Details

analyze421.0ms (10%)

Algorithm

1×

Search

True	Other	False	Iter
0%	12.5%	87.5%	0
0%	12.5%	87.5%	1
0%	12.5%	87.5%	2
3.1%	9.3%	87.5%	3
3.1%	6.2%	90.7%	4
4.7%	4.7%	90.7%	5
4.7%	3.5%	91.8%	6
5.6%	2.5%	91.8%	7
5.9%	1.8%	92.3%	8
6.4%	1.3%	92.3%	9
6.6%	0.9%	92.5%	10
6.8%	0.6%	92.5%	11
6.9%	0.5%	92.6%	12
7%	0.3%	92.6%	13
7.1%	0.2%	92.7%	14

Compiler

Compiled 24 to 17 computations (29.2% saved)

sample50.0ms (1.2%)

Algorithm

1×

intervals

Results

21.0ms	256×	body	128	valid
10.0ms	261×	pre	128	true
0.0ms	5×	body	128	invalid

Compiler

Compiled 39 to 28 computations (28.2% saved)

simplify142.0ms (3.4%)

Algorithm

1×	egg-herbie

Rules

1186×	`fma-def_binary64`
913×	`fma-neg_binary64`
520×	`distribute-rgt-in_binary64`
481×	`div-sub_binary64`
441×	`unsub-neg_binary64`

Counts

1 → 2

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	9	16
1	20	16
2	39	14
3	78	14
4	233	14
5	529	14
6	976	14
7	1686	14
8	1746	14
9	1952	14
10	2334	14
11	2818	14
12	3104	14
13	4560	14
14	4195	14
15	4799	14

prune6.0ms (0.2%)

Pruning

3 alts after pruning (3 fresh and 0 done)

	Kept	Total
New	2	2
Fresh	1	1
Picked	0	0
Done	0	0
Total	3	3

Error

0.1b

Counts

3 → 2

Alt Table

Status	Error	Program
	0.2b	(*.f64 m (fma.f64 m (/.f64 (-.f64 1 m) v) -1))
▶	0.1b	(.f64 (-.f64 (/.f64 (.f64 m (-.f64 1 m)) v) 1) m)

Compiler

Compiled 73 to 49 computations (32.9% saved)

localize13.0ms (0.3%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(-.f64 (/.f64 (*.f64 m (-.f64 1 m)) v) 1)
✓	0.0b	(*.f64 m (-.f64 1 m))
✓	0.1b	(/.f64 (*.f64 m (-.f64 1 m)) v)
✓	0.1b	(.f64 (-.f64 (/.f64 (.f64 m (-.f64 1 m)) v) 1) m)

series68.0ms (1.6%)

Counts

4 → 80

Calls

4 calls:

26.0ms	(.f64 (-.f64 (/.f64 (.f64 m (-.f64 1 m)) v) 1) m)
20.0ms	(/.f64 (*.f64 m (-.f64 1 m)) v)
17.0ms	(-.f64 (/.f64 (*.f64 m (-.f64 1 m)) v) 1)
4.0ms	(*.f64 m (-.f64 1 m))

rewrite79.0ms (1.9%)

Algorithm

1×	rewrite-expression-head

Rules

55×	`add-sqr-sqrt_binary64`
49×	`*-un-lft-identity_binary64`
40×	`add-cube-cbrt_binary64`
39×	`prod-diff_binary64`
19×	`add-exp-log_binary64`

Counts

4 → 153

Calls

4 calls:

18.0ms	(.f64 (-.f64 (/.f64 (.f64 m (-.f64 1 m)) v) 1) m)
15.0ms	(-.f64 (/.f64 (*.f64 m (-.f64 1 m)) v) 1)
13.0ms	(*.f64 m (-.f64 1 m))
13.0ms	(/.f64 (*.f64 m (-.f64 1 m)) v)

simplify195.0ms (4.6%)

Algorithm

1×	egg-herbie

Rules

589×	`fma-def_binary64`
482×	`distribute-rgt-in_binary64`
447×	`distribute-lft-in_binary64`
328×	`fma-neg_binary64`
240×	`associate-l_binary64`

Counts

233 → 245

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	201	3371
1	413	2852
2	1688	2595
3	4507	2594
4	4922	2594

prune470.0ms (11.2%)

Pruning

7 alts after pruning (7 fresh and 0 done)

	Pruned	Kept	Total
New	238	7	245
Fresh	1	0	1
Picked	1	0	1
Done	0	0	0
Total	240	7	247

