Details

analyze109.0ms (3.7%)

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%	18.7%	12.6%	7
68.7%	12.5%	18.8%	8
68.7%	12.5%	18.8%	9
68.7%	9.4%	22%	10
68.7%	9.4%	22%	11
68.7%	7.8%	23.5%	12
68.7%	7.8%	23.5%	13
68.7%	7%	24.3%	14

Compiler

Compiled 11 to 7 computations (36.4% saved)

sample21.0ms (0.7%)

Algorithm

1×

intervals

Results

11.0ms	256×	body	128	valid
1.0ms	26×	body	128	overflowed

Compiler

Compiled 23 to 15 computations (34.8% saved)

simplify10.0ms (0.3%)

Algorithm

1×	egg-herbie

Rules

1×	`+-commutative_binary64`

Counts

1 → 0

Iterations

Useful iterations: 0 (0.0ms)

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

prune3.0ms (0.1%)

Pruning

1 alts after pruning (1 fresh and 0 done)

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

Error

0.5b

Counts

1 → 1

Alt Table

Status	Error	Program
▶	0.5b	(/.f64 (exp.f64 a) (+.f64 (exp.f64 a) (exp.f64 b)))

Compiler

Compiled 20 to 12 computations (40% saved)

localize5.0ms (0.2%)

Local error

Found 2 expressions with local error:

0.0b	(+.f64 (exp.f64 a) (exp.f64 b))
0.5b	(/.f64 (exp.f64 a) (+.f64 (exp.f64 a) (exp.f64 b)))

rewrite38.0ms (1.3%)

Algorithm

1×	rewrite-expression-head

Error

0.3b

Rules

22×	`*-un-lft-identity_binary64`
12×	`times-frac_binary64`
12×	`add-sqr-sqrt_binary64`
12×	`add-cube-cbrt_binary64`
5×	`distribute-lft-out_binary64`

Counts

2 → 52

Calls

2 calls:

5.0ms	(/.f64 (exp.f64 a) (+.f64 (exp.f64 a) (exp.f64 b)))
3.0ms	(+.f64 (exp.f64 a) (exp.f64 b))

Compiler

Compiled 753 to 152 computations (79.8% saved)

series70.0ms (2.4%)

Error

0.0b

Counts

2 → 23

Calls

2 calls:

29.0ms	(/.f64 (exp.f64 a) (+.f64 (exp.f64 a) (exp.f64 b)))
22.0ms	(+.f64 (exp.f64 a) (exp.f64 b))

Compiler

Compiled 1106 to 721 computations (34.8% saved)

simplify94.0ms (3.2%)

Algorithm

1×	egg-herbie

Rules

873×	`fma-neg_binary64`
433×	`associate-+l+_binary64`
393×	`fma-def_binary64`
366×	`times-frac_binary64`
272×	`associate-/l*_binary64`

Counts

75 → 52

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	161	1647
1	415	1535
2	1225	1529
3	4847	1529
4	5679	1529

prune64.0ms (2.2%)

Pruning

3 alts after pruning (3 fresh and 0 done)

	Pruned	Kept	Total
New	49	3	52
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	50	3	53

