Details

analyze42.0ms (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)

sample765.0ms (22.6%)

Results

733.0ms	8256×	body	128	valid
4.0ms	31×	body	128	invalid

Compiler

Compiled 32 to 20 computations (37.5% saved)

simplify7.0ms (0.2%)

Algorithm

1×	egg-herbie

Rules

1×	`+-commutative_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	7	13
1	8	13

Stop Event

1×

saturated

Counts

1 → 1

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

0.3b

Counts

2 → 1

Alt Table

Status	Error	Program
▶	0.3b	(/.f64 (exp.f64 a) (+.f64 (exp.f64 a) (exp.f64 b)))

Compiler

Compiled 30 to 18 computations (40% saved)

localize5.0ms (0.2%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.0b	(exp.f64 a)
✓	0.0b	(+.f64 (exp.f64 a) (exp.f64 b))
✓	0.3b	(/.f64 (exp.f64 a) (+.f64 (exp.f64 a) (exp.f64 b)))

series36.0ms (1.1%)

Counts

3 → 52

Calls

3 calls:

31.0ms	(/.f64 (exp.f64 a) (+.f64 (exp.f64 a) (exp.f64 b)))
4.0ms	(+.f64 (exp.f64 a) (exp.f64 b))
1.0ms	(exp.f64 a)

rewrite54.0ms (1.6%)

Algorithm

1×	batch-egg-rewrite

Rules

793×	`log1p-expm1-u_binary64`
793×	`expm1-log1p-u_binary64`
485×	`prod-diff_binary64`
89×	`egg-rr`
77×	`add-sqr-sqrt_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	7	24
1	147	24
2	2102	24

Stop Event

1×	node limit

Counts

3 → 89

Calls

3 calls:

52.0ms	(exp.f64 a)
52.0ms	(+.f64 (exp.f64 a) (exp.f64 b))
52.0ms	(/.f64 (exp.f64 a) (+.f64 (exp.f64 a) (exp.f64 b)))

simplify30.0ms (0.9%)

Algorithm

1×	egg-herbie

Rules

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

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	107	1054
1	348	1015
2	1201	999

Stop Event

1×	node limit

Counts

141 → 125

prune137.0ms (4%)

Pruning

3 alts after pruning (3 fresh and 0 done)

	Pruned	Kept	Total
New	147	3	150
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	148	3	151

Error

Counts

151 → 3

Alt Table

Status	Error	Program
▶	0.0b	(exp.f64 (-.f64 a (log.f64 (+.f64 (exp.f64 a) (exp.f64 b)))))
	0.3b	(pow.f64 (/.f64 (+.f64 (exp.f64 a) (exp.f64 b)) (exp.f64 a)) -1)
	23.7b	(-.f64 (/.f64 (exp.f64 a) (+.f64 1 (exp.f64 a))) (/.f64 (*.f64 b (exp.f64 a)) (pow.f64 (+.f64 1 (exp.f64 a)) 2)))

Compiler

Compiled 2666 to 1189 computations (55.4% saved)

localize7.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.0b	(+.f64 (exp.f64 a) (exp.f64 b))
✓	0.0b	(exp.f64 (-.f64 a (log.f64 (+.f64 (exp.f64 a) (exp.f64 b)))))
✓	1.7b	(-.f64 a (log.f64 (+.f64 (exp.f64 a) (exp.f64 b))))
✓	3.5b	(log.f64 (+.f64 (exp.f64 a) (exp.f64 b)))

series645.0ms (19.1%)

Counts

3 → 72

Calls

3 calls:

311.0ms	(log.f64 (+.f64 (exp.f64 a) (exp.f64 b)))
179.0ms	(-.f64 a (log.f64 (+.f64 (exp.f64 a) (exp.f64 b))))
155.0ms	(exp.f64 (-.f64 a (log.f64 (+.f64 (exp.f64 a) (exp.f64 b)))))

rewrite59.0ms (1.8%)

Algorithm

1×	batch-egg-rewrite

Rules

814×	`prod-diff_binary64`
327×	`fma-def_binary64`
176×	`fma-neg_binary64`
174×	`expm1-udef_binary64`
174×	`log1p-udef_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	9	36
1	187	36
2	2608	36

Stop Event

1×	node limit

Counts

3 → 141

Calls

3 calls:

56.0ms	(exp.f64 (-.f64 a (log.f64 (+.f64 (exp.f64 a) (exp.f64 b)))))
56.0ms	(-.f64 a (log.f64 (+.f64 (exp.f64 a) (exp.f64 b))))
56.0ms	(log.f64 (+.f64 (exp.f64 a) (exp.f64 b)))

simplify51.0ms (1.5%)