Error

Counts

247 → 7

Alt Table

Status	Error	Program
	0.3b	(.f64 (-.f64 (/.f64 (/.f64 (.f64 m (-.f64 1 m)) (sqrt.f64 v)) (sqrt.f64 v)) 1) m)
	9.8b	(.f64 (+.f64 (sqrt.f64 (/.f64 (.f64 m (-.f64 1 m)) v)) 1) (.f64 (-.f64 (sqrt.f64 (/.f64 (.f64 m (-.f64 1 m)) v)) 1) m))
	13.0b	(/.f64 (.f64 (-.f64 (.f64 (/.f64 (.f64 m (-.f64 1 m)) v) (/.f64 (.f64 m (-.f64 1 m)) v)) (.f64 1 1)) m) (+.f64 (/.f64 (.f64 m (-.f64 1 m)) v) 1))
	6.0b	(-.f64 (/.f64 (pow.f64 m 2) v) (+.f64 (/.f64 (pow.f64 m 3) v) m))
	1.5b	(.f64 (.f64 (fma.f64 m (/.f64 (-.f64 1 m) v) -1) (*.f64 (cbrt.f64 m) (cbrt.f64 m))) (cbrt.f64 m))
▶	0.2b	(.f64 (-.f64 (.f64 (*.f64 m (-.f64 1 m)) (/.f64 1 v)) 1) m)
	0.6b	(.f64 (.f64 (fma.f64 m (/.f64 (-.f64 1 m) v) -1) (sqrt.f64 m)) (sqrt.f64 m))

Compiler

Compiled 5111 to 3120 computations (39% saved)

localize17.0ms (0.4%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(-.f64 (.f64 (.f64 m (-.f64 1 m)) (/.f64 1 v)) 1)
	0.0b	(*.f64 m (-.f64 1 m))
✓	0.1b	(.f64 (-.f64 (.f64 (*.f64 m (-.f64 1 m)) (/.f64 1 v)) 1) m)
✓	0.3b	(.f64 (.f64 m (-.f64 1 m)) (/.f64 1 v))

series64.0ms (1.5%)

Counts

3 → 72

Calls

3 calls:

26.0ms	(.f64 (-.f64 (.f64 (*.f64 m (-.f64 1 m)) (/.f64 1 v)) 1) m)
20.0ms	(.f64 (.f64 m (-.f64 1 m)) (/.f64 1 v))
18.0ms	(-.f64 (.f64 (.f64 m (-.f64 1 m)) (/.f64 1 v)) 1)

rewrite69.0ms (1.6%)

Algorithm

1×	rewrite-expression-head

Rules

50×	`add-exp-log_binary64`
25×	`prod-exp_binary64`
17×	`add-cbrt-cube_binary64`
16×	`associate-r_binary64`
16×	`add-sqr-sqrt_binary64`

Counts

3 → 95

Calls

3 calls:

21.0ms	(.f64 (-.f64 (.f64 (*.f64 m (-.f64 1 m)) (/.f64 1 v)) 1) m)
17.0ms	(-.f64 (.f64 (.f64 m (-.f64 1 m)) (/.f64 1 v)) 1)
16.0ms	(.f64 (.f64 m (-.f64 1 m)) (/.f64 1 v))

simplify170.0ms (4%)

Algorithm

1×	egg-herbie

Rules

563×	`fma-neg_binary64`
426×	`distribute-rgt-in_binary64`
418×	`distribute-lft-in_binary64`
269×	`*-commutative_binary64`
264×	`fma-def_binary64`

Counts

167 → 166

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	155	2272
1	362	1923
2	1133	1908
3	3710	1902
4	4626	1902
5	5011	1902

prune306.0ms (7.3%)

Pruning

6 alts after pruning (5 fresh and 1 done)

	Pruned	Kept	Total
New	236	1	237
Fresh	2	4	6
Picked	0	1	1
Done	0	0	0
Total	238	6	244

Error

Counts

244 → 6

Alt Table

Status	Error	Program
▶	0.3b	(.f64 (-.f64 (/.f64 (/.f64 (.f64 m (-.f64 1 m)) (sqrt.f64 v)) (sqrt.f64 v)) 1) m)
	9.8b	(.f64 (+.f64 (sqrt.f64 (/.f64 (.f64 m (-.f64 1 m)) v)) 1) (.f64 (-.f64 (sqrt.f64 (/.f64 (.f64 m (-.f64 1 m)) v)) 1) m))
	27.5b	(.f64 (/.f64 m v) (-.f64 m (.f64 m m)))
✓	0.2b	(.f64 (-.f64 (.f64 (*.f64 m (-.f64 1 m)) (/.f64 1 v)) 1) m)
	6.0b	(-.f64 (/.f64 (pow.f64 m 2) v) (+.f64 (/.f64 (pow.f64 m 3) v) m))
	0.6b	(.f64 (.f64 (fma.f64 m (/.f64 (-.f64 1 m) v) -1) (sqrt.f64 m)) (sqrt.f64 m))

