate-/l*_binary64`
240×	`associate--l+_binary64`

Counts

133 → 112

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	103	1020
1	302	981
2	1070	965
3	5042	965

prune123.0ms (2.9%)

Pruning

4 alts after pruning (4 fresh and 0 done)

	Pruned	Kept	Total
New	108	4	112
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	109	4	113

Error

Counts

113 → 4

Alt Table

Status	Error	Program
▶	0.8b	(/.f64 (exp.f64 a) (fma.f64 (sqrt.f64 (exp.f64 b)) (sqrt.f64 (exp.f64 b)) (exp.f64 a)))
	0.8b	(expm1.f64 (log1p.f64 (/.f64 (exp.f64 a) (+.f64 (exp.f64 a) (exp.f64 b)))))
	12.4b	(/.f64 1 (+.f64 1 (exp.f64 b)))
	24.9b	(+.f64 (/.f64 (exp.f64 a) (+.f64 1 (exp.f64 a))) (-.f64 (.f64 (exp.f64 a) (+.f64 (/.f64 (.f64 b b) (pow.f64 (+.f64 1 (exp.f64 a)) 3)) (/.f64 (pow.f64 b 3) (pow.f64 (+.f64 1 (exp.f64 a)) 3)))) (fma.f64 1/6 (/.f64 (.f64 (exp.f64 a) (pow.f64 b 3)) (pow.f64 (+.f64 1 (exp.f64 a)) 2)) (fma.f64 1/2 (.f64 (/.f64 (.f64 b (exp.f64 a)) (pow.f64 (+.f64 1 (exp.f64 a)) 2)) b) (.f64 (exp.f64 a) (+.f64 (/.f64 b (pow.f64 (+.f64 1 (exp.f64 a)) 2)) (/.f64 (pow.f64 b 3) (pow.f64 (+.f64 1 (exp.f64 a)) 4))))))))

Compiler

Compiled 2353 to 1070 computations (54.5% saved)

localize6.0ms (0.2%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.0b	(sqrt.f64 (exp.f64 b))
✓	0.0b	(fma.f64 (sqrt.f64 (exp.f64 b)) (sqrt.f64 (exp.f64 b)) (exp.f64 a))
✓	0.8b	(/.f64 (exp.f64 a) (fma.f64 (sqrt.f64 (exp.f64 b)) (sqrt.f64 (exp.f64 b)) (exp.f64 a)))

series50.0ms (1.2%)

Counts

3 → 52

Calls

3 calls:

36.0ms	(/.f64 (exp.f64 a) (fma.f64 (sqrt.f64 (exp.f64 b)) (sqrt.f64 (exp.f64 b)) (exp.f64 a)))
11.0ms	(fma.f64 (sqrt.f64 (exp.f64 b)) (sqrt.f64 (exp.f64 b)) (exp.f64 a))
3.0ms	(sqrt.f64 (exp.f64 b))

rewrite178.0ms (4.1%)

Algorithm

3×	egg-rewrite

Rules

53×	`egg`
45×	`egg`
40×	`egg`

Counts

3 → 138

Calls

3 calls:

81.0ms	(sqrt.f64 (exp.f64 b))
48.0ms	(/.f64 (exp.f64 a) (fma.f64 (sqrt.f64 (exp.f64 b)) (sqrt.f64 (exp.f64 b)) (exp.f64 a)))
46.0ms	(fma.f64 (sqrt.f64 (exp.f64 b)) (sqrt.f64 (exp.f64 b)) (exp.f64 a))

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	8	13
1	155	13
2	1868	13
3	5057	13
0	7	8
1	129	8
2	1411	8
3	5279	8
0	4	5
1	74	5
2	798	5
3	4858	5
4	5574	5

simplify56.0ms (1.3%)

Algorithm

1×	egg-herbie

Rules

498×	`fma-def_binary64`
490×	`associate-+l+_binary64`
475×	`times-frac_binary64`
303×	`associate-/l*_binary64`
240×	`associate--l+_binary64`

Counts

190 → 170

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	114	1063
1	328	1022
2	1142	1003
3	5252	1003

prune191.0ms (4.5%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	217	0	217
Fresh	0	3	3
Picked	0	1	1
Done	0	0	0
Total	217	4	221