Error

Counts

53 → 3

Alt Table

Status	Error	Program
	20.8b	(-.f64 (.f64 (+.f64 (/.f64 (.f64 b b) (pow.f64 (+.f64 1 (exp.f64 a)) 2)) 1) (/.f64 (exp.f64 a) (+.f64 1 (exp.f64 a)))) (fma.f64 1/2 (.f64 (/.f64 (.f64 b (exp.f64 a)) (pow.f64 (+.f64 1 (exp.f64 a)) 2)) b) (/.f64 (*.f64 b (exp.f64 a)) (pow.f64 (+.f64 1 (exp.f64 a)) 2))))
	15.7b	(+.f64 (fma.f64 1/6 (/.f64 (pow.f64 a 3) (+.f64 1 (exp.f64 b))) (fma.f64 1/2 (.f64 (/.f64 a (+.f64 1 (exp.f64 b))) a) (/.f64 1 (+.f64 1 (exp.f64 b))))) (-.f64 (-.f64 (+.f64 (/.f64 a (+.f64 1 (exp.f64 b))) (fma.f64 2 (pow.f64 (/.f64 a (+.f64 1 (exp.f64 b))) 3) (/.f64 (.f64 a a) (pow.f64 (+.f64 1 (exp.f64 b)) 3)))) (fma.f64 7/6 (/.f64 (pow.f64 a 3) (pow.f64 (+.f64 1 (exp.f64 b)) 2)) (/.f64 a (pow.f64 (+.f64 1 (exp.f64 b)) 2)))) (.f64 (.f64 (/.f64 a (pow.f64 (+.f64 1 (exp.f64 b)) 2)) a) (+.f64 3/2 (/.f64 a (pow.f64 (+.f64 1 (exp.f64 b)) 2))))))
▶	0.3b	(exp.f64 (-.f64 a (log.f64 (+.f64 (exp.f64 b) (exp.f64 a)))))

Compiler

Compiled 1169 to 513 computations (56.1% saved)

localize8.0ms (0.3%)

Local error

Found 4 expressions with local error:

0.0b	(exp.f64 (-.f64 a (log.f64 (+.f64 (exp.f64 b) (exp.f64 a)))))
0.0b	(+.f64 (exp.f64 b) (exp.f64 a))
1.7b	(-.f64 a (log.f64 (+.f64 (exp.f64 b) (exp.f64 a))))
2.5b	(log.f64 (+.f64 (exp.f64 b) (exp.f64 a)))

rewrite121.0ms (4.1%)

Algorithm

1×	rewrite-expression-head

Error

Rules

37×	`*-un-lft-identity_binary64`
29×	`add-sqr-sqrt_binary64`
25×	`add-cube-cbrt_binary64`
24×	`prod-diff_binary64`
19×	`exp-sum_binary64`

Counts

4 → 112

Calls

4 calls:

8.0ms	(-.f64 a (log.f64 (+.f64 (exp.f64 b) (exp.f64 a))))
5.0ms	(exp.f64 (-.f64 a (log.f64 (+.f64 (exp.f64 b) (exp.f64 a)))))
4.0ms	(+.f64 (exp.f64 b) (exp.f64 a))
3.0ms	(log.f64 (+.f64 (exp.f64 b) (exp.f64 a)))

Compiler

Compiled 2317 to 424 computations (81.7% saved)

series128.0ms (4.4%)

Error

Counts

4 → 44

Calls

4 calls:

34.0ms	(exp.f64 (-.f64 a (log.f64 (+.f64 (exp.f64 b) (exp.f64 a)))))
28.0ms	(-.f64 a (log.f64 (+.f64 (exp.f64 b) (exp.f64 a))))
24.0ms	(log.f64 (+.f64 (exp.f64 b) (exp.f64 a)))
11.0ms	(+.f64 (exp.f64 b) (exp.f64 a))

Compiler

Compiled 2125 to 1537 computations (27.7% saved)

simplify137.0ms (4.7%)

Algorithm

1×	egg-herbie

Rules

905×	`fma-neg_binary64`
369×	`times-frac_binary64`
275×	`exp-prod_binary64`
229×	`sub-neg_binary64`
216×	`cancel-sign-sub-inv_binary64`

Counts

156 → 138

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	275	3427
1	665	2953
2	2195	2678
3	4320	2673
4	4961	2673

prune59.0ms (2%)

Pruning

2 alts after pruning (2 fresh and 0 done)

	Pruned	Kept	Total
New	136	2	138
Fresh	2	0	2
Picked	1	0	1
Done	0	0	0
Total	139	2	141

Error

Counts

141 → 2

Alt Table

Status	Error	Program
	11.5b	(exp.f64 (-.f64 a (+.f64 (log1p.f64 (exp.f64 a)) (/.f64 b (+.f64 1 (exp.f64 a))))))
▶	0.5b	(expm1.f64 (log1p.f64 (/.f64 (exp.f64 a) (+.f64 (exp.f64 a) (exp.f64 b)))))