Compiler

Compiled 4936 to 3083 computations (37.5% saved)

localize9.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.0b	(*.f64 m (-.f64 1 m))
✓	0.1b	(.f64 (-.f64 (/.f64 (/.f64 (.f64 m (-.f64 1 m)) (sqrt.f64 v)) (sqrt.f64 v)) 1) m)
✓	0.2b	(/.f64 (*.f64 m (-.f64 1 m)) (sqrt.f64 v))
✓	0.3b	(/.f64 (/.f64 (*.f64 m (-.f64 1 m)) (sqrt.f64 v)) (sqrt.f64 v))

series94.0ms (2.2%)

Counts

3 → 52

Calls

3 calls:

39.0ms	(.f64 (-.f64 (/.f64 (/.f64 (.f64 m (-.f64 1 m)) (sqrt.f64 v)) (sqrt.f64 v)) 1) m)
31.0ms	(/.f64 (*.f64 m (-.f64 1 m)) (sqrt.f64 v))
23.0ms	(/.f64 (/.f64 (*.f64 m (-.f64 1 m)) (sqrt.f64 v)) (sqrt.f64 v))

rewrite53.0ms (1.3%)

Algorithm

1×	rewrite-expression-head

Rules

114×	`times-frac_binary64`
72×	`add-sqr-sqrt_binary64`
63×	`sqrt-prod_binary64`
57×	`*-un-lft-identity_binary64`
52×	`add-cube-cbrt_binary64`

Counts

3 → 158

Calls

3 calls:

22.0ms	(.f64 (-.f64 (/.f64 (/.f64 (.f64 m (-.f64 1 m)) (sqrt.f64 v)) (sqrt.f64 v)) 1) m)
9.0ms	(/.f64 (/.f64 (*.f64 m (-.f64 1 m)) (sqrt.f64 v)) (sqrt.f64 v))
7.0ms	(/.f64 (*.f64 m (-.f64 1 m)) (sqrt.f64 v))

simplify135.0ms (3.2%)

Algorithm

1×	egg-herbie

Rules

553×	`associate-/r*_binary64`
505×	`associate-*r/_binary64`
392×	`associate-/r/_binary64`
323×	`distribute-rgt-in_binary64`
310×	`distribute-lft-in_binary64`

Counts

210 → 236

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	217	4321
1	516	3995
2	1637	3840
3	4722	3840
4	4961	3840

prune241.0ms (5.7%)

Pruning

6 alts after pruning (4 fresh and 2 done)

	Pruned	Kept	Total
New	307	0	307
Fresh	0	4	4
Picked	0	1	1
Done	0	1	1
Total	307	6	313

Error

Counts

313 → 6

Alt Table

Status	Error	Program
✓	0.3b	(.f64 (-.f64 (/.f64 (/.f64 (.f64 m (-.f64 1 m)) (sqrt.f64 v)) (sqrt.f64 v)) 1) m)
	9.8b	(.f64 (+.f64 (sqrt.f64 (/.f64 (.f64 m (-.f64 1 m)) v)) 1) (.f64 (-.f64 (sqrt.f64 (/.f64 (.f64 m (-.f64 1 m)) v)) 1) m))
	27.5b	(.f64 (/.f64 m v) (-.f64 m (.f64 m m)))
✓	0.2b	(.f64 (-.f64 (.f64 (*.f64 m (-.f64 1 m)) (/.f64 1 v)) 1) m)
	6.0b	(-.f64 (/.f64 (pow.f64 m 2) v) (+.f64 (/.f64 (pow.f64 m 3) v) m))
▶	0.6b	(.f64 (.f64 (fma.f64 m (/.f64 (-.f64 1 m) v) -1) (sqrt.f64 m)) (sqrt.f64 m))

Compiler

Compiled 7304 to 3552 computations (51.4% saved)

localize8.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(/.f64 (-.f64 1 m) v)
✓	0.1b	(fma.f64 m (/.f64 (-.f64 1 m) v) -1)
✓	0.2b	(*.f64 (fma.f64 m (/.f64 (-.f64 1 m) v) -1) (sqrt.f64 m))
✓	0.4b	(.f64 (.f64 (fma.f64 m (/.f64 (-.f64 1 m) v) -1) (sqrt.f64 m)) (sqrt.f64 m))

series55.0ms (1.3%)

Counts

4 → 72

Calls

4 calls:

22.0ms	(*.f64 (fma.f64 m (/.f64 (-.f64 1 m) v) -1) (sqrt.f64 m))
18.0ms	(.f64 (.f64 (fma.f64 m (/.f64 (-.f64 1 m) v) -1) (sqrt.f64 m)) (sqrt.f64 m))
8.0ms	(fma.f64 m (/.f64 (-.f64 1 m) v) -1)
6.0ms	(/.f64 (-.f64 1 m) v)

rewrite21.0ms (0.5%)