Algorithm

1×	egg-herbie

Rules

591×	`fma-def_binary64`
485×	`times-frac_binary64`
400×	`associate-/l*_binary64`
217×	`sub-neg_binary64`
203×	`cancel-sign-sub-inv_binary64`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	138	1993
1	471	1932
2	1828	1690

Stop Event

1×	node limit

Counts

213 → 194

prune177.0ms (5.2%)

Pruning

3 alts after pruning (2 fresh and 1 done)

	Pruned	Kept	Total
New	242	2	244
Fresh	2	0	2
Picked	0	1	1
Done	0	0	0
Total	244	3	247

Error

Counts

247 → 3

Alt Table

Status	Error	Program
✓	0.0b	(exp.f64 (-.f64 a (log.f64 (+.f64 (exp.f64 a) (exp.f64 b)))))
	0.3b	(/.f64 (sqrt.f64 (exp.f64 a)) (/.f64 (+.f64 (exp.f64 a) (exp.f64 b)) (sqrt.f64 (exp.f64 a))))
▶	0.3b	(exp.f64 (-.f64 (-.f64 a (/.f64 a (+.f64 1 (exp.f64 b)))) (log1p.f64 (exp.f64 b))))

Compiler

Compiled 5577 to 2282 computations (59.1% saved)

localize9.0ms (0.3%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(exp.f64 (-.f64 (-.f64 a (/.f64 a (+.f64 1 (exp.f64 b)))) (log1p.f64 (exp.f64 b))))
✓	0.0b	(+.f64 1 (exp.f64 b))
✓	0.0b	(/.f64 a (+.f64 1 (exp.f64 b)))
✓	0.5b	(log1p.f64 (exp.f64 b))

series299.0ms (8.9%)

Counts

4 → 44

Calls

4 calls:

148.0ms	(exp.f64 (-.f64 (-.f64 a (/.f64 a (+.f64 1 (exp.f64 b)))) (log1p.f64 (exp.f64 b))))
132.0ms	(log1p.f64 (exp.f64 b))
17.0ms	(/.f64 a (+.f64 1 (exp.f64 b)))
2.0ms	(+.f64 1 (exp.f64 b))

rewrite63.0ms (1.9%)

Algorithm

1×	batch-egg-rewrite

Rules

562×	`fma-def_binary64`
304×	`fma-neg_binary64`
220×	`expm1-udef_binary64`
220×	`log1p-udef_binary64`
121×	`add-sqr-sqrt_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	11	41
1	241	41
2	3486	41

Stop Event

1×	node limit

Counts

4 → 120

Calls

4 calls:

61.0ms	(exp.f64 (-.f64 (-.f64 a (/.f64 a (+.f64 1 (exp.f64 b)))) (log1p.f64 (exp.f64 b))))
61.0ms	(+.f64 1 (exp.f64 b))
61.0ms	(/.f64 a (+.f64 1 (exp.f64 b)))
61.0ms	(log1p.f64 (exp.f64 b))

simplify38.0ms (1.1%)

Algorithm

1×	egg-herbie

Rules

891×	`fma-def_binary64`
327×	`cancel-sign-sub-inv_binary64`
265×	`times-frac_binary64`
225×	`associate-/l*_binary64`
169×	`associate-*r/_binary64`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	134	1275
1	436	1193
2	1598	989

Stop Event

1×	node limit

Counts

164 → 161

prune132.0ms (3.9%)

Pruning

3 alts after pruning (1 fresh and 2 done)

	Pruned	Kept	Total
New	161	0	161
Fresh	0	1	1
Picked	0	1	1
Done	0	1	1
Total	161	3	164

Error

Counts

164 → 3

Alt Table

Status	Error	Program
✓	0.0b	(exp.f64 (-.f64 a (log.f64 (+.f64 (exp.f64 a) (exp.f64 b)))))
▶	0.3b	(/.f64 (sqrt.f64 (exp.f64 a)) (/.f64 (+.f64 (exp.f64 a) (exp.f64 b)) (sqrt.f64 (exp.f64 a))))
✓	0.3b	(exp.f64 (-.f64 (-.f64 a (/.f64 a (+.f64 1 (exp.f64 b)))) (log1p.f64 (exp.f64 b))))

