Details

analyze2.0ms (0.1%)

Algorithm

1×

Search

True	Other	False	Iter
0%	100%	0%	0
0%	100%	0%	1
50%	50%	0%	2
50%	25%	25%	3
62.5%	12.5%	25%	4
68.7%	6.2%	25%	5
71.8%	3.1%	25%	6
73.4%	1.6%	25%	7
74.2%	0.8%	25%	8
74.6%	0.4%	25%	9
74.8%	0.2%	25%	10
74.9%	0.1%	25%	11
74.9%	0%	25%	12
74.9%	0%	25%	13
74.9%	0%	25%	14

Compiler

Compiled 10 to 8 computations (20% saved)

sample561.0ms (25.7%)

Infinites

0% of outputs are infinite.

Results

517.0ms	8251×	body	128	valid
1.0ms	5×	body	2048	valid

Compiler

Compiled 29 to 23 computations (20.7% saved)

simplify6.0ms (0.3%)

Algorithm

1×	egg-herbie

Rules

2×	`+-commutative_binary64`
1×	`1-exp_binary64`

Counts

1 → 1

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	7	12
1	11	12
2	10	12

prune1.0ms (0.1%)

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

0.1b

Counts

2 → 1

Alt Table

Status	Error	Program
▶	0.1b	(/.f64 x (+.f64 1 (sqrt.f64 (+.f64 x 1))))

Compiler

Compiled 27 to 21 computations (22.2% saved)

localize5.0ms (0.2%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.0b	(+.f64 1 (sqrt.f64 (+.f64 x 1)))
✓	0.0b	(sqrt.f64 (+.f64 x 1))
✓	0.1b	(/.f64 x (+.f64 1 (sqrt.f64 (+.f64 x 1))))

series58.0ms (2.7%)

Counts

3 → 12

Calls

3 calls:

41.0ms	(/.f64 x (+.f64 1 (sqrt.f64 (+.f64 x 1))))
9.0ms	(sqrt.f64 (+.f64 x 1))
8.0ms	(+.f64 1 (sqrt.f64 (+.f64 x 1)))

rewrite17.0ms (0.8%)

Algorithm

1×	rewrite-expression-head

Rules

44×	`*-un-lft-identity_binary64`
30×	`add-sqr-sqrt_binary64`
21×	`distribute-lft-out_binary64`
18×	`times-frac_binary64`
16×	`add-cube-cbrt_binary64`

Counts

3 → 82

Calls

3 calls:

6.0ms	(/.f64 x (+.f64 1 (sqrt.f64 (+.f64 x 1))))
4.0ms	(+.f64 1 (sqrt.f64 (+.f64 x 1)))
3.0ms	(sqrt.f64 (+.f64 x 1))

simplify120.0ms (5.5%)

Algorithm

1×	egg-herbie

Rules

733×	`fma-neg_binary64`
333×	`associate-/r*_binary64`
321×	`associate-/l/_binary64`
303×	`associate-*l/_binary64`
284×	`cancel-sign-sub-inv_binary64`

Counts

94 → 108

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	123	1335
1	263	1239
2	634	1227
3	1878	1212
4	4323	1211
5	4987	1211
6	4875	1211

prune141.0ms (6.5%)

Pruning

4 alts after pruning (4 fresh and 0 done)

	Pruned	Kept	Total
New	104	4	108
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	105	4	109

Error

Counts

109 → 4

Alt Table

Status	Error	Program
	20.4b	(*.f64 (sqrt.f64 x) (/.f64 (sqrt.f64 x) (+.f64 1 (sqrt.f64 (+.f64 x 1)))))
	1.6b	(expm1.f64 (log1p.f64 (/.f64 x (+.f64 1 (sqrt.f64 (+.f64 x 1))))))
	21.5b	(-.f64 (+.f64 (.f64 1/16 (pow.f64 x 3)) (.f64 1/2 x)) (*.f64 1/8 (pow.f64 x 2)))
▶	0.2b	(*.f64 x (/.f64 1 (+.f64 1 (sqrt.f64 (+.f64 x 1)))))

Compiler

Compiled 1644 to 1263 computations (23.2% saved)

localize6.0ms (0.3%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.0b	(+.f64 1 (sqrt.f64 (+.f64 x 1)))
	0.0b	(sqrt.f64 (+.f64 x 1))
✓	0.1b	(*.f64 x (/.f64 1 (+.f64 1 (sqrt.f64 (+.f64 x 1)))))
✓	0.1b	(/.f64 1 (+.f64 1 (sqrt.f64 (+.f64 x 1))))

series83.0ms (3.8%)

Counts

2 → 8

Calls

2 calls:

44.0ms	(*.f64 x (/.f64 1 (+.f64 1 (sqrt.f64 (+.f64 x 1)))))
39.0ms	(/.f64 1 (+.f64 1 (sqrt.f64 (+.f64 x 1))))

rewrite24.0ms (1.1%)

Algorithm

1×	rewrite-expression-head

Rules

60×	`*-un-lft-identity_binary64`
45×	`add-sqr-sqrt_binary64`
38×	`times-frac_binary64`
28×	`distribute-lft-out_binary64`
24×	`associate-r_binary64`

Counts

2 → 96

Calls

2 calls:

10.0ms	(*.f64 x (/.f64 1 (+.f64 1 (sqrt.f64 (+.f64 x 1)))))
6.0ms	(/.f64 1 (+.f64 1 (sqrt.f64 (+.f64 x 1))))

simplify119.0ms (5.4%)

Algorithm

1×	egg-herbie

Rules

663×	`fma-def_binary64`
374×	`associate-/l*_binary64`
327×	`cancel-sign-sub-inv_binary64`
296×	`fma-neg_binary64`
269×	`unswap-sqr_binary64`

Counts

104 → 127

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	103	1514
1	244	1358
2	627	1344
3	1566	1326
4	4228	1326
5	4914	1326
6	5000	1326
7	4866	1326

prune135.0ms (6.2%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	185	0	185
Fresh	0	3	3
Picked	0	1	1
Done	0	0	0
Total	185	4	189

Error

Counts

189 → 4

Alt Table

Status	Error	Program
	20.4b	(*.f64 (sqrt.f64 x) (/.f64 (sqrt.f64 x) (+.f64 1 (sqrt.f64 (+.f64 x 1)))))
▶	1.6b	(expm1.f64 (log1p.f64 (/.f64 x (+.f64 1 (sqrt.f64 (+.f64 x 1))))))
	21.5b	(-.f64 (+.f64 (.f64 1/16 (pow.f64 x 3)) (.f64 1/2 x)) (*.f64 1/8 (pow.f64 x 2)))
✓	0.2b	(*.f64 x (/.f64 1 (+.f64 1 (sqrt.f64 (+.f64 x 1)))))

Compiler

Compiled 3175 to 2605 computations (18% saved)

localize7.0ms (0.3%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.0b	(+.f64 1 (sqrt.f64 (+.f64 x 1)))
	0.0b	(sqrt.f64 (+.f64 x 1))
	0.1b	(/.f64 x (+.f64 1 (sqrt.f64 (+.f64 x 1))))
✓	1.6b	(expm1.f64 (log1p.f64 (/.f64 x (+.f64 1 (sqrt.f64 (+.f64 x 1))))))

series43.0ms (2%)

Counts

1 → 4

Calls

1 calls:

43.0ms

(expm1.f64 (log1p.f64 (/.f64 x (+.f64 1 (sqrt.f64 (+.f64 x 1))))))

rewrite1.0ms (0%)

Algorithm

1×	rewrite-expression-head

Rules

1×	`*-un-lft-identity_binary64`
1×	`add-sqr-sqrt_binary64`
1×	`add-cube-cbrt_binary64`
1×	`add-cbrt-cube_binary64`
1×	`add-exp-log_binary64`

Counts

1 → 11

Calls

1 calls:

0.0ms

(expm1.f64 (log1p.f64 (/.f64 x (+.f64 1 (sqrt.f64 (+.f64 x 1))))))

simplify63.0ms (2.9%)

Algorithm

1×	egg-herbie

Rules

363×	`distribute-rgt-neg-in_binary64`
305×	`distribute-lft-neg-in_binary64`
273×	`fma-def_binary64`
251×	`distribute-lft-out--_binary64`
230×	`times-frac_binary64`

Counts

15 → 25

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	38	248
1	78	219
2	177	214
3	504	205
4	1749	205
5	4790	205
6	5035	205

prune85.0ms (3.9%)

Pruning

4 alts after pruning (2 fresh and 2 done)

	Pruned	Kept	Total
New	133	0	133
Fresh	0	2	2
Picked	0	1	1
Done	0	1	1
Total	133	4	137

Error

Counts

137 → 4

Alt Table

Status	Error	Program
▶	20.4b	(*.f64 (sqrt.f64 x) (/.f64 (sqrt.f64 x) (+.f64 1 (sqrt.f64 (+.f64 x 1)))))
✓	1.6b	(expm1.f64 (log1p.f64 (/.f64 x (+.f64 1 (sqrt.f64 (+.f64 x 1))))))
	21.5b	(-.f64 (+.f64 (.f64 1/16 (pow.f64 x 3)) (.f64 1/2 x)) (*.f64 1/8 (pow.f64 x 2)))
✓	0.2b	(*.f64 x (/.f64 1 (+.f64 1 (sqrt.f64 (+.f64 x 1)))))