Algorithm

1×	rewrite-expression-head

Rules

36×	`add-sqr-sqrt_binary64`
32×	`*-un-lft-identity_binary64`
20×	`add-cube-cbrt_binary64`
18×	`times-frac_binary64`
13×	`add-cbrt-cube_binary64`

Counts

4 → 101

Calls

4 calls:

5.0ms	(.f64 (.f64 (fma.f64 m (/.f64 (-.f64 1 m) v) -1) (sqrt.f64 m)) (sqrt.f64 m))
5.0ms	(/.f64 (-.f64 1 m) v)
5.0ms	(*.f64 (fma.f64 m (/.f64 (-.f64 1 m) v) -1) (sqrt.f64 m))
0.0ms	(fma.f64 m (/.f64 (-.f64 1 m) v) -1)

simplify118.0ms (2.8%)

Algorithm

1×	egg-herbie

Rules

645×	`fma-neg_binary64`
339×	`div-sub_binary64`
261×	`exp-prod_binary64`
251×	`times-frac_binary64`
238×	`*-commutative_binary64`

Counts

173 → 168

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	167	2812
1	379	2480
2	1039	2349
3	3116	2347
4	4544	2347
5	5036	2347

prune111.0ms (2.6%)

Pruning

6 alts after pruning (3 fresh and 3 done)

	Pruned	Kept	Total
New	168	0	168
Fresh	0	3	3
Picked	0	1	1
Done	0	2	2
Total	168	6	174

Error

Counts

174 → 6

Alt Table

Status	Error	Program
✓	0.3b	(.f64 (-.f64 (/.f64 (/.f64 (.f64 m (-.f64 1 m)) (sqrt.f64 v)) (sqrt.f64 v)) 1) m)
	9.8b	(.f64 (+.f64 (sqrt.f64 (/.f64 (.f64 m (-.f64 1 m)) v)) 1) (.f64 (-.f64 (sqrt.f64 (/.f64 (.f64 m (-.f64 1 m)) v)) 1) m))
	27.5b	(.f64 (/.f64 m v) (-.f64 m (.f64 m m)))
✓	0.2b	(.f64 (-.f64 (.f64 (*.f64 m (-.f64 1 m)) (/.f64 1 v)) 1) m)
	6.0b	(-.f64 (/.f64 (pow.f64 m 2) v) (+.f64 (/.f64 (pow.f64 m 3) v) m))
✓	0.6b	(.f64 (.f64 (fma.f64 m (/.f64 (-.f64 1 m) v) -1) (sqrt.f64 m)) (sqrt.f64 m))

Compiler

Compiled 3373 to 1787 computations (47% saved)

regimes449.0ms (10.7%)

Accuracy

Total 0.2b remaining (87.2%)

Threshold costs 0.2b (87.2%)

Counts

147 → 1

Compiler

Compiled 7293 to 4948 computations (32.2% saved)

simplify3.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

3×	`+-commutative_binary64`
3×	`*-commutative_binary64`
3×	`sub-neg_binary64`
1×	`/-rgt-identity_binary64`
1×	`neg-sub0_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	10	16
1	19	16
2	23	16
3	25	16
4	26	16
5	24	16

end0.0ms (0%)

Compiler: Compiled 13 to 9 computations (30.8% saved)

sample833.0ms (19.8%)

Algorithm

1×

intervals

Results

313.0ms	8000×	body	128	valid
169.0ms	8062×	pre	128	true
2.0ms	62×	body	128	invalid

Compiler

Compiled 138 to 94 computations (31.9% saved)

Details

analyze421.0ms (10%)

sample50.0ms (1.2%)

simplify142.0ms (3.4%)

prune6.0ms (0.2%)

localize13.0ms (0.3%)

series68.0ms (1.6%)

rewrite79.0ms (1.9%)

simplify195.0ms (4.6%)

prune470.0ms (11.2%)

localize17.0ms (0.4%)

series64.0ms (1.5%)

rewrite69.0ms (1.6%)

simplify170.0ms (4%)

prune306.0ms (7.3%)

localize9.0ms (0.2%)

series94.0ms (2.2%)

rewrite53.0ms (1.3%)

simplify135.0ms (3.2%)

prune241.0ms (5.7%)

localize8.0ms (0.2%)

series55.0ms (1.3%)

rewrite21.0ms (0.5%)

simplify118.0ms (2.8%)

prune111.0ms (2.6%)

regimes449.0ms (10.7%)

simplify3.0ms (0.1%)

end0.0ms (0%)

sample833.0ms (19.8%)

Profiling