Error

Counts

221 → 4

Alt Table

Status	Error	Program
✓	0.8b	(/.f64 (exp.f64 a) (fma.f64 (sqrt.f64 (exp.f64 b)) (sqrt.f64 (exp.f64 b)) (exp.f64 a)))
▶	0.8b	(expm1.f64 (log1p.f64 (/.f64 (exp.f64 a) (+.f64 (exp.f64 a) (exp.f64 b)))))
	12.4b	(/.f64 1 (+.f64 1 (exp.f64 b)))
	24.9b	(+.f64 (/.f64 (exp.f64 a) (+.f64 1 (exp.f64 a))) (-.f64 (.f64 (exp.f64 a) (+.f64 (/.f64 (.f64 b b) (pow.f64 (+.f64 1 (exp.f64 a)) 3)) (/.f64 (pow.f64 b 3) (pow.f64 (+.f64 1 (exp.f64 a)) 3)))) (fma.f64 1/6 (/.f64 (.f64 (exp.f64 a) (pow.f64 b 3)) (pow.f64 (+.f64 1 (exp.f64 a)) 2)) (fma.f64 1/2 (.f64 (/.f64 (.f64 b (exp.f64 a)) (pow.f64 (+.f64 1 (exp.f64 a)) 2)) b) (.f64 (exp.f64 a) (+.f64 (/.f64 b (pow.f64 (+.f64 1 (exp.f64 a)) 2)) (/.f64 (pow.f64 b 3) (pow.f64 (+.f64 1 (exp.f64 a)) 4))))))))

Compiler

Compiled 4036 to 1718 computations (57.4% saved)

localize7.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(log1p.f64 (/.f64 (exp.f64 a) (+.f64 (exp.f64 a) (exp.f64 b))))
	0.0b	(+.f64 (exp.f64 a) (exp.f64 b))
✓	0.0b	(expm1.f64 (log1p.f64 (/.f64 (exp.f64 a) (+.f64 (exp.f64 a) (exp.f64 b)))))
	0.8b	(/.f64 (exp.f64 a) (+.f64 (exp.f64 a) (exp.f64 b)))

series680.0ms (15.8%)

Counts

2 → 48

Calls

2 calls:

650.0ms	(log1p.f64 (/.f64 (exp.f64 a) (+.f64 (exp.f64 a) (exp.f64 b))))
30.0ms	(expm1.f64 (log1p.f64 (/.f64 (exp.f64 a) (+.f64 (exp.f64 a) (exp.f64 b)))))

rewrite109.0ms (2.5%)

Algorithm

2×	egg-rewrite

Rules

49×	`egg`
16×	`egg`

Counts

2 → 65

Calls

2 calls:

56.0ms	(expm1.f64 (log1p.f64 (/.f64 (exp.f64 a) (+.f64 (exp.f64 a) (exp.f64 b)))))
51.0ms	(log1p.f64 (/.f64 (exp.f64 a) (+.f64 (exp.f64 a) (exp.f64 b))))

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	9	13
1	166	13
2	2188	13
3	5058	13
0	8	15
1	165	15
2	2175	15
3	5029	15

simplify95.0ms (2.2%)

Algorithm

1×	egg-herbie

Rules

357×	`times-frac_binary64`
337×	`cancel-sign-sub-inv_binary64`
229×	`associate-/r*_binary64`
223×	`unswap-sqr_binary64`
211×	`associate-/l*_binary64`

Counts

113 → 96

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	229	2778
1	754	2674
2	3642	2499
3	4991	2499

prune214.0ms (5%)

Pruning

4 alts after pruning (2 fresh and 2 done)

	Pruned	Kept	Total
New	207	1	208
Fresh	1	1	2
Picked	0	1	1
Done	0	1	1
Total	208	4	212

Error

Counts

212 → 4

Alt Table

Status	Error	Program
✓	0.8b	(/.f64 (exp.f64 a) (fma.f64 (sqrt.f64 (exp.f64 b)) (sqrt.f64 (exp.f64 b)) (exp.f64 a)))
✓	0.8b	(expm1.f64 (log1p.f64 (/.f64 (exp.f64 a) (+.f64 (exp.f64 a) (exp.f64 b)))))
▶	12.4b	(expm1.f64 (log1p.f64 (/.f64 1 (+.f64 1 (exp.f64 b)))))
	24.9b	(+.f64 (/.f64 (exp.f64 a) (+.f64 1 (exp.f64 a))) (-.f64 (.f64 (exp.f64 a) (+.f64 (/.f64 (.f64 b b) (pow.f64 (+.f64 1 (exp.f64 a)) 3)) (/.f64 (pow.f64 b 3) (pow.f64 (+.f64 1 (exp.f64 a)) 3)))) (fma.f64 1/6 (/.f64 (.f64 (exp.f64 a) (pow.f64 b 3)) (pow.f64 (+.f64 1 (exp.f64 a)) 2)) (fma.f64 1/2 (.f64 (/.f64 (.f64 b (exp.f64 a)) (pow.f64 (+.f64 1 (exp.f64 a)) 2)) b) (.f64 (exp.f64 a) (+.f64 (/.f64 b (pow.f64 (+.f64 1 (exp.f64 a)) 2)) (/.f64 (pow.f64 b 3) (pow.f64 (+.f64 1 (exp.f64 a)) 4))))))))