Compiler

Compiled 2198 to 1749 computations (20.4% saved)

localize6.0ms (0.3%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.0b	(+.f64 1 (sqrt.f64 (+.f64 x 1)))
	0.0b	(sqrt.f64 (+.f64 x 1))
✓	0.0b	(/.f64 (sqrt.f64 x) (+.f64 1 (sqrt.f64 (+.f64 x 1))))
✓	0.2b	(*.f64 (sqrt.f64 x) (/.f64 (sqrt.f64 x) (+.f64 1 (sqrt.f64 (+.f64 x 1)))))

series113.0ms (5.2%)

Counts

2 → 4

Calls

2 calls:

72.0ms	(/.f64 (sqrt.f64 x) (+.f64 1 (sqrt.f64 (+.f64 x 1))))
41.0ms	(*.f64 (sqrt.f64 x) (/.f64 (sqrt.f64 x) (+.f64 1 (sqrt.f64 (+.f64 x 1)))))

rewrite36.0ms (1.6%)

Algorithm

1×	rewrite-expression-head

Rules

109×	`*-un-lft-identity_binary64`
86×	`add-sqr-sqrt_binary64`
76×	`times-frac_binary64`
73×	`sqrt-prod_binary64`
52×	`distribute-lft-out_binary64`

Counts

2 → 134

Calls

2 calls:

14.0ms	(*.f64 (sqrt.f64 x) (/.f64 (sqrt.f64 x) (+.f64 1 (sqrt.f64 (+.f64 x 1)))))
7.0ms	(/.f64 (sqrt.f64 x) (+.f64 1 (sqrt.f64 (+.f64 x 1))))

simplify129.0ms (5.9%)

Algorithm

1×	egg-herbie

Rules

861×	`fma-neg_binary64`
610×	`fma-def_binary64`
361×	`associate-/l*_binary64`
342×	`cancel-sign-sub-inv_binary64`
342×	`times-frac_binary64`

Counts

138 → 143

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	129	2881
1	294	2630
2	880	2596
3	2525	2587
4	4564	2587
5	5069	2587

prune110.0ms (5%)

Pruning

4 alts after pruning (1 fresh and 3 done)

	Pruned	Kept	Total
New	201	0	201
Fresh	0	1	1
Picked	0	1	1
Done	0	2	2
Total	201	4	205

Error

Counts

205 → 4

Alt Table

Status	Error	Program
✓	20.4b	(*.f64 (sqrt.f64 x) (/.f64 (sqrt.f64 x) (+.f64 1 (sqrt.f64 (+.f64 x 1)))))
✓	1.6b	(expm1.f64 (log1p.f64 (/.f64 x (+.f64 1 (sqrt.f64 (+.f64 x 1))))))
	21.5b	(-.f64 (+.f64 (.f64 1/16 (pow.f64 x 3)) (.f64 1/2 x)) (*.f64 1/8 (pow.f64 x 2)))
✓	0.2b	(*.f64 x (/.f64 1 (+.f64 1 (sqrt.f64 (+.f64 x 1)))))

Compiler

Compiled 4059 to 2604 computations (35.8% saved)

regimes201.0ms (9.2%)

Accuracy

Total 0.2b remaining (95.9%)

Threshold costs 0.2b (95.9%)

Counts

97 → 1

Compiler

Compiled 2562 to 1996 computations (22.1% saved)

simplify2.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

1×	`+-commutative_binary64`
1×	`1-exp_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	8	13
1	11	13
2	9	13

end112.0ms (5.1%)

Compiler: Compiled 71 to 56 computations (21.1% saved)

Details

analyze2.0ms (0.1%)

sample561.0ms (25.7%)

simplify6.0ms (0.3%)

prune1.0ms (0.1%)

localize5.0ms (0.2%)

series58.0ms (2.7%)

rewrite17.0ms (0.8%)

simplify120.0ms (5.5%)

prune141.0ms (6.5%)

localize6.0ms (0.3%)

series83.0ms (3.8%)

rewrite24.0ms (1.1%)

simplify119.0ms (5.4%)

prune135.0ms (6.2%)

localize7.0ms (0.3%)

series43.0ms (2%)

rewrite1.0ms (0%)

simplify63.0ms (2.9%)

prune85.0ms (3.9%)

localize6.0ms (0.3%)

series113.0ms (5.2%)

rewrite36.0ms (1.6%)

simplify129.0ms (5.9%)

prune110.0ms (5%)

regimes201.0ms (9.2%)

simplify2.0ms (0.1%)

end112.0ms (5.1%)

Profiling