Compiler

Compiled 1423 to 553 computations (61.1% saved)

localize8.0ms (0.3%)

Local error

Found 4 expressions with local error:

0.0b	(log1p.f64 (/.f64 (exp.f64 a) (+.f64 (exp.f64 a) (exp.f64 b))))
0.0b	(expm1.f64 (log1p.f64 (/.f64 (exp.f64 a) (+.f64 (exp.f64 a) (exp.f64 b)))))
0.0b	(+.f64 (exp.f64 a) (exp.f64 b))
0.5b	(/.f64 (exp.f64 a) (+.f64 (exp.f64 a) (exp.f64 b)))

rewrite53.0ms (1.8%)

Algorithm

1×	rewrite-expression-head

Error

Rules

24×	`*-un-lft-identity_binary64`
14×	`add-sqr-sqrt_binary64`
14×	`add-cube-cbrt_binary64`
12×	`times-frac_binary64`
6×	`add-cbrt-cube_binary64`

Counts

4 → 74

Calls

4 calls:

9.0ms	(/.f64 (exp.f64 a) (+.f64 (exp.f64 a) (exp.f64 b)))
3.0ms	(+.f64 (exp.f64 a) (exp.f64 b))
0.0ms	(log1p.f64 (/.f64 (exp.f64 a) (+.f64 (exp.f64 a) (exp.f64 b))))
0.0ms	(expm1.f64 (log1p.f64 (/.f64 (exp.f64 a) (+.f64 (exp.f64 a) (exp.f64 b)))))

Compiler

Compiled 1184 to 294 computations (75.2% saved)

series263.0ms (9%)

Error

Counts

4 → 44

Calls

4 calls:

94.0ms	(expm1.f64 (log1p.f64 (/.f64 (exp.f64 a) (+.f64 (exp.f64 a) (exp.f64 b)))))
80.0ms	(log1p.f64 (/.f64 (exp.f64 a) (+.f64 (exp.f64 a) (exp.f64 b))))
30.0ms	(/.f64 (exp.f64 a) (+.f64 (exp.f64 a) (exp.f64 b)))
13.0ms	(+.f64 (exp.f64 a) (exp.f64 b))

Compiler

Compiled 5048 to 3623 computations (28.2% saved)

simplify123.0ms (4.2%)

Algorithm

1×	egg-herbie

Rules

374×	`times-frac_binary64`
262×	`associate-+r+_binary64`
242×	`sub-neg_binary64`
221×	`associate-/r*_binary64`
218×	`+-commutative_binary64`

Counts

118 → 103

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	367	4343
1	987	3656
2	4253	3611
3	5068	3611

prune54.0ms (1.9%)

Pruning

2 alts after pruning (1 fresh and 1 done)

	Pruned	Kept	Total
New	103	0	103
Fresh	0	1	1
Picked	0	1	1
Done	0	0	0
Total	103	2	105

Error

Counts

105 → 2

Alt Table

Status	Error	Program
▶	11.5b	(exp.f64 (-.f64 a (+.f64 (log1p.f64 (exp.f64 a)) (/.f64 b (+.f64 1 (exp.f64 a))))))
✓	0.5b	(expm1.f64 (log1p.f64 (/.f64 (exp.f64 a) (+.f64 (exp.f64 a) (exp.f64 b)))))

Compiler

Compiled 2258 to 1147 computations (49.2% saved)

localize9.0ms (0.3%)

Local error

Found 4 expressions with local error:

0.0b	(exp.f64 (-.f64 a (+.f64 (log1p.f64 (exp.f64 a)) (/.f64 b (+.f64 1 (exp.f64 a))))))
0.0b	(/.f64 b (+.f64 1 (exp.f64 a)))
0.0b	(+.f64 1 (exp.f64 a))
0.3b	(log1p.f64 (exp.f64 a))

rewrite90.0ms (3.1%)

Algorithm

1×	rewrite-expression-head

Error

Rules

46×	`*-un-lft-identity_binary64`
25×	`add-sqr-sqrt_binary64`
23×	`add-cube-cbrt_binary64`
17×	`exp-sum_binary64`
14×	`add-log-exp_binary64`