Compiler

Compiled 3560 to 2112 computations (40.7% saved)

localize8.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(sqrt.f64 (exp.f64 a))
	0.0b	(+.f64 (exp.f64 a) (exp.f64 b))
✓	0.2b	(/.f64 (+.f64 (exp.f64 a) (exp.f64 b)) (sqrt.f64 (exp.f64 a)))
✓	0.3b	(/.f64 (sqrt.f64 (exp.f64 a)) (/.f64 (+.f64 (exp.f64 a) (exp.f64 b)) (sqrt.f64 (exp.f64 a))))

series49.0ms (1.4%)

Counts

3 → 52

Calls

3 calls:

27.0ms	(/.f64 (sqrt.f64 (exp.f64 a)) (/.f64 (+.f64 (exp.f64 a) (exp.f64 b)) (sqrt.f64 (exp.f64 a))))
19.0ms	(/.f64 (+.f64 (exp.f64 a) (exp.f64 b)) (sqrt.f64 (exp.f64 a)))
3.0ms	(sqrt.f64 (exp.f64 a))

rewrite55.0ms (1.6%)

Algorithm

1×	batch-egg-rewrite

Rules

537×	`prod-diff_binary64`
205×	`fma-def_binary64`
175×	`expm1-udef_binary64`
175×	`log1p-udef_binary64`
165×	`log-pow_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	9	42
1	193	33
2	2797	33

Stop Event

1×	node limit

Counts

3 → 97

Calls

3 calls:

53.0ms	(sqrt.f64 (exp.f64 a))
53.0ms	(/.f64 (+.f64 (exp.f64 a) (exp.f64 b)) (sqrt.f64 (exp.f64 a)))
53.0ms	(/.f64 (sqrt.f64 (exp.f64 a)) (/.f64 (+.f64 (exp.f64 a) (exp.f64 b)) (sqrt.f64 (exp.f64 a))))

simplify35.0ms (1%)

Algorithm

1×	egg-herbie

Rules

620×	`fma-def_binary64`
465×	`times-frac_binary64`
364×	`associate--l+_binary64`
288×	`associate-/l*_binary64`
211×	`associate-r_binary64`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	128	1368
1	423	1307
2	1494	1256

Stop Event

1×	node limit

Counts

149 → 136

prune151.0ms (4.5%)

Pruning

3 alts after pruning (0 fresh and 3 done)

	Pruned	Kept	Total
New	216	0	216
Fresh	0	0	0
Picked	0	1	1
Done	0	2	2
Total	216	3	219

Error

Counts

219 → 3

Alt Table

Status	Error	Program
✓	0.0b	(exp.f64 (-.f64 a (log.f64 (+.f64 (exp.f64 a) (exp.f64 b)))))
✓	0.3b	(/.f64 (sqrt.f64 (exp.f64 a)) (/.f64 (+.f64 (exp.f64 a) (exp.f64 b)) (sqrt.f64 (exp.f64 a))))
✓	0.3b	(exp.f64 (-.f64 (-.f64 a (/.f64 a (+.f64 1 (exp.f64 b)))) (log1p.f64 (exp.f64 b))))

Compiler

Compiled 4477 to 1684 computations (62.4% saved)

regimes467.0ms (13.8%)

Accuracy

Total 0.4b remaining (52.7%)

Threshold costs 0.4b (52.7%)

Counts

108 → 1

Compiler

Compiled 9773 to 6697 computations (31.5% saved)

simplify2.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

3×	`+-commutative_binary64`
2×	`sub-neg_binary64`
1×	`*-commutative_binary64`
1×	`neg-sub0_binary64`
1×	`neg-mul-1_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	11	19
1	14	19
2	19	19
3	21	19
4	22	19

Stop Event

1×

saturated

end55.0ms (1.6%)

Compiler: Compiled 67 to 46 computations (31.3% saved)

Details

analyze42.0ms (1.2%)

sample765.0ms (22.6%)

simplify7.0ms (0.2%)

prune1.0ms (0%)

localize5.0ms (0.2%)

series36.0ms (1.1%)

rewrite54.0ms (1.6%)

simplify30.0ms (0.9%)

prune137.0ms (4%)

localize7.0ms (0.2%)

series645.0ms (19.1%)

rewrite59.0ms (1.8%)

simplify51.0ms (1.5%)

prune177.0ms (5.2%)

localize9.0ms (0.3%)

series299.0ms (8.9%)

rewrite63.0ms (1.9%)

simplify38.0ms (1.1%)

prune132.0ms (3.9%)

localize8.0ms (0.2%)

series49.0ms (1.4%)

rewrite55.0ms (1.6%)

simplify35.0ms (1%)

prune151.0ms (4.5%)

regimes467.0ms (13.8%)

simplify2.0ms (0.1%)

end55.0ms (1.6%)

Profiling