Details

analyze47.0ms (0.9%)

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)

sample849.0ms (16.6%)

Results

818.0ms	8256×	body	128	valid
3.0ms	31×	body	128	invalid

Compiler

Compiled 32 to 20 computations (37.5% saved)

simplify8.0ms (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

0.5b

Counts

2 → 1

Alt Table

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

series32.0ms (0.6%)

Counts

2 → 48

Calls

2 calls:

28.0ms	(/.f64 (exp.f64 a) (+.f64 (exp.f64 a) (exp.f64 b)))
4.0ms	(+.f64 (exp.f64 a) (exp.f64 b))

rewrite12.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

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))

simplify86.0ms (1.7%)

Algorithm

1×	egg-herbie

Rules

806×	`fma-neg_binary64`
536×	`times-frac_binary64`
493×	`fma-def_binary64`
389×	`associate-/l*_binary64`
245×	`associate-/r*_binary64`

Counts

100 → 108

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	168	1981
1	449	1869
2	1403	1853
3	4915	1853
4	5640	1853

prune118.0ms (2.3%)

Pruning

3 alts after pruning (3 fresh and 0 done)

	Pruned	Kept	Total
New	105	3	108
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	106	3	109

Error

Counts

109 → 3

Alt Table

Status	Error	Program
	0.5b	(expm1.f64 (log1p.f64 (/.f64 (exp.f64 a) (+.f64 (exp.f64 a) (exp.f64 b)))))
	10.0b	(-.f64 (+.f64 (/.f64 1 (+.f64 1 (exp.f64 b))) (/.f64 a (+.f64 1 (exp.f64 b)))) (/.f64 a (pow.f64 (+.f64 1 (exp.f64 b)) 2)))
▶	0.5b	(*.f64 (sqrt.f64 (exp.f64 a)) (/.f64 (sqrt.f64 (exp.f64 a)) (+.f64 (exp.f64 b) (exp.f64 a))))

Compiler

Compiled 2299 to 865 computations (62.4% saved)

localize7.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(+.f64 (exp.f64 b) (exp.f64 a))
✓	0.2b	(sqrt.f64 (exp.f64 a))
✓	0.3b	(*.f64 (sqrt.f64 (exp.f64 a)) (/.f64 (sqrt.f64 (exp.f64 a)) (+.f64 (exp.f64 b) (exp.f64 a))))
✓	0.4b	(/.f64 (sqrt.f64 (exp.f64 a)) (+.f64 (exp.f64 b) (exp.f64 a)))

series73.0ms (1.4%)

Counts

4 → 60

Calls

4 calls:

36.0ms	(/.f64 (sqrt.f64 (exp.f64 a)) (+.f64 (exp.f64 b) (exp.f64 a)))
28.0ms	(*.f64 (sqrt.f64 (exp.f64 a)) (/.f64 (sqrt.f64 (exp.f64 a)) (+.f64 (exp.f64 b) (exp.f64 a))))
4.0ms	(+.f64 (exp.f64 b) (exp.f64 a))
3.0ms	(sqrt.f64 (exp.f64 a))

rewrite39.0ms (0.8%)

Algorithm

1×	rewrite-expression-head

Rules

69×	`*-un-lft-identity_binary64`
58×	`add-sqr-sqrt_binary64`
52×	`times-frac_binary64`
41×	`add-cube-cbrt_binary64`
38×	`sqrt-prod_binary64`

Counts

4 → 143

Calls

4 calls:

16.0ms	(*.f64 (sqrt.f64 (exp.f64 a)) (/.f64 (sqrt.f64 (exp.f64 a)) (+.f64 (exp.f64 b) (exp.f64 a))))
6.0ms	(/.f64 (sqrt.f64 (exp.f64 a)) (+.f64 (exp.f64 b) (exp.f64 a)))
3.0ms	(+.f64 (exp.f64 b) (exp.f64 a))
2.0ms	(sqrt.f64 (exp.f64 a))

simplify141.0ms (2.8%)

Algorithm

1×	egg-herbie

Rules

480×	`fma-neg_binary64`
329×	`associate-/l/_binary64`
271×	`cancel-sign-sub-inv_binary64`
183×	`sub-neg_binary64`
166×	`distribute-rgt-in_binary64`

