Details

analyze3.0ms (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)

sample793.0ms (33%)

Results

766.0ms	8254×	body	128	valid
1.0ms	2×	body	2048	valid

Compiler

Compiled 29 to 23 computations (20.7% saved)

simplify6.0ms (0.2%)

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

0.2b

Counts

2 → 1

Alt Table

Status	Error	Program
▶	0.2b	(/.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))
✓	0.2b	(/.f64 x (+.f64 1 (sqrt.f64 (+.f64 x 1))))

series56.0ms (2.3%)

Counts

3 → 12

Calls

3 calls:

40.0ms	(/.f64 x (+.f64 1 (sqrt.f64 (+.f64 x 1))))
9.0ms	(sqrt.f64 (+.f64 x 1))
7.0ms	(+.f64 1 (sqrt.f64 (+.f64 x 1)))

rewrite17.0ms (0.7%)

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:

5.0ms	(/.f64 x (+.f64 1 (sqrt.f64 (+.f64 x 1))))
5.0ms	(+.f64 1 (sqrt.f64 (+.f64 x 1)))
3.0ms	(sqrt.f64 (+.f64 x 1))

simplify94.0ms (3.9%)

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

prune93.0ms (3.9%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	105	3	108
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	105	4	109

Error

Counts

109 → 4

Alt Table

Status	Error	Program
	18.7b	(*.f64 (sqrt.f64 x) (/.f64 (sqrt.f64 x) (+.f64 1 (sqrt.f64 (+.f64 x 1)))))
✓	0.2b	(/.f64 x (+.f64 1 (sqrt.f64 (+.f64 x 1))))
	35.8b	(cbrt.f64 (pow.f64 (/.f64 x (+.f64 1 (sqrt.f64 (+.f64 x 1)))) 3))
▶	7.7b	(/.f64 x (+.f64 1 (cbrt.f64 (pow.f64 (sqrt.f64 (+.f64 x 1)) 3))))

Compiler

Compiled 1625 to 1248 computations (23.2% saved)

localize7.0ms (0.3%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.0b	(sqrt.f64 (+.f64 x 1))
✓	0.2b	(pow.f64 (sqrt.f64 (+.f64 x 1)) 3)
✓	0.2b	(/.f64 x (+.f64 1 (cbrt.f64 (pow.f64 (sqrt.f64 (+.f64 x 1)) 3))))
✓	7.6b	(cbrt.f64 (pow.f64 (sqrt.f64 (+.f64 x 1)) 3))

series66.0ms (2.7%)

Counts

3 → 12

Calls

3 calls:

38.0ms	(/.f64 x (+.f64 1 (cbrt.f64 (pow.f64 (sqrt.f64 (+.f64 x 1)) 3))))
18.0ms	(pow.f64 (sqrt.f64 (+.f64 x 1)) 3)
9.0ms	(cbrt.f64 (pow.f64 (sqrt.f64 (+.f64 x 1)) 3))

rewrite21.0ms (0.9%)

Algorithm

1×	rewrite-expression-head

Rules

38×	`*-un-lft-identity_binary64`
22×	`add-sqr-sqrt_binary64`
22×	`add-cube-cbrt_binary64`
20×	`cbrt-prod_binary64`
16×	`sqrt-prod_binary64`

Counts

3 → 106

Calls

3 calls:

9.0ms	(/.f64 x (+.f64 1 (cbrt.f64 (pow.f64 (sqrt.f64 (+.f64 x 1)) 3))))
3.0ms	(cbrt.f64 (pow.f64 (sqrt.f64 (+.f64 x 1)) 3))
3.0ms	(pow.f64 (sqrt.f64 (+.f64 x 1)) 3)

simplify104.0ms (4.3%)

Algorithm

1×	egg-herbie

Rules

541×	`associate-l_binary64`
520×	`fma-neg_binary64`
409×	`associate-r_binary64`
348×	`fma-def_binary64`
328×	`log-prod_binary64`

Counts

118 → 155

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	166	1622
1	351	1542
2	955	1504
3	3471	1493
4	4633	1490
5	4917	1490

prune134.0ms (5.6%)

Pruning

4 alts after pruning (2 fresh and 2 done)

	Pruned	Kept	Total
New	184	0	184
Fresh	0	2	2
Picked	0	1	1
Done	0	1	1
Total	184	4	188

Error

Counts

188 → 4

Alt Table

Status	Error	Program
▶	18.7b	(*.f64 (sqrt.f64 x) (/.f64 (sqrt.f64 x) (+.f64 1 (sqrt.f64 (+.f64 x 1)))))
✓	0.2b	(/.f64 x (+.f64 1 (sqrt.f64 (+.f64 x 1))))
	35.8b	(cbrt.f64 (pow.f64 (/.f64 x (+.f64 1 (sqrt.f64 (+.f64 x 1)))) 3))
✓	7.7b	(/.f64 x (+.f64 1 (cbrt.f64 (pow.f64 (sqrt.f64 (+.f64 x 1)) 3))))

Compiler

Compiled 3260 to 2633 computations (19.2% 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))
✓	0.0b	(/.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)))))

series106.0ms (4.4%)

Counts

2 → 4

Calls

2 calls:

65.0ms	(/.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)))))

rewrite33.0ms (1.4%)

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

simplify118.0ms (4.9%)

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

prune117.0ms (4.9%)

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
✓	18.7b	(*.f64 (sqrt.f64 x) (/.f64 (sqrt.f64 x) (+.f64 1 (sqrt.f64 (+.f64 x 1)))))
✓	0.2b	(/.f64 x (+.f64 1 (sqrt.f64 (+.f64 x 1))))
▶	35.8b	(cbrt.f64 (pow.f64 (/.f64 x (+.f64 1 (sqrt.f64 (+.f64 x 1)))) 3))
✓	7.7b	(/.f64 x (+.f64 1 (cbrt.f64 (pow.f64 (sqrt.f64 (+.f64 x 1)) 3))))

Compiler

Compiled 4066 to 2610 computations (35.8% saved)

localize7.0ms (0.3%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.0b	(sqrt.f64 (+.f64 x 1))
	0.2b	(/.f64 x (+.f64 1 (sqrt.f64 (+.f64 x 1))))
✓	0.2b	(pow.f64 (/.f64 x (+.f64 1 (sqrt.f64 (+.f64 x 1)))) 3)
✓	35.4b	(cbrt.f64 (pow.f64 (/.f64 x (+.f64 1 (sqrt.f64 (+.f64 x 1)))) 3))

series179.0ms (7.5%)

Counts

2 → 8

Calls

2 calls:

90.0ms	(pow.f64 (/.f64 x (+.f64 1 (sqrt.f64 (+.f64 x 1)))) 3)
89.0ms	(cbrt.f64 (pow.f64 (/.f64 x (+.f64 1 (sqrt.f64 (+.f64 x 1)))) 3))

rewrite28.0ms (1.2%)

Algorithm

1×	rewrite-expression-head

Rules

104×	`*-un-lft-identity_binary64`
72×	`times-frac_binary64`
68×	`add-sqr-sqrt_binary64`
54×	`cbrt-prod_binary64`
48×	`cube-prod_binary64`

Counts

2 → 136

Calls

2 calls:

9.0ms	(pow.f64 (/.f64 x (+.f64 1 (sqrt.f64 (+.f64 x 1)))) 3)
8.0ms	(cbrt.f64 (pow.f64 (/.f64 x (+.f64 1 (sqrt.f64 (+.f64 x 1)))) 3))

simplify113.0ms (4.7%)

Algorithm

1×	egg-herbie

Rules

744×	`times-frac_binary64`
465×	`associate-/l*_binary64`
298×	`unswap-sqr_binary64`
228×	`fma-def_binary64`
182×	`associate-/l/_binary64`

Counts

144 → 121

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	170	3388
1	434	3039
2	1308	2967
3	4942	2964
4	4959	2964

prune125.0ms (5.2%)

Pruning

4 alts after pruning (0 fresh and 4 done)

	Pruned	Kept	Total
New	200	0	200
Fresh	0	0	0
Picked	0	1	1
Done	0	3	3
Total	200	4	204

Error

Counts

204 → 4

Alt Table

Status	Error	Program
✓	18.7b	(*.f64 (sqrt.f64 x) (/.f64 (sqrt.f64 x) (+.f64 1 (sqrt.f64 (+.f64 x 1)))))
✓	0.2b	(/.f64 x (+.f64 1 (sqrt.f64 (+.f64 x 1))))
✓	35.8b	(cbrt.f64 (pow.f64 (/.f64 x (+.f64 1 (sqrt.f64 (+.f64 x 1)))) 3))
✓	7.7b	(/.f64 x (+.f64 1 (cbrt.f64 (pow.f64 (sqrt.f64 (+.f64 x 1)) 3))))

Compiler

Compiled 3878 to 3103 computations (20% saved)

regimes79.0ms (3.3%)

Accuracy

Total 0.2b remaining (95.4%)

Threshold costs 0.2b (95.4%)

Counts

40 → 1

Compiler

Compiled 1050 to 814 computations (22.5% saved)

simplify2.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

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

Iterations

Useful iterations: 0 (0.0ms)

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

end86.0ms (3.6%)

Compiler: Compiled 64 to 50 computations (21.9% saved)

Details

analyze3.0ms (0.1%)

sample793.0ms (33%)

simplify6.0ms (0.2%)

prune1.0ms (0.1%)

localize5.0ms (0.2%)

series56.0ms (2.3%)

rewrite17.0ms (0.7%)

simplify94.0ms (3.9%)

prune93.0ms (3.9%)

localize7.0ms (0.3%)

series66.0ms (2.7%)

rewrite21.0ms (0.9%)

simplify104.0ms (4.3%)

prune134.0ms (5.6%)

localize7.0ms (0.3%)

series106.0ms (4.4%)

rewrite33.0ms (1.4%)

simplify118.0ms (4.9%)

prune117.0ms (4.9%)

localize7.0ms (0.3%)

series179.0ms (7.5%)

rewrite28.0ms (1.2%)

simplify113.0ms (4.7%)

prune125.0ms (5.2%)

regimes79.0ms (3.3%)

simplify2.0ms (0.1%)

end86.0ms (3.6%)

Profiling