Details

analyze41.0ms (1.2%)

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)

sample807.0ms (23.1%)

Results

778.0ms	8256×	body	128	valid
2.0ms	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

prune1.0ms (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)

localize6.0ms (0.2%)

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)))

series35.0ms (1%)

Counts

2 → 48

Calls

2 calls:

30.0ms	(/.f64 (exp.f64 a) (+.f64 (exp.f64 a) (exp.f64 b)))
5.0ms	(+.f64 (exp.f64 a) (exp.f64 b))

rewrite48.0ms (1.4%)

Algorithm

2×	batch-egg-rewrite

Rules

70× egg-rr

Counts

2 → 70

Calls

2 calls:

47.0ms	((/.f64 (exp.f64 a) (+.f64 (exp.f64 a) (exp.f64 b))) (+.f64 (exp.f64 a) (exp.f64 b)))
0.0ms	()

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	7	21
1	147	21
2	1998	21
3	5794	21
0	0	0
1	0	0

simplify37.0ms (1.1%)

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

118 → 98

Iterations

Useful iterations: 2 (0.0ms)

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

prune108.0ms (3.1%)

Pruning

4 alts after pruning (4 fresh and 0 done)

	Pruned	Kept	Total
New	94	4	98
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	95	4	99

Error

Counts

99 → 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)))
	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))))))))
	12.4b	(/.f64 1 (+.f64 1 (exp.f64 b)))
	0.8b	(expm1.f64 (log1p.f64 (/.f64 (exp.f64 a) (+.f64 (exp.f64 a) (exp.f64 b)))))

Compiler

Compiled 2184 to 1029 computations (52.9% saved)

localize7.0ms (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)))

series48.0ms (1.4%)

Counts

3 → 52

Calls

3 calls:

34.0ms	(/.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))
2.0ms	(sqrt.f64 (exp.f64 b))

rewrite48.0ms (1.4%)

Algorithm

2×	batch-egg-rewrite

Rules

78× egg-rr

Counts

3 → 78

Calls

2 calls:

46.0ms	((/.f64 (exp.f64 a) (fma.f64 (sqrt.f64 (exp.f64 b)) (sqrt.f64 (exp.f64 b)) (exp.f64 a))) (fma.f64 (sqrt.f64 (exp.f64 b)) (sqrt.f64 (exp.f64 b)) (exp.f64 a)) (sqrt.f64 (exp.f64 b)))
0.0ms	()

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	8	26
1	155	26
2	1868	26
3	5057	26
0	0	0
1	0	0

simplify45.0ms (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

130 → 112

Iterations

Useful iterations: 2 (0.0ms)

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

prune111.0ms (3.2%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	142	0	142
Fresh	0	3	3
Picked	0	1	1
Done	0	0	0
Total	142	4	146

Error

Counts

146 → 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)))
	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))))))))
	12.4b	(/.f64 1 (+.f64 1 (exp.f64 b)))
▶	0.8b	(expm1.f64 (log1p.f64 (/.f64 (exp.f64 a) (+.f64 (exp.f64 a) (exp.f64 b)))))

Compiler

Compiled 2805 to 1232 computations (56.1% 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)))

series701.0ms (20%)

Counts

2 → 48

Calls

2 calls:

672.0ms	(log1p.f64 (/.f64 (exp.f64 a) (+.f64 (exp.f64 a) (exp.f64 b))))
29.0ms	(expm1.f64 (log1p.f64 (/.f64 (exp.f64 a) (+.f64 (exp.f64 a) (exp.f64 b)))))

rewrite52.0ms (1.5%)

Algorithm

2×	batch-egg-rewrite

Rules

64× egg-rr

Counts

2 → 64

Calls

2 calls:

51.0ms	((expm1.f64 (log1p.f64 (/.f64 (exp.f64 a) (+.f64 (exp.f64 a) (exp.f64 b))))) (log1p.f64 (/.f64 (exp.f64 a) (+.f64 (exp.f64 a) (exp.f64 b)))))
0.0ms	()