Counts

203 → 204

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	291	4659
1	777	4419
2	2854	4329
3	4820	4329
4	5061	4329

prune168.0ms (3.3%)

Pruning

3 alts after pruning (2 fresh and 1 done)

	Pruned	Kept	Total
New	230	0	230
Fresh	0	2	2
Picked	0	1	1
Done	0	0	0
Total	230	3	233

Error

Counts

233 → 3

Alt Table

Status	Error	Program
▶	0.5b	(expm1.f64 (log1p.f64 (/.f64 (exp.f64 a) (+.f64 (exp.f64 a) (exp.f64 b)))))
	10.0b	(-.f64 (+.f64 (/.f64 1 (+.f64 1 (exp.f64 b))) (/.f64 a (+.f64 1 (exp.f64 b)))) (/.f64 a (pow.f64 (+.f64 1 (exp.f64 b)) 2)))
✓	0.5b	(*.f64 (sqrt.f64 (exp.f64 a)) (/.f64 (sqrt.f64 (exp.f64 a)) (+.f64 (exp.f64 b) (exp.f64 a))))

Compiler

Compiled 5836 to 1826 computations (68.7% saved)

localize8.0ms (0.1%)

Local error

Found 4 expressions with local error:

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

series539.0ms (10.6%)

Counts

2 → 48

Calls

2 calls:

512.0ms	(log1p.f64 (/.f64 (exp.f64 a) (+.f64 (exp.f64 a) (exp.f64 b))))
27.0ms	(expm1.f64 (log1p.f64 (/.f64 (exp.f64 a) (+.f64 (exp.f64 a) (exp.f64 b)))))

rewrite1.0ms (0%)

Algorithm

1×	rewrite-expression-head

Rules

3×	`expm1-log1p-u_binary64`
2×	`*-un-lft-identity_binary64`
2×	`add-sqr-sqrt_binary64`
2×	`add-cube-cbrt_binary64`
2×	`add-cbrt-cube_binary64`

Counts

2 → 22

Calls

2 calls:

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

simplify77.0ms (1.5%)

Algorithm

1×	egg-herbie

Rules

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

Counts

70 → 67

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	251	3192
1	773	3027
2	3674	2850
3	5038	2850

prune182.0ms (3.6%)

Pruning

3 alts after pruning (1 fresh and 2 done)

	Pruned	Kept	Total
New	175	0	175
Fresh	0	1	1
Picked	0	1	1
Done	0	1	1
Total	175	3	178

Error

Counts

178 → 3

Alt Table

Status	Error	Program
✓	0.5b	(expm1.f64 (log1p.f64 (/.f64 (exp.f64 a) (+.f64 (exp.f64 a) (exp.f64 b)))))
▶	10.0b	(-.f64 (+.f64 (/.f64 1 (+.f64 1 (exp.f64 b))) (/.f64 a (+.f64 1 (exp.f64 b)))) (/.f64 a (pow.f64 (+.f64 1 (exp.f64 b)) 2)))
✓	0.5b	(*.f64 (sqrt.f64 (exp.f64 a)) (/.f64 (sqrt.f64 (exp.f64 a)) (+.f64 (exp.f64 b) (exp.f64 a))))

Compiler

Compiled 6017 to 3094 computations (48.6% saved)

localize9.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(pow.f64 (+.f64 1 (exp.f64 b)) 2)
✓	0.0b	(/.f64 a (pow.f64 (+.f64 1 (exp.f64 b)) 2))
✓	0.0b	(-.f64 (+.f64 (/.f64 1 (+.f64 1 (exp.f64 b))) (/.f64 a (+.f64 1 (exp.f64 b)))) (/.f64 a (pow.f64 (+.f64 1 (exp.f64 b)) 2)))
✓	0.0b	(/.f64 a (+.f64 1 (exp.f64 b)))

series182.0ms (3.6%)

Counts

4 → 40

Calls

4 calls:

78.0ms	(-.f64 (+.f64 (/.f64 1 (+.f64 1 (exp.f64 b))) (/.f64 a (+.f64 1 (exp.f64 b)))) (/.f64 a (pow.f64 (+.f64 1 (exp.f64 b)) 2)))
72.0ms	(/.f64 a (pow.f64 (+.f64 1 (exp.f64 b)) 2))
25.0ms	(/.f64 a (+.f64 1 (exp.f64 b)))
7.0ms	(pow.f64 (+.f64 1 (exp.f64 b)) 2)

rewrite309.0ms (6.1%)

Algorithm

1×	rewrite-expression-head

Rules

1602×	`*-un-lft-identity_binary64`
1022×	`times-frac_binary64`
558×	`prod-diff_binary64`
493×	`distribute-lft-out_binary64`
445×	`add-sqr-sqrt_binary64`

Counts

4 → 752

Calls

4 calls:

61.0ms	(-.f64 (+.f64 (/.f64 1 (+.f64 1 (exp.f64 b))) (/.f64 a (+.f64 1 (exp.f64 b)))) (/.f64 a (pow.f64 (+.f64 1 (exp.f64 b)) 2)))
6.0ms	(/.f64 a (pow.f64 (+.f64 1 (exp.f64 b)) 2))
5.0ms	(/.f64 a (+.f64 1 (exp.f64 b)))
3.0ms	(pow.f64 (+.f64 1 (exp.f64 b)) 2)

simplify792.0ms (15.5%)

Algorithm

1×	egg-herbie

Rules

583×	`fma-neg_binary64`
276×	`exp-prod_binary64`
245×	`distribute-rgt-neg-in_binary64`
240×	`fma-udef_binary64`
217×	`distribute-neg-frac_binary64`

Counts

792 → 590

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	635	50189
1	1442	32072
2	3039	23144
3	4446	23138
4	4882	23138

prune819.0ms (16.1%)

Pruning

3 alts after pruning (0 fresh and 3 done)

	Pruned	Kept	Total
New	590	0	590
Fresh	0	0	0
Picked	0	1	1
Done	0	2	2
Total	590	3	593

Error

Counts

593 → 3

Alt Table

Status	Error	Program
✓	0.5b	(expm1.f64 (log1p.f64 (/.f64 (exp.f64 a) (+.f64 (exp.f64 a) (exp.f64 b)))))
✓	10.0b	(-.f64 (+.f64 (/.f64 1 (+.f64 1 (exp.f64 b))) (/.f64 a (+.f64 1 (exp.f64 b)))) (/.f64 a (pow.f64 (+.f64 1 (exp.f64 b)) 2)))
✓	0.5b	(*.f64 (sqrt.f64 (exp.f64 a)) (/.f64 (sqrt.f64 (exp.f64 a)) (+.f64 (exp.f64 b) (exp.f64 a))))

Compiler

Compiled 35857 to 23331 computations (34.9% saved)

regimes533.0ms (10.5%)

Accuracy

Total 0.4b remaining (57.5%)

Threshold costs 0.4b (57.5%)

Counts

116 → 1

Compiler

Compiled 10423 to 7223 computations (30.7% saved)

simplify2.0ms (0%)

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	9	15
1	12	15
2	17	15
3	19	15
4	20	15
5	20	15

end63.0ms (1.2%)

Compiler: Compiled 73 to 49 computations (32.9% saved)

Details

analyze47.0ms (0.9%)

sample849.0ms (16.6%)

simplify8.0ms (0.2%)

prune1.0ms (0%)

localize5.0ms (0.1%)

series32.0ms (0.6%)

rewrite12.0ms (0.2%)

simplify86.0ms (1.7%)

prune118.0ms (2.3%)

localize7.0ms (0.1%)

series73.0ms (1.4%)

rewrite39.0ms (0.8%)

simplify141.0ms (2.8%)

prune168.0ms (3.3%)

localize8.0ms (0.1%)

series539.0ms (10.6%)

rewrite1.0ms (0%)

simplify77.0ms (1.5%)

prune182.0ms (3.6%)

localize9.0ms (0.2%)

series182.0ms (3.6%)

rewrite309.0ms (6.1%)

simplify792.0ms (15.5%)

prune819.0ms (16.1%)

regimes533.0ms (10.5%)

simplify2.0ms (0%)

end63.0ms (1.2%)

Profiling