Counts

4 → 100

Calls

4 calls:

11.0ms	(exp.f64 (-.f64 a (+.f64 (log1p.f64 (exp.f64 a)) (/.f64 b (+.f64 1 (exp.f64 a))))))
4.0ms	(/.f64 b (+.f64 1 (exp.f64 a)))
3.0ms	(+.f64 1 (exp.f64 a))
1.0ms	(log1p.f64 (exp.f64 a))

Compiler

Compiled 2299 to 1187 computations (48.4% saved)

series58.0ms (2%)

Error

Counts

4 → 23

Calls

4 calls:

18.0ms	(exp.f64 (-.f64 a (+.f64 (log1p.f64 (exp.f64 a)) (/.f64 b (+.f64 1 (exp.f64 a))))))
14.0ms	(log1p.f64 (exp.f64 a))
14.0ms	(/.f64 b (+.f64 1 (exp.f64 a)))
4.0ms	(+.f64 1 (exp.f64 a))

Compiler

Compiled 950 to 682 computations (28.2% saved)

simplify192.0ms (6.6%)

Algorithm

1×	egg-herbie

Rules

888×	`fma-neg_binary64`
334×	`fma-def_binary64`
233×	`exp-prod_binary64`
218×	`exp-diff_binary64`
171×	`associate-l_binary64`

Counts

123 → 77

Iterations

Useful iterations: 7 (0.0ms)

Iter	Nodes	Cost
0	205	2090
1	412	1962
2	1042	1933
3	3505	1929
4	4984	1929
5	4962	1929
6	4990	1929
7	4999	1926
8	4845	1926

prune34.0ms (1.2%)

Pruning

2 alts after pruning (0 fresh and 2 done)

	Pruned	Kept	Total
New	77	0	77
Fresh	0	0	0
Picked	0	1	1
Done	0	1	1
Total	77	2	79

Error

Counts

79 → 2

Alt Table

Status	Error	Program
✓	11.5b	(exp.f64 (-.f64 a (+.f64 (log1p.f64 (exp.f64 a)) (/.f64 b (+.f64 1 (exp.f64 a))))))
✓	0.5b	(expm1.f64 (log1p.f64 (/.f64 (exp.f64 a) (+.f64 (exp.f64 a) (exp.f64 b)))))

Compiler

Compiled 729 to 389 computations (46.6% saved)

regimes573.0ms (19.6%)

Accuracy

Total 0.2b remaining (27.3%)

Threshold costs 0.2b (27.3%)

Compiler

Compiled 14701 to 8544 computations (41.9% saved)

simplify3.0ms (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	10	17
1	15	17
2	21	17
3	23	17
4	24	17
5	23	17

end1.0ms (0%)

Compiler: Compiled 12 to 9 computations (25% saved)

sample602.0ms (20.5%)

Algorithm

1×

intervals

Results

297.0ms	8000×	body	128	valid
23.0ms	682×	body	128	overflowed

Compiler

Compiled 52 to 36 computations (30.8% saved)

Details

analyze109.0ms (3.7%)

sample21.0ms (0.7%)

simplify10.0ms (0.3%)

prune3.0ms (0.1%)

localize5.0ms (0.2%)

rewrite38.0ms (1.3%)

series70.0ms (2.4%)

simplify94.0ms (3.2%)

prune64.0ms (2.2%)

localize8.0ms (0.3%)

rewrite121.0ms (4.1%)

series128.0ms (4.4%)

simplify137.0ms (4.7%)

prune59.0ms (2%)

localize8.0ms (0.3%)

rewrite53.0ms (1.8%)

series263.0ms (9%)

simplify123.0ms (4.2%)

prune54.0ms (1.9%)

localize9.0ms (0.3%)

rewrite90.0ms (3.1%)

series58.0ms (2%)

simplify192.0ms (6.6%)

prune34.0ms (1.2%)

regimes573.0ms (19.6%)

simplify3.0ms (0.1%)

end1.0ms (0%)

sample602.0ms (20.5%)

Profiling