Compiler

Compiled 6481 to 3463 computations (46.6% saved)

localize11.0ms (0.3%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(log1p.f64 (/.f64 1 (+.f64 1 (exp.f64 b))))
✓	0.0b	(expm1.f64 (log1p.f64 (/.f64 1 (+.f64 1 (exp.f64 b)))))
✓	0.0b	(+.f64 1 (exp.f64 b))
✓	0.0b	(/.f64 1 (+.f64 1 (exp.f64 b)))

series263.0ms (6.1%)

Counts

4 → 32

Calls

4 calls:

246.0ms	(log1p.f64 (/.f64 1 (+.f64 1 (exp.f64 b))))
7.0ms	(/.f64 1 (+.f64 1 (exp.f64 b)))
7.0ms	(expm1.f64 (log1p.f64 (/.f64 1 (+.f64 1 (exp.f64 b)))))
3.0ms	(+.f64 1 (exp.f64 b))

rewrite323.0ms (7.5%)

Algorithm

4×	egg-rewrite

Rules

51×	`egg`
36×	`egg`
32×	`egg`
18×	`egg`

Counts

4 → 137

Calls

4 calls:

84.0ms	(+.f64 1 (exp.f64 b))
80.0ms	(expm1.f64 (log1p.f64 (/.f64 1 (+.f64 1 (exp.f64 b)))))
79.0ms	(/.f64 1 (+.f64 1 (exp.f64 b)))
77.0ms	(log1p.f64 (/.f64 1 (+.f64 1 (exp.f64 b))))

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	6	9
1	124	9
2	1437	9
3	4912	9
4	5071	9
0	5	6
1	98	6
2	1121	6
3	4710	6
4	5154	6
0	8	9
1	143	9
2	1627	9
3	4878	9
4	5024	9
0	7	11
1	142	11
2	1614	11
3	4823	11
4	4969	11

simplify80.0ms (1.9%)

Algorithm

1×	egg-herbie

Rules

700×	`cancel-sign-sub-inv_binary64`
532×	`fma-def_binary64`
479×	`unsub-neg_binary64`
448×	`unswap-sqr_binary64`
374×	`*-commutative_binary64`

Counts

169 → 133

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	47	345
1	119	333
2	300	319
3	786	304
4	2102	304
5	3142	304
6	4385	304
7	5179	304

prune122.0ms (2.8%)

Pruning

3 alts after pruning (1 fresh and 2 done)

	Pruned	Kept	Total
New	132	1	133
Fresh	1	0	1
Picked	1	0	1
Done	0	2	2
Total	134	3	137

Error

Counts

137 → 3

Alt Table

Status	Error	Program
✓	0.8b	(/.f64 (exp.f64 a) (fma.f64 (sqrt.f64 (exp.f64 b)) (sqrt.f64 (exp.f64 b)) (exp.f64 a)))
✓	0.8b	(expm1.f64 (log1p.f64 (/.f64 (exp.f64 a) (+.f64 (exp.f64 a) (exp.f64 b)))))
	12.7b	(/.f64 (fma.f64 (+.f64 1 (/.f64 1 (+.f64 1 (exp.f64 b)))) (+.f64 1 (/.f64 1 (+.f64 1 (exp.f64 b)))) -1) (+.f64 (+.f64 1 (/.f64 1 (+.f64 1 (exp.f64 b)))) 1))

Compiler

Compiled 1862 to 1447 computations (22.3% saved)

regimes596.0ms (13.9%)

Accuracy

Total 0.3b remaining (51.7%)

Threshold costs 0.3b (51.7%)

Counts

142 → 1

Compiler

Compiled 13155 to 9071 computations (31% saved)

simplify2.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

3×	`+-commutative_binary64`
2×	`*-commutative_binary64`
2×	`sub-neg_binary64`
1×	`*-rgt-identity_binary64`
1×	`neg-sub0_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	11	15
1	17	15
2	21	15
3	23	15
4	24	15
5	23	15

end59.0ms (1.4%)

Compiler: Compiled 79 to 57 computations (27.8% saved)

Details

analyze46.0ms (1.1%)

sample818.0ms (19%)

simplify6.0ms (0.2%)

prune2.0ms (0%)

localize5.0ms (0.1%)

series34.0ms (0.8%)

rewrite165.0ms (3.8%)

simplify52.0ms (1.2%)

prune123.0ms (2.9%)

localize6.0ms (0.2%)

series50.0ms (1.2%)

rewrite178.0ms (4.1%)

simplify56.0ms (1.3%)

prune191.0ms (4.5%)

localize7.0ms (0.2%)

series680.0ms (15.8%)

rewrite109.0ms (2.5%)

simplify95.0ms (2.2%)

prune214.0ms (5%)

localize11.0ms (0.3%)

series263.0ms (6.1%)

rewrite323.0ms (7.5%)

simplify80.0ms (1.9%)

prune122.0ms (2.8%)

regimes596.0ms (13.9%)

simplify2.0ms (0.1%)

end59.0ms (1.4%)

Profiling