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	9	28
1	166	28
2	2188	28
3	5058	28
0	0	0
1	0	0

simplify71.0ms (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

112 → 96

Iterations

Useful iterations: 2 (0.0ms)

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

prune202.0ms (5.8%)

Pruning

4 alts after pruning (2 fresh and 2 done)

	Pruned	Kept	Total
New	193	1	194
Fresh	1	1	2
Picked	0	1	1
Done	0	1	1
Total	194	4	198

Error

Counts

198 → 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)))
	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))))))))
▶	12.4b	(expm1.f64 (log1p.f64 (/.f64 1 (+.f64 1 (exp.f64 b)))))
✓	0.8b	(expm1.f64 (log1p.f64 (/.f64 (exp.f64 a) (+.f64 (exp.f64 a) (exp.f64 b)))))

Compiler

Compiled 6284 to 3403 computations (45.8% saved)

localize8.0ms (0.2%)

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)))

series256.0ms (7.3%)

Counts

4 → 32

Calls

4 calls:

240.0ms	(log1p.f64 (/.f64 1 (+.f64 1 (exp.f64 b))))
8.0ms	(expm1.f64 (log1p.f64 (/.f64 1 (+.f64 1 (exp.f64 b)))))
7.0ms	(/.f64 1 (+.f64 1 (exp.f64 b)))
2.0ms	(+.f64 1 (exp.f64 b))

rewrite86.0ms (2.5%)

Algorithm

2×	batch-egg-rewrite

Rules

120× egg-rr

Counts

4 → 120

Calls

2 calls:

84.0ms	((/.f64 1 (+.f64 1 (exp.f64 b))) (+.f64 1 (exp.f64 b)) (expm1.f64 (log1p.f64 (/.f64 1 (+.f64 1 (exp.f64 b))))) (log1p.f64 (/.f64 1 (+.f64 1 (exp.f64 b)))))
0.0ms	()

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	8	35
1	143	35
2	1627	35
3	4878	35
4	5024	35
0	0	0
1	0	0

simplify72.0ms (2%)

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

152 → 114

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

prune114.0ms (3.2%)

Pruning

3 alts after pruning (1 fresh and 2 done)

	Pruned	Kept	Total
New	113	1	114
Fresh	1	0	1
Picked	1	0	1
Done	0	2	2
Total	115	3	118

Error

Counts

118 → 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)))
	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))
✓	0.8b	(expm1.f64 (log1p.f64 (/.f64 (exp.f64 a) (+.f64 (exp.f64 a) (exp.f64 b)))))

Compiler

Compiled 1543 to 1197 computations (22.4% saved)

regimes518.0ms (14.8%)

Accuracy

Total 0.3b remaining (51.7%)

Threshold costs 0.3b (51.7%)

Counts

122 → 1

Compiler

Compiled 11529 to 8033 computations (30.3% 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

end60.0ms (1.7%)

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

Details

analyze41.0ms (1.2%)

sample807.0ms (23.1%)

simplify6.0ms (0.2%)

prune1.0ms (0%)

localize6.0ms (0.2%)

series35.0ms (1%)

rewrite48.0ms (1.4%)

simplify37.0ms (1.1%)

prune108.0ms (3.1%)

localize7.0ms (0.2%)

series48.0ms (1.4%)

rewrite48.0ms (1.4%)

simplify45.0ms (1.3%)

prune111.0ms (3.2%)

localize7.0ms (0.2%)

series701.0ms (20%)

rewrite52.0ms (1.5%)

simplify71.0ms (2%)

prune202.0ms (5.8%)

localize8.0ms (0.2%)

series256.0ms (7.3%)

rewrite86.0ms (2.5%)

simplify72.0ms (2%)

prune114.0ms (3.2%)

regimes518.0ms (14.8%)

simplify2.0ms (0.1%)

end60.0ms (1.7%)

Profiling